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Journal articles on the topic 'Dimensionless profile functions'
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1
Paul, Ashish, and Rudra Kanta Deka. "Chemical Reaction Effect on Transient Free Convective Flow past an Infinite Moving Vertical Cylinder." International Journal of Chemical Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/531513.
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An analysis is performed to study the heat and mass transfer on the flow past an infinite moving vertical cylinder, in the presence of first-order chemical reaction. The closed-form solutions of the dimensionless governing partial differential equations are obtained in terms of Bessel's functions and modified Bessel's functions by the Laplace transform technique. The transient velocity profiles, temperature profiles, and concentration profiles are studied for various sets of physical parameters, namely, the chemical reaction parameter, Prandtl number, Schmidt number, thermal Grashof number, mass Grashof number, and time. The skin friction, Nusselt number, and Sherwood number are also obtained and presented in graphs. It is observed that in presence of as well as increase in chemical reaction the flow velocity decreases. Also, in presence of destructive chemical reaction the concentration profile and Sherwood number tend to the steady state at large time.
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Maynes, D., and B. W. Webb. "Fully-Developed Thermal Transport in Combined Pressure and Electro-Osmotically Driven Flow in Microchannels." Journal of Heat Transfer 125, no. 5 (2003): 889–95. http://dx.doi.org/10.1115/1.1597624.
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Thermally fully-developed heat transfer has been analyzed for combined electro-osmotic and pressure driven flow in a circular microtube. The two classical thermal boundary conditions of constant wall heat flux and constant wall temperature were considered. Such a flow is established by the combination of an imposed pressure gradient and voltage potential gradient along the length of the tube. The induced flow rate and velocity profile are functions of the imposed potential gradient, electro-osmotic mobility of the fluid, the ratio of the duct radius to the Debye length, the established streamwise pressure gradient, and the fluid viscosity. The imposed voltage gradient results in Joule heating in the fluid, with an associated distributed volumetric source of energy. For this scenario, the solution for the fully developed, dimensionless temperature profile and corresponding Nusselt number have been determined. The fully-developed Nusselt number is found to depend on the duct radius/Debye length ratio (termed the relative duct radius), the dimensionless volumetric source, and a dimensionless parameter that characterizes the relative strengths of the two driving mechanisms. This parameter can take on both positive and negative values, depending on the signs of the streamwise voltage and pressure gradients imposed. Analytical results are presented and discussed for a range of the governing dimensionless parameters.
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Tong, Shih-Hsi, and Daniel C. H. Yang. "Rotor Profiles Synthesis for Lobe Pumps With Given Flow Rate Functions." Journal of Mechanical Design 127, no. 2 (2005): 287–94. http://dx.doi.org/10.1115/1.1798271.
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In this paper we present a complete synthesis procedure for lobe pumps with required flow rate functions. A dimensionless flow rate expression, called the “specific flow rate,” is used for our pump synthesis. This specific flow rate depends only on the pitch and deviation functions of the pump rotor, and it is independent of the individual pump size, neither pumping frequency. Another important design parameter used is the “lobe noncircularity,” which is defined as the ratio of the lobe length to the rotor center distance. It is found that the lobe noncircularity is linearly dependent on the ratio of maximum to minimum flow rate regardless of the type of flow rate function. As a result, our synthesis procedure can be simplified as (1) select a type of desirable flow rate function, (2) from the flow rate function derive the corresponding deviation function, (3) based on the deviation function generate the desired rotor profile, and (4) calculate the real pump size. Another advantage is that by using this method wide classes of lobe pumps can be designed. A detailed design example is presented for illustration. In addition, new lobe profiles are invented based on some typical flow rate functions.
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Poonia, Hemant, and R. C. Chaudhary. "MHD free convection and mass transfer flow over an infinite vertical porous plate with viscous dissipation." Theoretical and Applied Mechanics 37, no. 4 (2010): 263–87. http://dx.doi.org/10.2298/tam1004263p.
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An unsteady, two-dimensional, hydromagnetic, laminar mixed convective boundary layer flow of an incompressible and electrically-conducting fluid along an infinite vertical plate embedded in the porous medium with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and graphical results for velocity, temperature and concentration profiles within the boundary layer are discussed. The results show that increased cooling (Gr > 0) of the plate and the Eckert number leads to a rise in the velocity profile. Also, an increase in Eckert number leads to an increase in the temperature. Effects of Sc on velocity and concentration are discussed and shown graphically.
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Hersbach, Hans. "Sea Surface Roughness and Drag Coefficient as Functions of Neutral Wind Speed." Journal of Physical Oceanography 41, no. 1 (2011): 247–51. http://dx.doi.org/10.1175/2010jpo4567.1.
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Abstract Near the surface, it is commonly believed that the behavior of the (turbulent) atmospheric flow can be well described by a constant stress layer. In the case of a neutrally stratified surface layer, this leads to the well-known logarithmic wind profile that determines the relation between near-surface wind speed and magnitude of stress. The profile is set by a surface roughness length, which, over the ocean surface, is not constant; rather, it depends on the underlying (ocean wave) sea state. For instance, at the European Centre for Medium-Range Weather Forecasts this relation is parameterized in terms of surface stress itself, where the scale is set by kinematic viscosity for light wind and a Charnock parameter for strong wind. For given wind speed at a given height, the determination of the relation between surface wind and stress (expressed by a drag coefficient) leads to an implicit equation that is to be solved in an iterative way. In this paper a fit is presented that directly expresses the neutral drag coefficient and surface roughness in terms of wind speed without the need for iteration. Since the fit is formulated in purely dimensionless quantities, it is able to produce accurate results over the entire range in wind speed, level height, and values for the Charnock parameter for which the implicit set of equations is believed to be valid.
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Bhansali, A. P., and W. Z. Black. "Local, Instantaneous Heat Transfer Coefficients for Jet Impingement on a Phase Change Surface." Journal of Heat Transfer 118, no. 2 (1996): 334–42. http://dx.doi.org/10.1115/1.2825849.
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The local variation in the heat transfer coefficient for an axisymmetric, turbulent, submerged liquid jet impinging on a nonuniform boundary of a phase-change material is measured with an ultrasonic measurement technique. The time required for an acoustic wave to traverse the phase-change material is measured with an ultrasonic transducer and the time data are converted into local thickness profiles of the phase-change material via knowledge of the longitudinal acoustic velocity in the material. An energy balance at the melt interface between the impinging jet and the phase-change material is used in conjunction with the local thickness profile data to determine the local variation in the heat transfer coefficient. The phase-change material is originally flat, but its shape changes with time as the heated jet melts a complex shape into its surface. The heat transfer rate over the surface of the melting interface is shown to vary with time as a result of the changing shape of the phase change material. A deep cavity is melted into the solid at the stagnation point and secondary cavities are melted into the interface for certain jet flow rates and surface spacings between the jet nozzle and the melt interface. When secondary cavities are produced, secondary peaks in the local heat transfer coefficient are observed. The heat transfer data are formulated into two Nusselt number correlations that are functions of the dimensionless time, dimensionless radius, dimensionless jet-to-surface spacing, and jet Reynolds number. One correlation is formulated for all locations along the surface of the phase-change material except the stagnation point, and a second correlation is valid at the stagnation point.
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Sahoo, Goloka Behari, and David Luketina. "Bubbler design for reservoir destratification." Marine and Freshwater Research 54, no. 3 (2003): 271. http://dx.doi.org/10.1071/mf02045.
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Two important bubbler-performance criteria, the mechanical efficiency, ηmech, and the destratification time, Γ, were analysed as functions of two dimensionless parameters, G, the strength of stratification, and M, the source strength. Equations to estimate the optimum airflow rate (via M) and corresponding ηmech and Γ for a known linear stratification G in a reservoir were derived. Owing to difficulties in accurately determining the actual G, it was demonstrated that it is appropriate practice to reduce the design G value by around 10%. It was shown that the equivalent linear stratification method might lead to sub-optimal design for stratification profiles that deviate substantially from a linear profile. Rather, a bubble-plume model should be applied. Finally, the effects of incorporating changes in bubble radius in a bubble-plume model were examined. ηmech and Γ were found to be relatively insensitive to bubble radius; however, the ideal bubble size for maintaining a suitable oxygen dissolution efficiency is 1 mm.
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ROMANO, ANTONIO ENEA. "INHOMOGENEOUS COSMOLOGICAL MODELS AND H0 OBSERVATIONS." International Journal of Modern Physics D 21, no. 12 (2012): 1250085. http://dx.doi.org/10.1142/s021827181250085x.
