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Journal articles on the topic 'Mixed Convective Flow'

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Published: 5 June 2025

Last updated: 16 July 2025

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CARRIÈRE, PHILIPPE, and PETER A. MONKEWITZ. "Convective versus absolute instability in mixed Rayleigh–Bénard–Poiseuille convection." Journal of Fluid Mechanics 384 (April 10, 1999): 243–62. http://dx.doi.org/10.1017/s0022112098004145.

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Transition from convective to absolute instability in Rayleigh–Bénard convection in the presence of a uni-directional Poiseuille flow is studied. The evaluation of the long-time behaviour of the Green function in the horizontal plane allows the determination of regions of convective and absolute instability in the Rayleigh–Reynolds number plane as a function of Prandtl number. It is found that the mode reaching zero group velocity at the convective–absolute transition always corresponds to transverse rolls, while the system remains convectively unstable with respect to pure streamwise (longitudinal) rolls for all non-zero Reynolds numbers. Finally, the roll pattern within the entire wave packet and in particular near its centre is elucidated and possible connections between experiments and our findings are discussed.

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Mohd Kanafiah, Siti Farah Haryatie, Abdul Rahman Mohd Kasim, Syazwani Mohd Zokri, and Hussien Ali Muhammed Al Sharifi. "Mixed convection flow of Brinkman fluid with convective boundary condition at lower stagnation point of horizontal circular cylinder." Data Analytics and Applied Mathematics (DAAM) 2, no. 1 (2021): 01–10. http://dx.doi.org/10.15282/daam.v2i1.6310.

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Convective heat transfer occurs when heat is transferred from one level to another upon the motion of fluid. Understanding on the characteristics of fluid flow is essential since it will produce the desired output of the product. therefore, this paper examines the mixed convection flow at lower stagnation point of horizontal circular cylinder on Brinkman fluid saturated in porous region with convective boundary condition. The influence of Brinkman, mixed convection and conjugate parameter on the flow field are studied. To reduce the complexity of the equations, a suitable similarity transformation is used. The numerical results of governing equations are obtained via bvp4c tools in Matlab. The effect of mixed convection, Brinkman and conjugate parameter on the temperature and velocity profile, skin friction coefficient together with Nusselt number are analysed and portrayed in graph and table form. The velocity profile increased with improving mixed convection and conjugate value, but decreased with increasing Brinkman factor. It is also discovered that the temperature decrease when the mixed convection parameter increase. This theoretical results will benefit the researchers, particularly in the manufacturing industry, in validating experimental study data.

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Aly, Abdelraheem M., Mitsuteru Asai, and Ali J. Chamkha. "Analysis of unsteady mixed convection in lid-driven cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics method." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 8 (2015): 2000–2021. http://dx.doi.org/10.1108/hff-10-2014-0305.

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Purpose – The purpose of this paper is to model mixed convection in a square cavity included circular cylinders motion using an incompressible smoothed particle hydrodynamics (ISPH) technique. Design/methodology/approach – The problem is solved numerically by using the ISPH method. Findings – The SPH tool shows robust performance to simulate the rigid body motion in the mixed convective flow with heat transfer, and it may apply easily to complicated problems in 2D and 3D problem without difficulties. Originality/value – The application of the SPH method to mixed convective flow with heat transfer and its potential application easily to complicated 3D problems is original.

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Chowdhury, Kakali. "MHD Mixed Convective Nanofluid Flow: Effect of Heat Source and Corrugated Boundary." Nanomedicine & Nanotechnology Open Access 8, no. 3 (2023): 1–14. http://dx.doi.org/10.23880/nnoa-16000255.

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The problem of MHD mixed convection is analyzed in a lid driven cavity with corrugated wavy bottom wall filled with Cu-H2 O nanofluid in presence of internal heat source. The top and right walls of the cavity are maintained with a uniform cold temperature whereas the left wall and bottom wavy wall are kept adiabatic. The top wall is moving with a constant velocity upon its lid and a rectangular heat source is placed horizontally inside the cavity. The physical problem is characterized by 2D governing partial differential equations along with proper boundary conditions and are discretized using Galerkin’s finite element formulation. The study is executed by analyzing different ranges of geometrical, physical and nondimensional parameters namely, wave number of wavy surface (0 ≤ ≤ λ 4) , the ratio of heat source height and cavity height 1 3 1 20 a l  ≤ ≤      volume fraction of nanoparticle (0 ≤ ≤ ϕ 0.09) Hartmann number (0 ≤ ≤ Ha 90) and Richardson number (0.1≤ ≤ Ri 10) . The results indicate that heat transfer rate decreases with the increasing value of heat source height and cavity height ratio a L       . It decreases about 9% and 25% with the increasing ratio of a L from 1 20 to 1 10 and 1 5 respectively. It also reveals that heat transfer rate increases with the increasing value of wave number of corrugated wall. At Ri=1 and Ha=0 heat transfer rate increases about 9% and 16% with the increasing value of λ from 0 to 2 and 4 respectively for nanofluid with 6% of nanoparticle. Keywords: MHD; Nanoparticle; Nanofluid

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Viorel Popa, Catalin, Cong Tam Nguyen, Stéphane Fohanno, and Guillaume Polidori. "Transient mixed convection flow of nanofluids in a vertical tube." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 2 (2014): 376–89. http://dx.doi.org/10.1108/hff-01-2012-0017.