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We address some recent erroneous claim that H0 observations are difficult to accommodate with LTB cosmological models, showing how to construct solutions in agreement with an arbitrary value of H0 by rewriting the exact solution in terms of dimensionless parameters and functions. This approach can be applied to fully exploit LTB solutions in designing models alternative to dark energy without making any restrictive or implicit assumption about the inhomogeneity profile. The same solution can also be used to study structure formation in the regime in which perturbation theory is not enough and an exact solution of the Einstein's equation is required, or to estimate the effects of a local inhomogeneities on the apparent equation of state of dark energy.
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Mirbahar, Muhammad Nawaz, Kashif Ali Abro, and Abdul Wasim Shaikh. "Calorimetric Investigation for Thermal Plate of Casson Fluid via Fractional Derivative." Journal of Nanofluids 8, no. 8 (2019): 1668–75. http://dx.doi.org/10.1166/jon.2019.1720.
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The manuscript reveals the collective effects of the moving plate of Casson fluid in which magnetic, porous outcomes are under consideration. Thermal stratification is investigated to disclose the hidden phenomenon of mass concentration and temperature distribution. Fractional operator has been applied on the fundamental equations of Casson fluid namely Caputo-Fabrizio fractional operator based on sufficient memory operator. For the exact analysis of basic fractional governing equations of velocity profile, temperature distribution and mass concentration the integral transforms have been employed. The solutions of the dimensionless equations have been described in terms special functions in convoluted form. For the sake of non-fractional solution of the basic equations of the Casson fluid X = 1 in the obtained solutions has been implemented for the four type's fluid models. Finally, thermal conductivity of the fluid has been analyzed by estimating various different parametric values which result the increment in velocity profile along with porous permeability but reverse in transvers magnetic field on the flow.
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Kakac, S., W. Li, and R. M. Cotta. "Unsteady Laminar Forced Convection in Ducts With Periodic Variation of Inlet Temperature." Journal of Heat Transfer 112, no. 4 (1990): 913–20. http://dx.doi.org/10.1115/1.2910499.
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A theoretical and experimental study of laminar forced convection in the thermal entrance region of a rectangular duct, subjected to a sinusoidally varying inlet temperature, is presented. A general boundary condition of the fifth kind that accounts for both external convection and wall thermal capacitance effects is considered, and an analytical solution is obtained through extending the generalized integral transform technique. The variations of amplitudes and phase lags of centerline and bulk temperatures are determined as functions of modified Biot number, fluid-to-wall thermal capacitance ratio, and dimensionless inlet frequency. An apparatus has been designed, built, and used for the experimental study to provide validation of the mathematical modeling employed. Good agreement is obtained when the nonuniform sinusoidally varying inlet temperature profile obtained by experiments is incorporated into the theoretical model.
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Pinkel, Robert. "The Poisson Link between Internal Wave and Dissipation Scales in the Thermocline. Part I: Probability Density Functions and the Poisson Modeling of Vertical Strain." Journal of Physical Oceanography 50, no. 12 (2020): 3403–24. http://dx.doi.org/10.1175/jpo-d-19-0286.1.
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AbstractThe irregular nature of vertical density profiles is a ubiquitous characteristic of the ocean thermocline. This distortion can be quantified by tracking a set of constant-density (isopycnal) surfaces over time. Examination of 30 000 km of vertical density profile data from seven Pacific Ocean sites indicates that the statistics of isopycnal vertical separation follow the gamma probability distribution, the continuous representation of a Poisson process. All aspects of this process are specified by a single parameter κ0, of order 0.5–2 m−1 across the Pacific. When vertical wavenumber spectra of vertical strain are nondimensionalized by κ0, the variability in these pan-Pacific spectra reduce from a factor of 20 to a factor of 2. Given that numerous dimensionless metrics such as the Richardson number, Froude number, Burger number, etc., are required to specify dynamical balances in the sea, it is intriguing that a single-parameter model describes all aspects of the statistics of vertical strain over the range of scales ~2–200 m. While both internal wave and vortical motions are present in the data, the waves dominate the strain signal at these sites. The high-wavenumber cutoff in the strain spectrum is set by the nonsinusoidal waveform of short-vertical-scale internal waves. As large-scale numerical models improve in resolution, they should replicate this Poisson structure in order to properly model plankton variability, vertical diffusion, horizontal dispersion, sound propagation, and other fine-scale phenomena.
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Deng, Lichi, and Michael J. King. "Theoretical Investigation of the Transition From Spontaneous to Forced Imbibition." SPE Journal 24, no. 01 (2018): 215–29. http://dx.doi.org/10.2118/190309-pa.
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Summary Spontaneous and forced imbibition are recognized as important recovery mechanisms in naturally fractured reservoirs because the capillary force controls the movement of the fluid between the matrix and the fracture. For unconventional reservoirs, imbibition is also important because the capillary pressure is more dominant in these tighter formations, and a theoretical understanding of the flow mechanism for the imbibition process will benefit the understanding of important multiphase-flow phenomena such as waterblocking. In this paper, a new semianalytic method is presented to examine the interaction between spontaneous and forced imbibition and to quantitatively represent the transient imbibition process. The methodology solves the partial-differential equation (PDE) of unsteady-state immiscible, incompressible flow with arbitrary saturation-dependent functions using the normalized water flux concept, which is identical to the fractional-flow terminology used in the traditional Buckley-Leverett analysis. The result gives a universal inherent relationship between time, normalized water flux, saturation profile, and the ratio between cocurrent and total flux. The current analysis also develops a novel stability envelope outside of which the flow becomes unstable caused by strong capillary forces, and the characteristic dimensionless parameter shown in the envelope is derived from the intrinsic properties of the rock and fluid system, and it can describe the relative magnitude of capillary and viscous forces at the continuum scale. This dimensionless parameter is consistently applicable in both capillary-dominated and viscous-dominated flow conditions.
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Szidarovszky, F., K. Hutter, and S. Yakowitz. "Computational Ice-Divide Analysis of a Cold Plane Ice Sheet Under Steady Conditions." Annals of Glaciology 12 (1989): 170–77. http://dx.doi.org/10.1017/s0260305500007151.
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The dimensionless form of the field equations and boundary conditions governing plane flow of a grounded cold ice sheet emerge from balance statements of mass, momentum, and energy. They constitute an amended version of a reduced model of ice-sheet flow, due to Morland (1984) and Hutter (1983), and circumvent the restrictions imposed by the reduced model, namely the neglect of the longitudinal stretching effects. The amended version permits satisfaction of mass balance at the ice divide for arbitrary basal sliding conditions and gives a better reproduction of the local flow features. Under very mild simplifying assumptions, namely that horizontal thermal conduction can be ignored close to the divide, we present a numerical analysis of the ice divide which has second-order accuracy. This analysis permits determination of the temperature profile, velocity, and stress distributions in a symmetric ice divide, provided that the ice-divide height, the local behavior of the accumulation and surface-temperature functions, and the geothermal heat flow are prescribed.
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Szidarovszky, F., K. Hutter, and S. Yakowitz. "Computational Ice-Divide Analysis of a Cold Plane Ice Sheet Under Steady Conditions." Annals of Glaciology 12 (1989): 170–77. http://dx.doi.org/10.3189/s0260305500007151.
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The dimensionless form of the field equations and boundary conditions governing plane flow of a grounded cold ice sheet emerge from balance statements of mass, momentum, and energy. They constitute an amended version of a reduced model of ice-sheet flow, due to Morland (1984) and Hutter (1983), and circumvent the restrictions imposed by the reduced model, namely the neglect of the longitudinal stretching effects. The amended version permits satisfaction of mass balance at the ice divide for arbitrary basal sliding conditions and gives a better reproduction of the local flow features.Under very mild simplifying assumptions, namely that horizontal thermal conduction can be ignored close to the divide, we present a numerical analysis of the ice divide which has second-order accuracy. This analysis permits determination of the temperature profile, velocity, and stress distributions in a symmetric ice divide, provided that the ice-divide height, the local behavior of the accumulation and surface-temperature functions, and the geothermal heat flow are prescribed.
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Duran, Ignacio, and Stephane Moreau. "Solution of the quasi-one-dimensional linearized Euler equations using flow invariants and the Magnus expansion." Journal of Fluid Mechanics 723 (April 16, 2013): 190–231. http://dx.doi.org/10.1017/jfm.2013.118.
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AbstractThe acoustic and entropy transfer functions of quasi-one-dimensional nozzles are studied analytically for both subsonic and choked flows with and without shock waves. The present analytical study extends both the compact nozzle solution obtained by Marble & Candel (J. Sound Vib., vol. 55, 1977, pp. 225–243) and the effective nozzle length proposed by Stow, Dowling & Hynes (J. Fluid Mech., vol. 467, 2002, pp. 215–239) and by Goh & Morgans (J. Sound Vib., vol. 330, 2011, pp. 5184–5198) to non-zero frequencies for both modulus and phase through an asymptotic expansion of the linearized Euler equations. It also extends the piecewise-linear approximation of the velocity profile in the nozzle proposed by Moase, Brear & Manzie (J. Fluid Mech., vol. 585, 2007, pp. 281–304) to any arbitrary profile or equivalently any nozzle geometry. The equations are written as a function of three variables, namely the dimensionless mass, total temperature and entropy fluctuations, yielding a first-order linear system of differential equations with varying coefficients, which is solved using the Magnus expansion. The solution shows that both the modulus and the phase of the transfer functions of the nozzle have a strong dependence on the frequency. This holds for both choked flows and subsonic converging–diverging nozzles. The method is used to compare two different nozzle geometries with the same inlet and outlet Mach numbers, showing that, even if the compact solution predicts no differences between the transfer functions of the two nozzles, significant differences are found at non-zero frequencies. A parametric study is finally performed to calculate the indirect to direct noise ratio for a model combustor, showing that this ratio decreases at higher frequencies.
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Uddin, Mohammed Nasir, Aki Farhana, and Md Abdul Alim. "Numerical study of magneto-hydrodynamic (MHD) mixed convection flow in a lid-driven triangular cavity." Journal of Naval Architecture and Marine Engineering 12, no. 1 (2015): 21–32. http://dx.doi.org/10.3329/jname.v12i1.12910.
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In the present paper, the effect of magneto-hydrodynamic (MHD) on mixed convection flow within a lid-driven triangular cavity has been numerically investigated. The bottom wall of the cavity is considered as heated. Besides, the left and the inclined wall of the triangular cavity are assumed to be cool and adiabatic. The cooled wall of the cavity is moving up in the vertical direction. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Rayleigh number, Hartmann number and the cavity aspect ratio. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters Rayleigh number Ra (103-104), Prandtl number Pr (0.7 - 3) and Hartmann number Ha (5 - 50). The numerical results are presented in terms of stream functions, temperature profile and Nussult numbers. It is found that the streamlines, isotherms, average Nusselt number, average fluid bulk temperature and dimensionless temperature in the cavity strongly depend on the Rayleigh number, Hartmann number and Prandtl number.
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Kartashev, S. V., and Yu V. Kozhukhov. "Improving the quality of design calculations of viscous flow in low-flow centrifugal compressor stages by methods of computational fluid dynamics through reasonable application of different turbulence models." Omsk Scientific Bulletin, no. 176 (2021): 24–30. http://dx.doi.org/10.25206/1813-8225-2021-176-24-30.
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The paper considers the issue of improving the quality of the numerical experiment in the calculation of viscous gas in the flowing part of a low-flow centrifugal compressor stage. The choice of turbulence model in creating a calculation model for calculations by methods of computational fluid dynamics is substantiated. As object of research is chosen low-flow stage with conditional flow coefficient Ф=0,008 and relative width at impeller outlet b2 /D2 =0,0133. The issue of qualitative modeling of friction losses in low-flow stages is of fundamental importance and is directly related to the choice of turbulence model. It is shown that the choice of low-Reynolds turbulence models in the case of unloaded and discontinuous low-flow stages can be made from the main common models (SpalartAllmaras, SST, k-ω) based on the economy of calculations, speed of convergence, solution stability and adequacy of the obtained results. For models with wall functions, the quality of the mesh model and the observance of the dimensionless distance to the wall y+ throughout the calculation domain are particularly important. For highReynolds turbulence models, at values of y+=25...50 on all friction surfaces of the computational domain in the optimal mode of operation, the grid independence of the solution for the entire gas-dynamic characteristic is ensured. It is unacceptable for y+ to fall into the transition region of 4...15 between the viscous sublayer and the region of the logarithmic velocity profile
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Tanzosh, John P., and H. A. Stone. "Motion of a rigid particle in a rotating viscous flow: an integral equation approach." Journal of Fluid Mechanics 275 (September 25, 1994): 225–56. http://dx.doi.org/10.1017/s002211209400234x.
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A boundary integral method is presented for analysing particle motion in a rotating fluid for flows where the Taylor number ${\cal T}$ is arbitrary and the Reynolds number is small. The method determines the surface traction and drag on a particle, and also the velocity field at any location in the fluid.Numerical results show that the dimensionless drag on a spherical particle translating along the rotation axis of an unbounded fluid is determined by the empirical formula $D/6\pi = 1+(4/7){\cal T}^{1/2}+(8/9\pi){\cal T}$, which incorporates known results for the low and high Taylor number limits. Streamline portraits show that a critical Taylor number ${\cal T}_c\ap 50$ exists at which the character of the flow changes. For ${\cal T} < {\cal T}_c$ the flow field appears as a perturbation of a Stokes flow with a superimposed swirling motion. For ${\cal T} > {\cal T}_c$ the flow field develops two detached recirculating regions of trapped fluid located fore and aft of the particle. The recirculating regions grow in size and move farther from the particle with increasing Taylor number. This recirculation functions to deflect fluid away from the translating particle, thereby generating a columnar flow structure. The flow between the recirculating regions and the particle has a plug-like velocity profile, moving slightly slower than the particle and undergoing a uniform swirling motion. The flow in this region is matched to the particle velocity in a thin Ekman layer adjacent to the particle surface.A further study examines the translation of spheroidal particles. For large Taylor numbers, the drag is determined by the equatorial radius; details of the body shape are less important.
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Jan, C. D., and C. L. Chen. "Gradually varied open-channel flow profiles normalized by critical depth and analytically solved by using Gaussian hypergeometric functions." Hydrology and Earth System Sciences 17, no. 3 (2013): 973–87. http://dx.doi.org/10.5194/hess-17-973-2013.
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Abstract. The equation of one-dimensional gradually varied flow (GVF) in sustaining and non-sustaining open channels is normalized using the critical depth, yc, and then analytically solved by the direct integration method with the use of the Gaussian hypergeometric function (GHF). The GHF-based solution so obtained from the yc-based dimensionless GVF equation is more useful and versatile than its counterpart from the GVF equation normalized by the normal depth, yn, because the GHF-based solutions of the yc-based dimensionless GVF equation for the mild (M) and adverse (A) profiles can asymptotically reduce to the yc-based dimensionless horizontal (H) profiles as yc/yn → 0. An in-depth analysis of the yc-based dimensionless profiles expressed in terms of the GHF for GVF in sustaining and adverse wide channels has been conducted to discuss the effects of yc/yn and the hydraulic exponent N on the profiles. This paper has laid the foundation to compute at one sweep the yc-based dimensionless GVF profiles in a series of sustaining and adverse channels, which have horizontal slopes sandwiched in between them, by using the GHF-based solutions.
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Jan, C. D., and C. L. Chen. "Gradually-varied open-channel flow profiles normalized by critical depth and analytically solved by using Gaussian hypergeometric functions." Hydrology and Earth System Sciences Discussions 9, no. 10 (2012): 11791–828. http://dx.doi.org/10.5194/hessd-9-11791-2012.
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Abstract. The equation of one-dimensional gradually-varied flow (GVF) in sustaining and non-sustaining open channels is normalized using the critical depth, hc, and then analytically solved by the direct integration method with the use of the Gaussian hypergeometric function (GHF). The GHF-based solution so obtained from the hc-based dimensionless GVF equation is more useful and versatile than its counterpart from the GVF equation normalized by the normal depth, hn, because the GHF-based solutions of the hc-based dimensionless GVF equation for the mild (M) and adverse (A) profiles can asymptotically reduce to the hc-based dimensionless horizontal (H) profiles as hc/hn → 0. An in-depth analysis of the hc-based dimensionless profiles expressed in terms of the GHF for GVF in sustaining and adverse wide channels has been conducted to discuss the effects of hc/hn and the hydraulic exponent N on the profiles This paper has laid the foundation to compute at one sweep the hc-based dimensionless GVF profiles in a series of sustaining and adverse channels, which have horizontal slopes sandwiched in between them, by using the GHF-based solutions.
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Massoudi, Mehrdad, and C. Lakshmana Rao. "Vertical flow of a multiphase mixture in a channel." Mathematical Problems in Engineering 6, no. 6 (2001): 505–26. http://dx.doi.org/10.1155/s1024123x00001459.