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Purpose – In the present work, a theoretical model based on the full Navier-Stokes and energy equations for transient mixed convection in a vertical tube is extended to nanofluids with nanoparticle volume fraction up to 5 percent to ensure a Newtonian fluid behaviour. The paper aims to discuss these issues. Design/methodology/approach – The nanofluids considered, alumina/water and CuO/water, flow inside a vertical tube of circular cross-section, which is subjected to convective heat exchange at the outer surface. The transient regime is caused by a sudden change of nanofluid temperature at the tube inlet. The range of the Richardson number (1.6=Ri=2.5) investigated in this study corresponds to classic cases of mixed convection flow. Findings – Results have shown a significant reduction in the size of the recirculation zone near the wall when the particle volume fraction increases. This may be attributed to the viscosity increase with the volume fraction. Moreover, the flow structure clearly changes when the convective heat transfer coefficient is modified. A decrease of the wall temperature along the tube was found when increasing the convective heat transfer coefficient imposed at the tube external surface. Research limitations/implications – The problem formulation in 2D axisymmetric geometry includes the continuity, the Navier-Stokes and energy equations and is based on the stream function and vorticity; the numerical solution of equations is carried out using a finite difference method. Practical implications – From an economic point of view, this research paper is innovative in the sense that it considers nanofluids as a new and more efficient way to transfer heat. This paper could find applications for heat exchange purposes of compact systems with high thermal loads. Originality/value – Across the world, a still growing number of research teams are investigating nanofluids and their properties. Investigations concern several aspects such as the preparation of the nanofluids, as well as the applications of these nanofluids for convective heat transfer purposes. The dynamical study will consist in the instantaneous and spatial characterization of the dynamic flow field for different nanoparticle volume fractions.

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Rahman, M. M., M. M. Billah, and M. A. Alim. "Effect of Reynolds and Prandtl Numbers on Mixed Convection in an Obstructed Vented Cavity." Journal of Scientific Research 3, no. 2 (2011): 271–81. http://dx.doi.org/10.3329/jsr.v3i2.4344.

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A numerical investigation is conducted to analyze the steady flow and thermal fields as well as heat transfer characteristics in a vented square cavity with a built-in heat conducting horizontal solid circular obstruction. Hydrodynamic behavior, thermal characteristics and heat transfer results are obtained by solving the couple of Navier-Stokes and energy equations by using a weighted residuals Finite element method. The computation was made for different Reynolds number, Prandtl number ranging from 50 to 200 and from 0.71 to 7.1 at the three different convective regimes. Three different regimes are observed with increasing Ri: forced convection (with negligible free convection), mixed convection (comparable free and forced convection) and free convection dominated region (with higher free convection). The results are presented to show the effects of the Reynolds number, Prandtl number on flow pattern, thermal field and heat transfer characteristics at the three convective regimes. It is found that the flow and thermal field strongly depend on the Reynolds number, Prandtl number as well as Richardson number. As the Reynolds number and Prandtl number increase, the heat transfer rate increases but average fluid temperature in the cavity and temperature at the cylinder center decrease at the three convective regimes.Keywords: Mixed convection; Finite element method; Obstructed vented cavity; Prandtl number.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i2.4344 J. Sci. Res. 3 (2), 271-281 (2011)

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Aman, Fazlina, and Anuar Ishak. "Mixed Convection Boundary Layer Flow towards a Vertical Plate with a Convective Surface Boundary Condition." Mathematical Problems in Engineering 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/453457.

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The steady mixed convection flow towards an impermeable vertical plate with a convective surface boundary condition is investigated. The governing partial differential equations are first reduced to ordinary differential equations using a similarity transformation, before being solved numerically. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that dual solutions exist for the opposing flow, whereas for the assisting flow, the solution is unique. Moreover, increasing the convective parameter is to increase the skin friction coefficient and the heat transfer rate at the surface.

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Waqas, Muhammad, Muhammad Mudassar Gulzar, Zeeshan Asghar, Z. Ali, Waqar Azeem Khan, and Abdul Sattar Dogonchi. "A theoretical investigation for mixed convection impact in non-Newtonian nanofluid stratified flow subjected to magnetic field." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 8 (2019): 2948–63. http://dx.doi.org/10.1108/hff-12-2018-0769.

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Purpose The purpose of this study is to elaborate mixed convection impact in stratified nanofluid flow by convectively heated moving surface. Rheological relations of second-grade fluid are used for formulation. Magnetic field, heat absorption/generation and convective conditions are considered for modeling. Design/methodology/approach Convergent solutions are achieved using homotopy procedure. Findings The authors found opposing behavior for radiation and thermal stratification variables against thermal field. Originality/value No such analysis has yet been reported.