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The flow of a multiphase mixture consisting of a viscous fluid and solid particles between two vertical plates is studied. The theory of interacting continua or mixture theory is used. Constitutive relations for the stress tensor of the granular materials and the interaction force are presented and discussed. The flow of interest is an ideal one where we assume the flow to be steady and fully developed; the mixture is flowing between two long vertical plates. The non-linear boundary value problem is solved numerically, and the results are presented for the dimensionless velocity profiles and the volume fraction as functions of various dimensionless numbers.
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Ansah, J., R. S. Knowles, and T. A. Blasingame. "A Semi-Analytic (p/z) Rate-Time Relation for the Analysis and Prediction of Gas Well Performance." SPE Reservoir Evaluation & Engineering 3, no. 06 (2000): 525–33. http://dx.doi.org/10.2118/66280-pa.
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Summary In this paper we present a rigorous theoretical development of solutions for boundary-dominated gas flow during reservoir depletion. These solutions were derived by directly coupling the stabilized flow equation with the gas material balance equation. Due to the highly nonlinear nature of the gas flow equation, pseudo pressure and pseudotime functions have been used over the years for the analysis of production rate and cumulative production data. While the pseudo pressure and pseudotime functions do provide a rigorous linearization of the gas flow equation, these transformations do not provide direct solutions. In addition, the pseudotime function requires the average reservoir pressure history, which in most cases is simply not available. Our approach uses functional models to represent the viscosity-compressibility product as a function of the reservoir pressure/z-factor (p/z) profile. These models provide approximate, but direct, solutions for modeling gas flow during the boundary-dominated flow period. For convenience, the solutions are presented in terms of dimensionless variables and expressed as type curve plots. Other products of this work are explicit relations for p/z and Gp(t). These solutions can be easily adapted for field applications such as the prediction of rate or cumulative production. We also provide verification of our new flow rate and pressure solutions using the results of numerical simulation and we demonstrate the application of these solutions using a field example. Introduction We focus here on the development and application of semi-analytic solutions for modeling gas well performance¾with particular emphasis on production rate analysis using decline type curves. Our emphasis on decline curve analysis arises both from its usefulness in viewing the entire well history, as well as its familiarity in the industry as a straightforward and consistent analysis approach. More importantly, the approach does not specifically require reservoir pressure data (although pressure data are certainly useful). Decline curve analysis typically involves a plot of production rate, qg and/or other rate functions (e.g., cumulative production, rate integral, rate integral derivative, etc.) vs. time (or a time-like function) on a log-log scale. This plot is matched against a theoretical model, either analytically as a functional form or graphically in the form of type curves. From this analysis formation properties are estimated. Production forecasts can then be made by extrapolation of the matched data trends. The specific formation parameters that can be obtained from decline curve analysis are original gas in place (OGIP), permeability or flow capacity, and the type and strength of the reservoir drive mechanism. In addition, we can establish the future performance of individual wells, and the estimated ultimate recovery (EUR). Attempts to theoretically model the production rate performance of gas and oil wells date as far back as the early part of this century. In 1921, a detailed summary of the most important developments in this area was documented in the Manual for the Oil and Gas Industry.1 Several efforts2,3 were made over the years immediately thereafter, and probably the most significant contribution towards the development of the modern decline curve analysis concept is the classic paper by Arps,2 written in 1944. In this work Arps presented a set of exponential and hyperbolic equations for production rate analysis. Although the basis of Arps' development was statistical (and therefore empirical), these historic results have found widespread appeal in the oil and gas industry. The continuous use of the so-called "Arps equations" is primarily due to the explicit form of the relations, which makes these equations quite useful for practical applications. The next major development in production decline analysis technology occurred in 1980, when Fetkovich4 presented a unified type curve which combined the Arps empirical equations with the analytical rate solutions for bounded reservoir systems.
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Campo, Antonio, Oronzio Manca, and Biagio Morrone. "Numerical Investigation of the Natural Convection Flows for Low-Prandtl Fluids in Vertical Parallel-Plates Channels." Journal of Applied Mechanics 73, no. 1 (2005): 96–107. http://dx.doi.org/10.1115/1.1991867.
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Laminar natural convection of metallic fluids (Pr⪡1) between vertical parallel plate channels with isoflux heating is investigated numerically in this work. The full elliptic Navier-Stokes and energy equations have been solved with the combination of the stream function and vorticity method and the finite-volume technique. An enlarged computational domain is employed to take into account the flow and thermal diffusion effects. Results are presented in terms of velocity and temperature profiles. The investigation also focuses on the flow and thermal development inside the channel; the outcomes show that fully developed flow is attained up to Ra=103, whereas the thermal fully developed condition is attained up to Ra=104. Further, correlation equations for the dimensionless induced flow rate, maximum dimensionless wall temperatures, and average Nusselt numbers as functions of the descriptive geometrical and thermal parameters covering the collection of channel Grashof numbers 1.32×103⩽Gr∕A⩽5.0×106 and aspect ratios 5⩽A⩽15. Comparison with experimental measurements has been presented to assess the validity of the numerical computational procedure.
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Cheung, F. B., S. W. Shiah, D. H. Cho, and L. Baker. "Turbulent Natural Convection in a Horizontal Layer of Small-Prandtl-Number Fluid." Journal of Heat Transfer 113, no. 4 (1991): 919–25. http://dx.doi.org/10.1115/1.2911222.
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Turbulent natural convection in a horizontal layer of liquid metal confined between two infinite rigid plates is studied theoretically. The layer, with uniformly distributed energy sources in the fluid, is heated from below and cooled from above. An approximate analysis of the Boussinesq equations of motion is performed for the case of small-Prandtl-number fluids to determine the temperature profiles in three different thermal regions of the layer. By matching these profiles in the regions of overlap, analytical expressions are derived for the lower and upper surface Nusselt numbers and the dimensionless turbulent core temperature as functions of the internal and external Rayleigh numbers defined respectively in terms of the volumetric heating rate and surface-to-surface temperature difference of the layer. Comparison of the present results with heat transfer data for liquid mercury is made and found to be good.
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Prasad, Ramachandra, and Bhaskar Reddy. "Radiation and mass transfer effects on an unsteady MHD free convection flow past a heated vertical plate in a porous medium with viscous dissipation." Theoretical and Applied Mechanics 34, no. 2 (2007): 135–60. http://dx.doi.org/10.2298/tam0702135p.
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An unsteady, two-dimensional, hydromagnetic, laminar free convective boundary-layer flow of an incompressible, Newtonian, electrically-conducting and radiating fluid past an infinite heated vertical porous plate with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and graphical results for velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and Sherwood number are presented and discussed. It is observed that, when the radiation parameter increases, the velocity and temperature decrease in the boundary layer, whereas when thermal and solutal Grashof increases the velocity increases.
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., Deepti, and B. P. Garg. "Combined Effects of Periodic Suction and Permeability on MHD Oscillatory Flow of Rivlin Ericksen Fluid past a Moving Semi-infinite Porous Plate in the Presence of Thermal Radiation." SAMRIDDHI : A Journal of Physical Sciences, Engineering and Technology 11, no. 02 (2019): 93–108. http://dx.doi.org/10.18090/samriddhi.v11i02.3.
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In this paper the behaviour of unsteady flow of viscous incompressible and electrically conducting Rivlin Ericksen fluid past a semi-infinite vertical porous plate having variable permeability under thermal radiation effects is examined. Further the time dependent suction is assumed at the plate which is moving with constant velocity whereas the free stream velocity is assumed to be oscillating with time. The dimensionless governing equations for the fluid flow under investigation are reduced to set of ordinary differential equations using two term harmonic and non-harmonic functions and solved analytically under relevant boundary conditions. Further the analytical results obtained for velocity, temperature and concentration profiles are evaluated numerically and their variation with different flow parameters are shown graphically. Also, the variation behaviour of Skin friction, Nusselt number and Schmidt number along with their amplitudes and phase angles for pertinent parameters is displayed graphically.
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El Harfouf, A., A. Wakif, and S. Hayani Mounir. "Semi-Analytical Resolution of a Squeezing Unsteady Nanofluid Flow Between Two Parallel Plates Using Homotopy Perturbation Method (HPM)." WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER 16 (January 19, 2021): 1–13. http://dx.doi.org/10.37394/232012.2021.16.1.