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Hayat, T., F. Haider, and A. Alsaedi. "Darcy-Forchheimer flow with nonlinear mixed convection." Applied Mathematics and Mechanics 41, no. 11 (2020): 1685–96. http://dx.doi.org/10.1007/s10483-020-2680-8.

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Abstract An analysis of the mixed convective flow of viscous fluids induced by a nonlinear inclined stretching surface is addressed. Heat and mass transfer phenomena are analyzed with additional effects of heat generation/absorption and activation energy, respectively. The nonlinear Darcy-Forchheimer relation is deliberated. The dimensionless problem is obtained through appropriate transformations. Convergent series solutions are obtained by utilizing an optimal homotopic analysis method (OHAM). Graphs depicting the consequence of influential variables on physical quantities are presented. Enhancement in the velocity is observed through the local mixed convection parameter while an opposite trend of the concentration field is noted for the chemical reaction rate parameter.

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Norhafizah Md, Sarif, Sallhe Mohd Zuki, and Roslinda Nazar. "Mixed convection over a horizontal circular cylinder embedded in porous medium immersed in a nanofluid with convective boundary conditions at lower stagnation point: A numerical solution." MATEC Web of Conferences 189 (2018): 02004. http://dx.doi.org/10.1051/matecconf/201818902004.

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This study aims to examine the effect of governing parameters on the flow and heat transfer of the steady mixed convection flow embedded in porous medium with convective boundary conditions. The resulting system of nonlinear partial differential equations is solved numerically. The special case at the lower stagnation point of the cylinder is observed and the case where bottom surface of the cylinder is heated by convection from hot fluids is considered. Numerical solutions are obtained for the velocity, temperature and nanoparticle volume fraction profiles for two values of governing parameters namely convective parameter γ and Lewis number Le. It is found that as the convective parameter γ increases, velocity profile, temperature and nanoparticle volume fraction profile also increases.

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Chamkha, Ali J., Hossam A. Nabwey, Z. M. A. Abdelrahman, and A. M. Rashad. "Mixed Bioconvective Flow Over a Wedge in Porous Media Drenched with a Nanofluid." Journal of Nanofluids 8, no. 8 (2019): 1692–703. http://dx.doi.org/10.1166/jon.2019.1728.

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A mathematical model is accentuated the mixed bioconvective flow on a vertical wedge in a Darcy porous medium filled with a nanofluid containing both nanoparticles and gyrotactic microorganisms. Thermophoresis and Brownian motion impacts are addressed to consolidate energy and concentration equations with passivelycontrolled boundary conditions. A mixed convective parameter for the whole regime of the mixed convective is appointed. The system of governing partial differential equations is converted into a non-similar set, which are then solved by an implicit finite difference method. By taking the impacts of the varying pertinent parameters, namely, the bioconvection nanofluids and wedge angle parameters in the entire mixed convection regime, the numerical results are analyzed graphically for the dimensionless the velocity, temperature, nanoparticle volume fraction and the density motile microorganisms profiles as well as the local Nusselt and motile microorganism numbers.

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Chamkha, Ali J., Hossam A. Nabwey, Z. M. A. Abdelrahman, and A. M. Rashad. "Mixed Bioconvective Flow Over a Wedge in Porous Media Drenched with a Nanofluid." Journal of Nanofluids 9, no. 1 (2020): 24–35. http://dx.doi.org/10.1166/jon.2020.1728.

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Jerng, Dong W., and Neil E. Todreas. "Mixed convective flow penetration in vertical channels." Nuclear Engineering and Design 146, no. 1-3 (1994): 391–408. http://dx.doi.org/10.1016/0029-5493(94)90345-x.

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Forth, S. A., and A. A. Wheeler. "Coupled convective and morphological instability in a simple model of the solidification of a binary alloy, including a shear flow." Journal of Fluid Mechanics 236 (March 1992): 61–94. http://dx.doi.org/10.1017/s0022112092001344.

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In this paper we provide a detailed description of the interaction of solutal convection and morphological instability in the presence of a model boundary-layer flow. We present a detailed investigation of the structure of the marginal surfaces in Rayleigh-number, Sekerka-number, Reynolds-number space associated with a linear stability analysis. We give mathematical arguments and physical mechanisms to explain the results and present a coherent description of this complicated situation. We identify two new modes, one convective and one morphological. We show that the oscillatory so-called ‘mixed’ modes that result from the coupling of morphological and convective modes play a central role in the unfolding of the solution structure by the shear flow. This flow has the effect of decoupling the convective and morphological modes.

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Suh, K. Y., N. E. Todreas, and W. M. Rohsenow. "Mixed Convective Low Flow Pressure Drop in Vertical Rod Assemblies: I—Predictive Model and Design Correlation." Journal of Heat Transfer 111, no. 4 (1989): 956–65. http://dx.doi.org/10.1115/1.3250811.

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A predictive theory has been developed for rod bundle frictional pressure drop characteristics under laminar and transitional mixed convection conditions on the basis of the intraassembly and intrasubchannel flow redistributions due to buoyancy for a wide spectrum of radial power profiles and for the geometric arrangements of practical design interest. Both the individual subchannel correlations and overall bundle design correlations have been formulated as multipliers applied to the isothermal friction factors at the same Reynolds numbers. Standard and modified subchannel friction factors have been obtained to be used with spatial-average and bulk-mean densities, respectively. A correlating procedure has been proposed to assess the effects of interacting subchannel flows, developing mixed convective flow, wire wrapping, power skew, rod number, and transition from laminar flow. In contrast to forced convection behavior, a strong rod number effect is present under mixed convection conditions in bundle geometries. The results of this study are of design importance in natural circulation conditions because the mixed convection frictional pressure losses exceed the corresponding isothermal values at the same Reynolds numbers.

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Rashad, Ahmed M., Waqar A. Khan, Saber M. M. EL-Kabeir, and Amal M. A. EL-Hakiem. "Mixed Convective Flow of Micropolar Nanofluid across a Horizontal Cylinder in Saturated Porous Medium." Applied Sciences 9, no. 23 (2019): 5241. http://dx.doi.org/10.3390/app9235241.

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The micropolar nanofluids are the potential liquids that enhance the thermophysical features and ability of heat transportation instead of base liquids. Alumina and Titania nanoparticles are mixed in a micropolar fluid. The impact of convective boundary condition is also examined with assisting and opposing flows of both nanofluids. The main objective of this study is to investigate mixed convective flow and heat transfer of micropolar nanofluids across a cylinder in a saturated porous medium. Non-similar variables are used to make the governing equations dimensionless. The local similar and non-similar solutions are obtained by using the Runge-Kutta-Fehlberg method of seventh order. The impacts of various embedded variables on the flow and heat transfer of micropolar nanofluids are investigated and interpreted graphically. It is demonstrated that the skin friction and heat transfer rates depend on solid volume fraction of nanoparticles, Biot number, mixed convection, and material parameters.

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Devi, Santosh, and Mukesh Kumar Sharma. "MHD Boundary Layer Flow over a Cone Embedded in Porous Media with Joule Heating and Viscous Dissipation." Defect and Diffusion Forum 401 (May 2020): 131–39. http://dx.doi.org/10.4028/www.scientific.net/ddf.401.131.

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Aim of the paper is to study the Magnetohydrodynamic boundary layer flow over a cone under the effect of joule heating and viscous dissipation. The surface of the cone is cooled and heated by the flowing fluid having constant temperature along with variable heat transfer coefficient.The surface of the cone is subjected under the convective heat flux. The governing equation for MHD boundary layer flow are non-linear partial differential equations, are transformed into ordinary differential equations using similarity techniques. The reduced ordinary coupled equations are solved with Runge-Kutta’s fourth order method followed by shooting techniques. The effects on flow and heat convection of various physical parameters pertinent to the modeled problem are computed and analyzed and shown through graphs. Keywords: Mixed convection, cone, Boundary layer, Joule Heating, Convective boundary condition.

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Vreugdenhil, Catherine A., and Bishakhdatta Gayen. "Ocean Convection." Fluids 6, no. 10 (2021): 360. http://dx.doi.org/10.3390/fluids6100360.

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Ocean convection is a key mechanism that regulates heat uptake, water-mass transformation, CO2 exchange, and nutrient transport with crucial implications for ocean dynamics and climate change. Both cooling to the atmosphere and salinification, from evaporation or sea-ice formation, cause surface waters to become dense and down-well as turbulent convective plumes. The upper mixed layer in the ocean is significantly deepened and sustained by convection. In the tropics and subtropics, night-time cooling is a main driver of mixed layer convection, while in the mid- and high-latitude regions, winter cooling is key to mixed layer convection. Additionally, at higher latitudes, and particularly in the sub-polar North Atlantic Ocean, the extensive surface heat loss during winter drives open-ocean convection that can reach thousands of meters in depth. On the Antarctic continental shelf, polynya convection regulates the formation of dense bottom slope currents. These strong convection events help to drive the immense water-mass transport of the globally-spanning meridional overturning circulation (MOC). However, convection is often highly localised in time and space, making it extremely difficult to accurately measure in field observations. Ocean models such as global circulation models (GCMs) are unable to resolve convection and turbulence and, instead, rely on simple convective parameterizations that result in a poor representation of convective processes and their impact on ocean circulation, air–sea exchange, and ocean biology. In the past few decades there has been markedly more observations, advancements in high-resolution numerical simulations, continued innovation in laboratory experiments and improvement of theory for ocean convection. The impacts of anthropogenic climate change on ocean convection are beginning to be observed, but key questions remain regarding future climate scenarios. Here, we review the current knowledge and future direction of ocean convection arising from sea–surface interactions, with a focus on mixed layer, open-ocean, and polynya convection.