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In this current work, the heat transfer analysis for the unsteady squeezing flow of a viscous nanofluid between two parallel plates considering Fourier heat flux model have been explored. The partial differential equations representing flow model are reduced to nonlinear ordinary differential equations by introducing a similarity transformation. The dimensionless and nonlinear ordinary differential equations of the velocity and temperatures functions obtained are solved by employing The Homotopy Perturbation Method (HPM). The results found in this peper are verified by comparing it with the results obtained using the numerical method RK4, The results obtained are agree with this numerical solution. The effects of different parameters on the velocity and temperature profiles are examined graphically, and numerical calculations for the skin friction coefficient and local Nusselt number are tabulated. It is found an excellent agreement in the comparative study with literature results.
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Boricic, Aleksandar, Milos Jovanovic, and Branko Boricic. "Unsteady magnetohydrodynamic thermal and diffusion boundary layer from a horizontal circular cylinder." Thermal Science 20, suppl. 5 (2016): 1367–80. http://dx.doi.org/10.2298/tsci16s5367b.
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The unsteady 2-D dynamic, thermal, and diffusion magnetohydrodynamic laminar boundary layer flow over a horizontal cylinder of incompressible and electrical conductivity fluid, in mixed convection in the presence of heat source or sink and chemical reactions. The present magnetic field is homogenous and perpendicular to the body surface. It is assumed that induction of outer magnetic field is a function of longitudinal co-ordinate outer electric field is neglected and magnetic Reynolds number is significantly lower than one, i. e. considered the problem is in approximation without induction. Fluid electrical conductivity is constant. Free stream velocity, temperature, and concentration on the body are functions of longitudinal co-ordinate. The developed governing boundary layer equations and associated boundary conditions are made dimensionless using a suitable similarity transformation and similarity parameters. System of non-dimensionless equations is solved using the implicit finite difference three-diagonal and iteration method. Numerical results are obtained and presented for different Prandtl, Eckart, and Schmidt numbers, and values: magnetic parameter, temperature, and diffusion parameters, buoyancy temperature parameters, thermal parameter, and chemical reaction parameter. Variation of velocity profiles, temperature and diffusion distributions, and many integral and differential characteristics, boundary layer, are evaluated numerically for different values of the magnetic field. Transient effects of velocity, temperature and diffusion are analyzed. A part of obtained results is given in the form of figures and corresponding conclusions.
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El Harfouf, A., A. Wakif, and S. Hayani Mounir. "Heat Transfer Analysis on Squeezing Unsteady MHD Nanofluid Flow Between Two Parallel Plates Considering Thermal Radiation, Magnetic and Viscous Dissipations Effects a Solution by Using Homotopy Perturbation Method." Sensor Letters 18, no. 2 (2020): 113–21. http://dx.doi.org/10.1166/sl.2020.4169.
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In this current work, the heat transfer analysis for the unsteady squeezing magnetohydrodynamic flow of a viscous nanofluid between two parallel plates in the presence of thermal radiation, viscous and magnetic dissipations impacts, considering Fourier heat flux model have been explored. The partial differential equations representing flow model are reduced to nonlinear ordinary differential equations by introducing a similarity transformation. The dimensionless and nonlinear ordinary differential equations of the velocity and temperatures functions obtained are solved by employing the homotopy perturbation method. The effects of different parameters on the velocity and temperature profiles are examined graphically, and numerical calculations for the skin friction coefficient and local Nusselt number are tabulated. It is found an excellent agreement in the comparative study with literature results. This present numerical exploration has great relevance, consequently a better understanding of the squeezing flow phenomena in the hydraulic lifts, power transmission, nano gastric tubes, reactor fluidization areas.
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Chen, Chien Hsin, Shen Jenn Hwang, and Yunn Lin Hwang. "Electroosmotic Flow and Heat Transfer in Microchannels: A Closed Form Solution." Applied Mechanics and Materials 319 (May 2013): 462–67. http://dx.doi.org/10.4028/www.scientific.net/amm.319.462.
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In this paper, an analysis has been conducted to explore the momentun and thermal transport characterastics of electroosmotic liquid flow in a microchannel under imposed constant wall heat flux boundary condition. The present formulation shows that the problem is governed by three parameters, namely, the length scale ratio (ratio of Debye length to half channel height), the Joule heating parameter (ratio of Joule heating to surface heat flux), and the Brinkman number. A closed form solution of the problem was obtained and the impact of viscous dissipation on the heat transfer behavior was investigated. Analytical exact solutions of dimensionless velocity and temperature profiles, normalized local velocity, volume flow rate, friction coefficient, mean fluid temperature, and the fully-developed Nusselt number were obtained as functions of the governing parameters. Especially, the effects of length scale ratio on major flow parameters (including the normalized local velocity, friction coefficient, and volumetric flow rate) were examined. Also, the viscous dissipation effect on thermal transport characteristics was discussed in depth.
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Kim, Si-Wan, Chin-Hoh Moeng, Jeffrey C. Weil, and Mary C. Barth. "Lagrangian Particle Dispersion Modeling of the Fumigation Process Using Large-Eddy Simulation." Journal of the Atmospheric Sciences 62, no. 6 (2005): 1932–46. http://dx.doi.org/10.1175/jas3435.1.
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Abstract A Lagrangian particle dispersion model (LPDM) is used to study fumigation of pollutants in and above the entrainment zone into a growing convective boundary layer. Probability density functions of particle location with height and time are calculated from particle trajectories driven by the sum of the resolved-scale velocity from a large-eddy simulation (LES) model and the stochastic subgrid-scale (SGS) velocity. The crosswind-integrated concentration (CWIC) fields show good agreement with water tank experimental data. A comparison of the LPDM output with an Eulerian diffusion model output based on the same LES flow shows qualitative agreement with each other except that a greater overshoot maximum of the ground-level concentration occurs in the Eulerian model. The dimensionless CWICs near the surface for sources located above the entrainment zone collapse to a nearly universal curve provided that the profiles are time shifted, where the shift depends on the source heights. The dimensionless CWICs for sources located within the entrainment zone show a different behavior. Thus, fumigation from sources above the entrainment zone and within the entrainment zone should be treated separately. An examination of the application of Taylor’s translation hypothesis to the fumigation process showed the importance of using the mean boundary layer wind speed as a function of time rather than the initial mean boundary layer wind speed, because the mean boundary layer wind speed decreases as the simulation proceeds. The LPDM using LES is capable of accurately simulating fumigation of particles into the convective boundary layer. This technique provides more computationally efficient simulations than Eulerian models.
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Charles, D. D., H. H. Rieke, and R. Purushothaman. "Well-Test Characterization of Wedge-Shaped, Faulted Reservoirs." SPE Reservoir Evaluation & Engineering 4, no. 03 (2001): 221–30. http://dx.doi.org/10.2118/72098-pa.