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Hayat, T., M. Waqas, S. A. Shehzad, and A. Alsaedi. "Mixed Convection Radiative Flow of Maxwell Fluid Near a Stagnation Point with Convective Condition." Journal of Mechanics 29, no. 3 (2013): 403–9. http://dx.doi.org/10.1017/jmech.2013.6.

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AbstractEffects of thermal radiation in mixed convection stagnation point flow over a moving surface subject to convective boundary conditions is addressed. Mathematical modeling is based upon constitutive equations of an incompressible Maxwell fluid. Nonlinear analysis is presented through implementation of homotopy analysis method. Numerical values of Local Nusselt number is computed and analyzed.

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Farouk, B. "Mixed Convective Flows Around a Slowly Rotating Isothermal Sphere." Journal of Heat Transfer 107, no. 2 (1985): 431–38. http://dx.doi.org/10.1115/1.3247433.

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The mixed convective flows generated by a heated rotating sphere have been investigated theoretically. The solutions are obtained by considering the full Navier-Stokes and energy equations along with the Boussinesq approximation. The governing equations are expressed in the R-θ-φ coordinates and due to the nature of the flow field generated, all three velocity components appear in the formulation. Due to the symmetry of the problem studied, ∂ξ/∂φ = 0, where ξ is any dependent variable considered. The R and θ momentum equations are expressed in the stream function-vorticity formulation. The resulting four coupled elliptic equations (for stream function, vorticity, vφ, and temperature) are solved numerically. Results have been obtained over a large range of Grashof and Reynolds (based on the rotational velocity of the sphere surface) numbers. The study reveals interesting flow patterns for the mixed convective problems. The gravitationally induced free convection is significant for the slowly rotating sphere where the Grashof number is of the order of or more than the square of the Reynolds number. The results are compared with previously published experimental observations and theoretical predictions based on the boundary layer theory.

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A. Mahdy, Taghreed H. Al-Arabi, Ahmed M. Rashad, and Wafaa Saad. "Time-Dependent Mixed Convection-Radiation Interaction Flow And Heat Transmission Of Hybrid Nanoliquid Along An Elongated Sheet." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 94, no. 2 (2022): 110–22. http://dx.doi.org/10.37934/arfmts.94.2.110122.

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Actually the article spotlights an aspects of thermal radiative on free-forced convective of a hybrid nanomaterial flow over a vertical elongated plate. Viscous dissipation with convective condition is exhibited. The primary PDEs governing the case paradigm is converted into a non-dimensional system due to feasible transformations. The acquired mathematical differential equations is solved using a the very vigorous computer algebra software MATLAB code. Graphs were presented to analyze the influence of multiple physical impacts of involving factors on the flow fluctuations of both hybrid nanoliquid velocity and temperature. Through these factors, both of Nusselt number and drag factor are manifested and argued amply. Comparison with earlier published data for steady and unsteady states flow is provided and it noticed to be in completely agreement. The outcomes point out that Nusselt number is an ascending function of unsteadiness and mixed convection factors.

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Hayat, T., S. A. Shehzad, A. Alsaedi, and M. S. Alhothuali. "Mixed Convection Stagnation Point Flow of Casson Fluid with Convective Boundary Conditions." Chinese Physics Letters 29, no. 11 (2012): 114704. http://dx.doi.org/10.1088/0256-307x/29/11/114704.

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Umavathi, Jawali C., Hafiz Muhammad Ali, and Sapnali Limbaraj Patil. "Triple diffusive mixed convection flow in a duct using convective boundary conditions." Mathematical Methods in the Applied Sciences 43, no. 15 (2020): 9223–44. http://dx.doi.org/10.1002/mma.6617.

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Hussain, Majid, Akhtar Ali, Shao-Wen Yao, Abdul Ghaffar, and Mustafa Inc. "Numerical investigation of ohmically dissipated mixed convective flow." Case Studies in Thermal Engineering 31 (March 2022): 101809. http://dx.doi.org/10.1016/j.csite.2022.101809.

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Patil, Prabhugouda Mallanagouda, Shashikant A., and Ebrahim Momoniat. "Transport phenomena in MHD mixed convective nanofluid flow." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 2 (2019): 769–91. http://dx.doi.org/10.1108/hff-04-2019-0365.

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Purpose This study aims to investigate the unsteady magnetohydrodynamic mixed convective nanofluid flow by using Buongiorno two-phase model to achieve an appropriate mechanism to improve the efficiency of solar energy systems by mitigating the energy losses. Design/methodology/approach The transport phenomena occurring in this physical problem are modelled using nonlinear partial differential equations and are non-dimensionalised by using non-similar transformations. The quasilinearisation technique is used to solve the resulting system with the help of a finite difference scheme. Findings The study reveals that the effect of the applied transverse magnetic parameter is to increase the temperature profile and to reduce the wall heat transfer rate. The Brownian diffusion and thermophoresis parameters that characterise the nanofluids contribute to the reduction in wall heat transfer rate. The presence of nanoparticles in the fluid gives rise to critical values for the thermophoresis parameter describing the behaviour of the wall heat and mass transfer rates. Wall heating and cooling are analysed by considering the percentage increase or percentage decrease in the heat and mass transfer rates in the presence of nanoparticles in the fluid. Research limitations/implications The investigation on wall cooling/heating leads to the analysis of control parameters applicable to the industrial design of thermal systems for energy storage, energy harvesting and cooling applications. Practical implications The analysis of the control parameters is of practical value to the solar industry. Social implications In countries, such as South Africa, daily power cuts are a reality. Any research into improving the quality of energy obtained from alternate sources is a national necessity. Originality/value From the literature survey in the present study, it is found that no similar work has been reported in the open literature that analyses the time-dependent mixed convection flow along the exponentially stretching surface in the presence of the effects of a magnetic field, nanoparticles and non-similar solutions.

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Kaladhar, Kolla, and Oluwole Daniel Makinde. "Thermal Radiation, Joule Heating and Hall Effects on Mixed Convective Navier Slip Flow in a Channel with Convective Heating." Diffusion Foundations 11 (August 2017): 162–81. http://dx.doi.org/10.4028/www.scientific.net/df.11.162.

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This paper examines the Navier slip, incompressible, laminar mixed convection flow between vertical plates with Joule heating and Hall effects. This research includes the thermal radiation with convective boundary conditions also. The resulting equations and boundary conditions are reduced into non dimensional form using appropriate transformations and solved numerically using shooting method coupled with fourth order Runge-Kutta-Fehlberg integration scheme.The influence of emerging parameters on fluid flow quantities have been presented graphically. Also, the nature of physical quantities is shown in tabular form.

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Dey, Debasish. "Mixed Convective MHD Micro-Polar Fluid Flow in a Porous Medium with Radiation Absorption." International Journal of Mathematical, Engineering and Management Sciences 4, no. 2 (2019): 387–99. http://dx.doi.org/10.33889/ijmems.2019.4.2-031.

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An unsteady mixed convective flow of micro-polar fluid in a porous medium has been considered in presence of transverse magnetic field, Dufour effects and radiation. Effects of radiation absorption and heat source/sink are taken into account. The Buoyancy force leads to free convection and oscillatory free stream velocity is responsible for forced convection. Partial differential equations governed by conservation principles of mass, momentum and energy are solved analytically using perturbation scheme. Effects of various parameters on the governing fluid motion are shown graphically and numerically in tabular form.

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Suslov, Sergey A. "Convective and absolute instabilities in non-Boussinesq mixed convection." Theoretical and Computational Fluid Dynamics 21, no. 4 (2007): 271–90. http://dx.doi.org/10.1007/s00162-007-0049-y.

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Bouazzaoui, Khaled, Mohammed Aiboudi, and Sameh Elsayed Ahmed. "Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow." International Journal of Differential Equations 2022 (January 10, 2022): 1–10. http://dx.doi.org/10.1155/2022/7331913.

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In this paper, we will study the existence of strong solutions for a nonlinear system of partial differential equations arising in convective flow, modeling a phenomenon of mixed convection created by a heated and diving plate in a porous medium saturated with a fluid. The main tools are Schäfer’s fixed-point theorem, the Fredholm alternative, and some theorems on second-order elliptic operators.

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Yahiaoui, Kamel, Driss Nehari, and Belkacem Draoui. "The Investigation of the Mixed Convection from a Confined Rotating Circular Cylinder." Periodica Polytechnica Mechanical Engineering 61, no. 3 (2017): 161. http://dx.doi.org/10.3311/ppme.9338.

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In this paper, a numerical study on the two-dimensional laminar mixed convective flow and heat transfer from an rotating circular horizontal and isothermal cylinder confined in a horizontal channel. The blockage ratio and the Prandtl number are fixed at 0.05 and 0.7 respectively. The continuity, momentum and energy equations are solved via the finite-volume method. Our results are in very good agreement with those resulting from preceding studies to Ri=0 and a=0, which makes it possible to validate on important extension of present work. The mixed convective flow and heat transfer is simulated by the Reynolds number is studied in the range 1 <Re <40, the Richardson number (Ri) demonstrating the influence of thermal buoyancy ranges from 0 to 1 and for rotational rate from α=0 to α=4. Major emphasis is given to the effect of rotating a circular cylinder on the mixed convection and also on the measurements of the local and average Nusselt numbers are also obtained. Furthermore, the representative streamlines and isotherm patterns are presented and discussed.

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Sampath Kumar, Poojari Borappa, Basavarajappa Mahanthesh, Bijjanal Jayanna Gireesha, and S. Manjunatha. "Mixed Convection 3D Radiating Flow and Mass Transfer of Eyring-Powell Nanofluid with Convective Boundary Condition." Defect and Diffusion Forum 388 (October 2018): 158–70. http://dx.doi.org/10.4028/www.scientific.net/ddf.388.158.