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Summary Two offshore, wedge-shaped reservoirs in south Louisiana were interpreted with pressure-buildup responses by comparing the results from simulated finite-element model studies. The importance of knowing the correct reservoir shape, and how it is used to interpret the generated boundary-pressure responses, is briefly discussed. Two different 3D computer models incorporating different wedge-shaped geometries simulated the test pressure-buildup response patterns. Variations in the two configurations are topologically expressed as a constant thickness and a nonconstant thickness, with smooth-surface, wedged-shaped reservoir models. The variable-thickness models are pinched-out updip at one end and faulted at the other end. Numerical well-test results demonstrated changes in the relationships between the pressure-derivative profile, the wellbore location, and the extent of partial penetration in the reservoir models. The wells were placed along the perpendicular bisector (top view) at distances starting from the apex at 5, 10, 20, 40, 50, 60, 80, and 90% of the reservoir length. Results demonstrate that boundary distance identification (such as distance, number, and type) based solely on the log-log derivative profile in rectangular and triangular wedge-shaped reservoirs should be strongly discouraged. Partial-penetration effects (PPE's) in wedge-shaped reservoirs are highly dependent on the wellbore location relative to the wedge, and the well-test-data analysis becomes more complex. Introduction The interpretation of the effect of reservoir shape on pressure-transient well-test data needs improvement. It is economically imperative to be able to generate an accurate estimate of reserves and producing potential. This is especially critical for independent operators who wish to participate in deepwater opportunities in the Gulf of Mexico. Proper interpretation of data extracted from cost-effective well tests is an integral part of describing, evaluating, and managing such reservoirs. Well-test information such as average reservoir pressure, transmissivity, pore volume, storativity, formation damage, deliverability, distance to the boundary, and completion efficiency are some of the technical inputs into economic and operational decisions. Several key economic decisions that operators have to make are:Should the reservoir be exploited?How many wells are needed to develop the reservoir?Is artificial lift necessary (and if so, when)? The identification of morphological demarcation components such as impermeable barriers (faults, intersecting faults, facies changes, erosional unconformities, and structural generated depositional pinchouts) and constant-pressure boundaries (aquifer or gas-cap) from well testing help to establish the reservoir boundaries, shape, and volume. One must remember that the geological entrapment structure or sedimentological body does not always define the reservoir's limits. Our present study provides insight into wedge-shaped reservoirs in the Gulf of Mexico. Seismic exploration can define geological shapes in either two or three dimensions in the subsurface. These shapes are expressions of the preserved structural history and depositional environments and are verified by observations of such structures in outcrops and present-day depositional environments. From a sedimentological viewpoint, the following sedimentary deposits can exhibit wedge-shaped geometries. Preserved barchan sand dunes, reworked transgressive sands, barrier-island sands, offshore bars, alluvial fan deposits, delta-front sheet sands, and lenticular channel sands form the more plausible pinchout, wedge-shaped geological models recognized in the Gulf of Mexico sedimentary sequence. Wedge-Shaped Reservoirs Reviewing the petroleum engineering literature, we found very few technical papers addressing wedge-shaped reservoir geometries and their effects on reservoir performance. Their detailed analytical results are discussed and applied to the interpretations of our model results. An overview of the conceptual models is presented as a quick orientation to emphasize some model issues. Horne and Temeng1 were the first to address the problem of recognizing, discriminating, and locating reservoir pinchouts with the Green's functions method proposed by Gringarten and Ramey2 in pressure-transient analysis. The analytical solution considered a dimensionless penetration depth of the well. Their results showed that pinchout boundaries appear similar to constant-pressure boundaries with respect to pressure-drawdown behavior and not as a perpendicular sealing boundary. Yaxley3 presented a set of simple equations for calculating the stabilized inflow performance of a well in infinite rectangular and wedge-shaped drainage systems. The basis for Yaxley's mathematical model is the application of transient linear flow (as opposed to radial flow conditions assumed for the reservoir) and the mathematical difference between a plane source and a line source in linear-flow drainage systems for various rectangular drainage shapes. The equations were derived from transient linear-flow relationships for a well located between parallel no-flow boundaries. This concept was applied to intersecting no-flow boundaries and an outer circular, no-flow, constant-pressure boundary. His approach involved a constant ßr that is interpreted as an extra pressure drop relative to a well of radius ro (radial distance to the well location), which is a result of the distortion of the radial streamline pattern. Chen and Raghavan4 developed a solution to compute pressure distributions in wedge-shaped drainage systems using Laplace transforms. Their mathematical approach overcame existing limitations in some of the previous solutions, which were mentioned earlier. By applying the inversion theorem to the Laplace transformation, they verified that the slope of the pressure profile is inversely proportional to the wedge angle of the drainage system. An examination of their results is important to the interpretation of our own simulated pressure-response issues. Generally, their model solutions showed three radial-flow periods in the absence of wellbore-storage effects. The radial-flow periods showed that:During an initial radial-flow period, neither of the impermeable boundaries registered either singly or jointly.In the second phase, one or two boundaries became evident on the pressure signature.A third radial-flow period exhibited a semi logarithmic slope proportional to p/?o, where ?o=the angle of the wedge.
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Wang, Cui, Zhiwei Ma, Juliana Y. Leung, and Stefan D. Zanon. "Correlating Stochastically Distributed Reservoir Heterogeneities with Steam-Assisted Gravity Drainage Production." Oil & Gas Sciences and Technology – Revue d’IFP Energies nouvelles 73 (2018): 9. http://dx.doi.org/10.2516/ogst/2017042.
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Application of big data analytics in reservoir engineering has gained wide attention in recent years. However, designing practical data-driven models for correlating petrophysical measurements and Steam-Assisted Gravity Drainage (SAGD) production profiles using actual field data remains difficult. Parameterization of the complex reservoir heterogeneities in these reservoirs is not trivial. In this study, a set of attributes pertinent to characterizing stochastic distributions of shales and lean zones is formulated and used for correlating against a number of production performance measures. A comprehensive investigation of the heterogeneous distribution (continuity, size, proportions, permeability, location, orientation and saturation) of shale barriers and lean zones is presented. First, a series of two-dimensional SAGD models based on typical Athabasca oil reservoir properties and operating conditions are constructed. Geostatistical techniques are applied to stochastically model shale barriers, which are imbedded in a region of degraded rock properties referred to as Low-Quality Sand or LQS, among a background of clean sand. Parameters including correlation lengths, orientation, proportions and permeability anisotropy of the different rock facies are varied. Within each facies, spatial variations in water saturation are modeled probabilistically. In contrast to many previous simulation studies, representative multiphase flow functions and capillarity models are assigned in accordance to individual facies. A set of input attributes based on facies proportions and dimensionless correlation lengths are formulated. Next, to facilitate the assessment of different scenarios, production performance is quantified by numerous dimensionless output attributes defined from recovery factor and steam-to-oil ratio profiles. An additional dimensionless indicator is implemented to capture the production time during which the instantaneous steam-to-oil ratio has exceeded a particular economic threshold. Finally, results of the sensitivity analysis are employed as training and testing datasets in a series of neural network models to correlate the pertinent system attributes and the production performance measures. These models are also used to assess the consequences of ignoring lateral variation of heterogeneities when extracting petrophysical (log) data from vertical delineation wells alone. An important contribution of this work is that it proposes a set of input attributes for correlating reservoir heterogeneity introduced by shale barriers and lean zones to SAGD production performance. It demonstrates that these input attributes, which can be extracted from petrophysical logs, are highly correlated with the ensuing recovery response and heat loss. This work also exemplifies the feasibility and utility of data-driven models in correlating SAGD performance. Furthermore, the proposed set of system variables and modeling approach can be applied directly in field-data analysis and scale-up study of experimental models to assist field-operation design and evaluation.
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Sudarshan Reddy, Y., K. S. Balamurugan, and G. Dharmaiah. "Perturbation Analysis of Rivlin-Ericksen Fluid on Heat Transfer in the Presence of Heat Absorption." Asian Journal of Engineering and Applied Technology 8, no. 3 (2020): 14–20. http://dx.doi.org/10.51983/ajeat-2019.8.3.1167.
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The problem of visco-elastic Rivlin-Ericksen fluid flow past a semi- infinite vertical plate embedded in a porous medium with variable temperature and suction in the presence of a uniform transverse magnetic field and thermal buoyancy effect is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and some graphical results such as visco-elastic parameter Rm, heat absorption parameter Q, Grashof number Gr, Prandtl number Pr, time t, suction velocity parameter A, moving velocity parameter Up and an exponential parameter ε, for the velocity and temperature profiles within the boundary layer are presented. Skin-friction coefficient, Nusselt numbers are also discussed with the help of the tables.
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Jha, Basant Kumar, and Muhammad Nasir Sarki. "Non-linear natural convection and mass transfer flow near a vertical moving porous plate with chemical reaction and Soret effect." Multidiscipline Modeling in Materials and Structures 15, no. 5 (2019): 846–58. http://dx.doi.org/10.1108/mmms-04-2018-0063.
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Purpose The purpose of this paper is to conduct a theoretical study on steady fully developed non-linear natural convection and mass transfer flow past an infinite vertical moving porous plate with chemical reaction and thermal diffusion effect. Closed-form expressions for dimensionless velocity, concentration, Sherwood number and skin-friction are obtained by solving the present mathematical model. Design/methodology/approach The fully developed steady non-linear natural convection and mass transfer flow near a vertical moving porous plate with chemical reaction and thermal diffusion effect is investigated. The non-linear density variation and Soret effect were taken into consideration. The dimensionless velocity, temperature and concentration profiles were obtained in terms of exponential functions, and were used to compute the governing parameters, skin-friction and Sherwood number. Findings The effect of coefficient of the non-linear density variation with the temperature (NDT) and concentration (NDC) parameter, chemical reaction parameter, thermal diffusion parameter are discussed with the aid of line graphs and tables. The analysis of the result shows that the velocity as well as skin-friction having higher values in the case of non-linear variation of density with temperature and concentration in comparison to linear variation of density with temperature and concentration. It is observed that the velocity and skin-friction increase with an increase in the Soret parameter. Originality/value The aim of this paper is to extend the work of Muthucumaraswamy (2002) by incorporating the thermal diffusion (Soret) effect and non-linear density variation with temperature (NDT) and concentration (NDC), on which, to the best knowledge of the authors, no studies have been carried out.
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El-Khatib, Noaman. "Waterflooding Performance of Communicating Stratified Reservoirs With Log-Normal Permeability Distribution." SPE Reservoir Evaluation & Engineering 2, no. 06 (1999): 542–49. http://dx.doi.org/10.2118/59071-pa.
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Summary An analytical solution is developed for waterflooding performance of layered reservoirs with a log-normal permeability distribution with complete crossflow between layers. The permeability distribution is characterized by the Dykstra-Parsons (DP) variation coefficient VDP or the standard deviation of the distribution sk. The performance is expressed in terms of vertical coverage as function of the producing water-oil ratio. Also an expression for the dimensionless time (pore volumes of injected water) at a given water-oil ratio is derived. Expressions are also derived for pseudorelative permeability functions and fractional flow curves that can be used in reservoir simulation. Correlation charts are also presented to enable graphical determination of the performance. The variables are combined in such a way that a single chart is constructed for the entire range of water-oil ratio, mobility ratio and permeability variation. Analogy to the Buckley-Leverett (BL) multiple-valued saturation profile is found to occur at low mobility ratios (M&lt;1) where a multiple-valued displacement front is formed. A procedure similar to the BL discontinuity is suggested to handle this situation. Successive layers with different permeabilities are allowed to move with the same velocity resulting in a single-valued profile with a discontinuity. No such behavior is observed for mobility ratios greater than unity. A criterion for the minimum mobility ratio at which this behavior occurs is presented as a function of the variation coefficient VDP. Introduction Waterflooding is still the recovery process responsible for most of the oil production by secondary recovery. Water injected into the reservoir displaces almost all of the oil except the residual oil saturation from the portions of the reservoir contacted or swept by water. The fraction of oil displaced from a contacted volume is known as the displacement efficiency and depends on the relative permeability characteristics of the rock as well as the viscosities of the displacing and displaced fluids. The extent to which a reservoir is swept by a displacing fluid is separated into areal and vertical sweep efficiencies. The areal sweep efficiency accounts for the nonlinearity of the flow patterns between injection and production wells. The vertical sweep efficiency or coverage is caused by the heterogeneity of the reservoir, i.e., variation of horizontal permeability in the vertical direction. The displacing fluid tends to move faster in zones with higher permeabilities, resulting in earlier breakthrough into producing wells. Both areal and vertical sweep efficiencies are highly dependent on the mobility ratio of the displacement process and depend on the volume of the injected fluid expressed in pore volumes. The vertical sweep efficiency, however, is mainly dependent on the permeability distribution in the producing layer. Because of the variation in the depositional environments, reservoir rocks usually exhibit random variations in their petrophysical properties. Porosity is usually found to have a normal distribution, while the permeability has a log-normal distribution. The log-normal distribution of permeability is characterized by two parameters: the mean permeability Km and the standard deviation sk The standard deviation sk can also be expressed in terms of the DP variation coefficient VDP. It may also be related to the Lorenz coefficient L. The methods available in the literature to predict the waterflooding performance of stratified reservoirs can be grouped into two categories depending on the assumption of communication or no communication between the different layers. The method of DP1 is the basis for performance prediction in noncommunicating stratified reservoirs. In addition to the basic equations presented in their work, they also presented correlations of the vertical coverage for log-normal permeability distributions in terms of mobility ratio and permeability variation coefficient at different values of the water-oil ratio. Also presented in their paper is a correlation of actual recovery factor vs. vertical coverage, initial water saturation, and water-oil ratio. This correlation was based on experimental runs performed on core plugs with permeability distributions determined by measuring the permeability at different locations on the core with a minipermeameter. Johnson2 later on combined the theoretical charts based on DP equations with the experimental correlation chart into a group of correlation charts from which the recovery factor at given values of water-oil ratio can be calculated directly without first computing the vertical coverage. Mobarek3 found discrepancies between results obtained by this method and results obtained using a numerical model. Muskat4 presented analytical solution for waterflooding performance of stratified systems with linear and exponential permeability distributions. Reznik et al.5 derived expressions for the variation of pressure drop or injection rate as function of injection time for the DP model. Prediction of waterflooding performance for communicating reservoirs was presented by Hiatt.6 This model assumes instantaneous crossflow between layers to keep the pressure gradient the same in all layers at any distance. Warren and Casgrove7 applied the Hiatt model to a system with log-normal permeability distribution and normal porosity distribution. Their method is semigraphical, semianalytical since they obtain values from plots of permeability and formation capacity distributions on probability graphs. Hearn8 used the same model of Hiatt to develop expressions for pseudorelative permeabilities that can be used in numerical reservoir simulation to reduce a three-dimensional model to a two-dimensional areal model with average (pseudo) functions for the vertical direction. El-Khatib9 extended the work of Hiatt to account for variable rock properties other than the absolute permeability. He also presented equations for the variation of the injectivity ratio with injection time and compared performance of communicating and noncommunicating systems. Since it is widely accepted that the permeability in reservoir rocks exhibits a log-normal distribution, the objective of this work is to present a solution in a closed form for the waterflooding performance of stratified reservoirs with such permeability distributions. This would be the limiting case for a stratified system composed of a very large number of layers. In such a case, it is reasonable to assume complete communication between the layers since it is highly unrealistic to assume such large number of layers to be separated by an equal number of thin insulating strata. Assumptions and Definitions The following assumptions are made:The sysstem is linear, horizontal and of constant thickness.The flow is isothermal, incompressible and obeys Darcy's law.
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Kordík, Jozef, and Zdeněk Trávníček. "Novel Nozzle Shapes for Synthetic Jet Actuators Intended to Enhance Jet Momentum Flux." Actuators 7, no. 3 (2018): 53. http://dx.doi.org/10.3390/act7030053.
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An axisymmetric synthetic jet actuator based on a loudspeaker and five types of flanged nozzles were experimentally tested and compared. The first (reference) type of nozzle was a common sharp-edged circular hole. The second type had a rounded lip on the inside. The third nozzle type was assembled from these two types of nozzles—it had a rounded lip on the inside and straight section on the outside. The fourth nozzle was assembled using orifice plates such that the rounded lips were at both inner and outer nozzle ends. The last nozzle was equipped with an auxiliary nozzle plate placed at a small distance downstream of the main nozzle. The actuators with particular nozzles were tested by direct measurement of the synthetic jet (SJ) time-mean thrust using precision scales. Velocity profiles at the actuator nozzle exit were measured by a hot-wire anemometer. Experiments were performed at eight power levels and at the actuator resonance frequency. The highest momentum flux was achieved by the nozzle equipped with an auxiliary nozzle plate. Namely, an enhancement was approximately 31% in comparison with an effect of the reference nozzle at the same input power. Furthermore, based on the cavity pressure and the experimental velocity profiles, parameters for a lumped element model (mass of moving fluid and pressure loss coefficient) were evaluated. These values were studied as functions of the dimensionless stroke length.
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Chen, Cheng, Bruce W. Melville, and N. A. K. Nandasena. "Investigations of Reduction Effect of Vertical Wall on Dam-Break-Simulated Tsunami Surge Exerted on Wharf Piles." Journal of Earthquake and Tsunami 12, no. 02 (2018): 1840006. http://dx.doi.org/10.1142/s1793431118400067.
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For a preliminary investigation of the impact of a tsunami surge on wharf piles, a tsunami flume was built in a laboratory, and a dam break flow was generated by a gate-reservoir system to simulate a tsunami surge. In addition, a vertical wall was installed in front of the wharf model so that its effect in reducing tsunami load could be studied. Five different tsunami surge strengths were generated by this gate-reservoir system. Wave transducers were used in the test flume to capture surge heights and velocities, and hence the surge front profiles, for different surge strengths. High-speed video cameras (210 frames per second) were used to record the flow motion of the tsunami surge, and pressure sensors (1000[Formula: see text]Hz in frequency) were used to capture the time histories of the tsunami pressure on the wharf piles. Four stages of tsunami surge motions were observed by this high-speed camera. Accordingly, the pressure time history can be divided into three phases. In our experimental range, pressures were influenced by surge height and wall height, but not by the wall position. Based on the dimensionless experimental data (pile heights, surge heights, vertical wall heights, and surge pressures), equations for estimating tsunami loads on wharf pile are proposed, expressing surge front (peak impact) pressure and quasi-steady pressure as functions of surge height, wall height, and pile height.
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Lippmann, Thomas C., and Anthony J. Bowen. "The Vertical Structure of Low-Frequency Motions in the Nearshore. Part II: Theory." Journal of Physical Oceanography 46, no. 12 (2016): 3713–27. http://dx.doi.org/10.1175/jpo-d-16-0015.1.