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Three-dimensional mixed convection flow, heat and mass transfer of Eyring-powell fluid over a convectively heated stretched sheet is inspected in this paper. The encouragement of Brownian motion, Thermophoresis and thermal radiations are accounted. Appropriate transformations are used to reduce the principal PDE’s into set of coupled highly non-linear ODE’s which are then solved numerically using RKF fourth-fifth order method. The consequence of several parameters on flow, heat and mass transfer characteristics are deliberated with the help of graphs and tables. It is observed that, the temperature and concentration profiles diminish for higher values mixed convection parameter.

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Tewari, S. S., and Y. Jaluria. "Mixed Convection Heat Transfer From Thermal Sources Mounted on Horizontal and Vertical Surfaces." Journal of Heat Transfer 112, no. 4 (1990): 975–87. http://dx.doi.org/10.1115/1.2910509.

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An experimental study is carried out on the fundamental aspects of the conjugate, mixed convective heat transfer from two finite width heat sources, which are of negligible thickness, have a uniform heat flux input at the surface, and are located on a flat plate in the horizontal or the vertical orientation. The heat sources are wide in the transverse direction and, therefore, a two-dimensional flow circumstance is simulated. The mixed convection parameter is varied over a fairly wide range to include the buoyancy-dominated and the mixed convection regimes. The circumstances of pure natural convection are also investigated. The convective mechanisms have been studied in detail by measuring the surface temperatures and determining the heat transfer coefficients for the two heated strips, which represent isolated thermal sources. Experimental results indicate that a stronger upstream heat source causes an increase in the surface temperature of a relatively weaker heat source, located downstream, by reducing its convective heat transfer coefficient. The influence of the upstream source is found to be strongly dependent on the surface orientation, especially in the pure natural convection and the buoyancy dominated regimes. The two heat sources are found to be essentially independent of each other, in terms of thermal effects, at a separation distance of more than about three strip widths for both the orientations. The results obtained are relevant to many engineering applications, such as the cooling of electronic systems, positioning of heating elements in furnaces, and safety considerations in enclosure fires.

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Hussain, Azad, Aysha Rehman, Sohail Nadeem, et al. "A Combined Convection Carreau–Yasuda Nanofluid Model over a Convective Heated Surface near a Stagnation Point: A Numerical Study." Mathematical Problems in Engineering 2021 (April 3, 2021): 1–14. http://dx.doi.org/10.1155/2021/6665743.

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The focus of this manuscript is on two-dimensional mixed convection non-Newtonian nanofluid flow near stagnation point over a stretched surface with convectively heated boundary conditions. The modeled equation representing nonlinear flow is transformed into a system of ordinary differential equations by implementing appropriate similarity transformations. The generated structure is numerically solved by applying the bvp4c method. Consequences of various involved parameters, e.g., stretching parameter, mixed convection parameter, thermophoresis parameter, Brownian movement parameter, Lewis number, Weissenberg number, Prandtl number, Biot number, buoyancy ratio parameter, mass and heat transport rates on temperature and velocity, the stretched surface, and nanoparticle concentration patterns are analyzed. Outcomes are shown graphically and displayed in tables. Velocity fluctuations are responded to by growing parameters of mixed convection and Weissenberg number. Concentration and thermal fields are also discovered for the Prandtl number. There are also flow line diagrams to analyze the behavior.

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Yu, D., T. A. Ameel, R. O. Warrington, and R. F. Barron. "Conjugate Heat Transfer With Buoyancy Effects From Micro-Chip Sized Repeated Heaters." Journal of Electronic Packaging 119, no. 4 (1997): 275–80. http://dx.doi.org/10.1115/1.2792249.

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Laminar mixed convection heat transfer across five in-line microchipsized heaters, surface mounted on printed circuit board (PCB), was investigated by the weighted residual finite element method. The effects of axial heat conduction within the PCB for both mixed convection and pure forced convection are reported. The flow regime considered was 200 ≤ Re ≤ 800 and 0 ≤ Gr ≤ 58,000. Internal heat generation was included in the microchip-sized blocks in order to accurately model the thermal response to predict the maximum temperature rise. On the outer PCB walls, convective heat transfer conditions were given. Thermophysical and transport properties based on materials used in the electronics industry, including orthotropic thermal conductivity in PCB, were used. The flow and solid domains were solved simultaneously. A sensitivity study of PCB heat transfer coefficients, isotropic thermal conductivity, thermal conductivity variations, and spacing effects was performed. The mixed convection transient heating process was compared with the steady-state formulation to estimate the influence of flow oscillation in heat transfer. It was found that the maximum temperature rise in the microchips predicted by pure forced convection was, at most, 10 percent higher than that predicted by mixed convection. The difference in maximum temperature between the trailing and leading chips in the array was 30 percent.

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Mahmoud, A. Mashkour. "Analysis of transient mixed convection in a horizontal channel partially heated from below." Eastern-European Journal of Enterprise Technologies 4, no. 8 (112) (2021): 16–22. https://doi.org/10.15587/1729-4061.2021.238649.