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AbstractField observations from a vertical stack of two-component current meters obtained from the 1994 Duck94 nearshore field experiment (presented in a companion paper by Lippmann, et al.) show significant vertical structure in energy, phase, and rotation of motions at low frequencies around 0.005 Hz. Low-frequency motions are typically modeled in the surfzone with the shallow-water (depth averaged) momentum equations that do not allow for any vertical structure. Following work from the shelf tidal community (Prandle), this study shows that the observations are consistent with the depth-varying momentum equations including shear stresses induced by a bottom boundary layer described by a constant eddy viscosity νt and bottom friction given by a constant drag coefficient and depth-averaged velocity . The bidirectional flow field is solved over arbitrary depth profiles varying only in the cross-shore direction h(x) in the presence of a vertically uniform mean alongshore current with cross-shore shear structure V(x). Analytic solutions are found to depend on νt, cd, h, ∂V/∂x, and the parameter , where σ and k are the radian frequency and alongshore wavenumber of the oscillating motion. Model behavior is explored by plotting solutions for a given parameter space as functions of the nondimensional depth H = λh and dimensionless friction parameter that combines the effects of bottom drag and vertical mixing. The behavioral changes in amplitude, phase shift, and rotational structure over the water column are qualitatively similar to those observed in the field.
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Ghalambaz, M., E. Izadpanahi, A. Noghrehabadi, and A. Chamkha. "Study of the boundary layer heat transfer of nanofluids over a stretching sheet: Passive control of nanoparticles at the surface." Canadian Journal of Physics 93, no. 7 (2015): 725–33. http://dx.doi.org/10.1139/cjp-2014-0370.
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The boundary layer heat and mass transfer of nanofluids over an isothermal stretching sheet is analyzed using a drift-flux model. The relative slip velocity between the nanoparticles and the base fluid is taken into account. The nanoparticles’ volume fractions at the surface of the sheet are considered to be adjusted passively. The thermal conductivity and the dynamic viscosity of the nanofluid are considered as functions of the local volume fraction of the nanoparticles. A non-dimensional parameter, heat transfer enhancement ratio, is introduced, which shows the alteration of the thermal convective coefficient of the nanofluid compared to the base fluid. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using the fourth-order Runge–Kutta and Newton–Raphson methods along with the shooting technique. The effects of six non-dimensional parameters, namely, the Prandtl number of the base fluid Prbf, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, variable thermal conductivity parameter Nc and the variable viscosity parameter Nv, on the velocity, temperature, and concentration profiles as well as the reduced Nusselt number and the enhancement ratio are investigated. Finally, case studies for Al2O3 and Cu nanoparticles dispersed in water are performed. It is found that increases in the ambient values of the nanoparticles volume fraction cause decreases in both the dimensionless shear stress f″(0) and the reduced Nusselt number Nur. Furthermore, an augmentation of the ambient value of the volume fraction of nanoparticles results in an increase the heat transfer enhancement ratio hnf/hbf. Therefore, using nanoparticles produces heat transfer enhancement from the sheet.
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Jaedong, Lee. "Analysis of Wireline Formation Test Data from Gas and Non-Darcy Flow Conditions." SPE Reservoir Evaluation & Engineering 2, no. 02 (1999): 116–24. http://dx.doi.org/10.2118/55970-pa.
Full textAbstract:
Summary Unlike liquid formation tests, in a gas formation test, both compressibility and viscosity vary with pressure, and non-Darcy flow is more likely. In this study, the gas formation rate analysis technique is developed to analyze gas pressure tests. We calculated gas pseudopotentials, utilized the geometric factor concept, and replaced Darcy's equation with Forchheimer's equation to study non-Darcy flow effects. The technique is applied to a field test, and the results are verified by history matching it with a three-dimensional near wellbore simulator. Introduction Wireline formation tests (WFT) can provide valuable, cost-effective information on undisturbed reservoir pressure (p*) vertical pressure gradients, formation fluid samples, formation fluid contacts, and an estimate of near-wellbore permeability. Various log responses (nuclear magnetic resonance, resistivity, acoustic) are calibrated with formation test permeabilities to obtain detailed permeability profiles.1,2 Permeability profiles are vital in identifying perforation and hydraulic fracturing intervals. Well-to-well correlation of permeability profiles can result in a lateral connectivity map, which can be used to calculate improved recovery efficiencies. A formation test is initiated when a probe from the tool is set against the formation. A measured volume of fluid is then withdrawn from the formation through the probe. The test continues with a buildup until the pressure stabilizes. Pressure in the tool is continuously monitored throughout the test. Historically, the cylindrical and the spherical flow analysis techniques are used to analyze wireline formation test data.3–5 An alternative to the conventional interpretation techniques has recently been developed by Kasap.6 In a recent publication, Kasap et al.7 compared conventional techniques with the formation rate analysis (FRA) technique and concluded that it was difficult to determine the spherical and the cylindrical flow periods for the conventional techniques that are applied to the buildup data only. The formation rate analysis technique combines the drawdown and the buildup data. Furthermore, early termination of the test would not hinder its analysis. Kasap et al.'s study was restricted to slightly compressible fluids, which is valid for testing liquid-saturated formations. For gases, however, both the compressibility and viscosity are strong functions of temperature and pressure and, thereby, variable during the test. Large gas compressibility and much smaller gas viscosity complicate the analysis. Gas flow because of low viscosity is more prone to non-Darcy flow effects. In this study, a new gas formation rate analysis (GFRA) technique is developed for gas formation testing. The technique calculates gas pseudopotentials and analyzes variation of pseudopotential versus formation rate during a formation test by utilizing the geometric factor concept. The technique is verified by history matching a field test with a three-dimensional (3D) near-wellbore simulation result. Analysis Technique The analysis technique is developed from the material balance considered for the volume of probe and flow lines. The mass rate of accumulation is equal to the difference between mass flow in from the formation and mass flow taken out by the pump. The mass flow rate in from the formation, pqf is defined; m f = ρ q f = M R T k G 0 r i L ∫ p ( t ) z μ d p , ( 1 ) where the density is substituted with an equation of state.8ri is the inner radius of the tool probe. G0 is the dimensionless geometric factor that accounts for flow geometry and is independent of flow rate, formation permeability, fluid viscosity, fluid type, and pressure drop in the system. A weak dependency to the wellbore radius can be ignored when the probe radius is about four times smaller than the wellbore radius. G0 also varies slightly with the probe radius. This variation, however, is not considered a drawback because the probe size of a formation test tool hardly changes. A one-time calculation of G0 is sufficient for a specific type of tool design. G0 is calculated from a numerical simulation of a specified formation test conducted with a specified tool. For the tests we analyzed, the probe size radius was 0.5 in., and the corresponding G0 was 4.27. We continue with the development of the analysis equations. The mass rate out from the tool is m d d = ρ q d d = p ( t ) M z R T q d d , ( 2 ) where ?qac is the pump drawdown rate. The mass rate of change or the accumulation rate, qdd in the tool is defined as m a c = ρ q a c = V s y s c t p ( t ) M z R T ∂ p ( t ) ∂ t , ( 3 ) where Vsys is the volume in the tool and ct is the compressibility of the fluid in the tool.
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Norouzi, M., and M. R. Rezaie. "Forced Convection Heat Transfer of a Giesekus Fluid in Circular Micro-Channels Subjected to a Constant Wall Temperature." Journal of Thermal Science and Engineering Applications 12, no. 1 (2019). http://dx.doi.org/10.1115/1.4044346.
Full textAbstract:
Abstract In this paper, an exact analytical solution for forced convective heat transfer of nonlinear viscoelastic fluid in isothermal circular micro-channel is presented. The nonlinear Giesekus constitutive equation is used to model the Giesekus fluid heat transfer in micro-channel with constant wall temperature, which is the main innovative aspect of the current study. This constitutive equation is a powerful tool and able to model the fractional viscometric functions, extensional viscosity, and elastic property. The solution of temperature profile and Nusselt number is obtained based on the Frobenius method. The effects of Weissenberg number, mobility factor, slip coefficient, and Navier index on temperature distribution, velocity profile, and Nusselt number are investigated in detail. The results show that the increases in both slip coefficient and Navier index cause the increases in slip velocity and maximum dimensionless temperature at the wall and the micro-channel center, respectively. Moreover, the Nusselt number has an upward trend with increases in slip coefficient and Navier index parameters. The results are indicated that the flow and temperature fields have a complex relation with mobility factor which controls the level of the nonlinearity of the Giesekus model. Additionally, three correlations for Nusselt number of Giesekus flow in micro-channel are presented.