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The heat convection phenomenon has been investigated numerically (mathematically) for a channel located horizontally and partially heated at a uniform heat flux with forced and free heat convection. The investigated horizontal channel with a fluid inlet and the enclosure was exposed to the heat source from the bottom while the channel upper side was kept with a constant temperature equal to fluid outlet temperature. Transient, laminar, incompressible and mixed convective flow is assumed within the channel. Therefore, the flow field is estimated using Navier Stokes equations, which involves the Boussinesq approximation. While the temperature field is calculated using the standard energy model, where, Re, Pr, Ri are Reynolds number, Prandtl number, and Richardson number, respectively. Reynolds number (Re) was changed during the test from 1 to 50 (1, 10, 25, and 50) for each case study, Richardson (Ri) number was changed during the test from 1 to 25 (1, 5, 10, 15, 20, and, 25). The average Nusselt number (Nu<sub>av</sub>) increases exponentially with the Reynold number for each Richardson number and the local Nusselt number (Nu<sub>I</sub>) rises in the heating point. Then gradually stabilized until reaching the endpoint of the channel while the local Nusselt number increases with a decrease in the Reynolds number over there. In addition, the streamlines and isotherms patterns in case of the very low value of the Reynolds number indicate very low convective heat transfer with all values of Richardson number. Furthermore, near the heat source, the fluid flow rate rise increases the convection heat transfer that clarified the Nusselt number behavior with Reynolds number indicating that maximum Nu No. are 6, 12, 27 and 31 for Re No. 1, 10, 25 and 50, respectively

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Celli, Michele, Leonardo S. de B. Alves, and Antonio Barletta. "Nonlinear stability analysis of Darcy’s flow with viscous heating." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2189 (2016): 20160036. http://dx.doi.org/10.1098/rspa.2016.0036.

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The nonlinear stability of a rectangular porous channel saturated by a fluid is here investigated. The aspect ratio of the channel is assumed to be variable. The channel walls are considered impermeable and adiabatic except for the horizontal top which is assumed to be isothermal. The viscous dissipation is acting inside the channel as internal heat generator. A basic throughflow is imposed, and the nonlinear convective stability is investigated by means of the generalized integral transform technique. The neutral stability curve is compared with the one obtained by the linear stability analysis already present in the literature. The growth rate analysis of different unstable modes is performed. The Nusselt number is investigated for several supercritical configurations in order to better understand how the system behaves when conditions far away from neutral stability are considered. The patterns of the neutrally stable convective cells are also reported. Nonlinear simulations support the results obtained by means of the linear stability analysis, confirming that viscous dissipation alone is indeed capable of inducing mixed convection. Low Gebhart or high Péclet numbers lead to a transient overheating of the originally motionless fluid before it settles in its convective steady state.

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RamReddy, Ch, P. V. S. N. Murthy, Ali J. Chamkha, and A. M. Rashad. "Soret effect on mixed convection flow in a nanofluid under convective boundary condition." International Journal of Heat and Mass Transfer 64 (September 2013): 384–92. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.04.032.

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Acharya, Nilankush, Raju Bag, and Prabir K. Kundu. "On the mixed convective carbon nanotube flow over a convectively heated curved surface." Heat Transfer 49, no. 4 (2020): 1713–35. http://dx.doi.org/10.1002/htj.21687.

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Chalavadi Sulochana, Sultana Begum, and Tirumala Prasanna Kumar. "MHD Mixed Convective Non-Newtonian Stagnation Point Flow Over an Inclined Stretching Sheet: Numerical Simulation." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 102, no. 1 (2023): 73–84. http://dx.doi.org/10.37934/arfmts.102.1.7384.

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This paper includes numerical simulation upon MHD mixed convective heat transfer properties of stagnation point flow across an angled stretched sheet. Boundary value problem is solved using similarity transformation approach with shooting technique. The impact of different corporeal constraints like mixed convection parameter, thermal radiation parameter, chemical reaction parameter, Brownian motion and thermophoresis, Casson parameter upon velocity and temp profile as well as skin-friction coefficient , Nusselt number, Sherwood number on velocity, temp concentration profile are shown graphically. Casson parameter increases velocity and diminishes temperature profile. Chemical reaction term decreases Sherwood number and increases concentration profile.

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Hdhiri, Najib, and Brahim Ben Beya. "Numerical study of laminar mixed convection flow in a lid-driven square cavity filled with porous media." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 4 (2018): 857–77. http://dx.doi.org/10.1108/hff-04-2016-0146.

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Purpose The purpose of this study is to produce a numerical model capable of predicting the mixed convection flows in a rectangular cavity filled with a porous medium and to analyze the effects of several parameters on convective flow in porous media in a differentially heated enclosure. Design/methodology/approach The authors used the finite volume method. Findings The authors predicted and analyzed the effects of Richardson number, Darcy number, porosity values and Prandtl number in heat transfer and fluid flow. On other hand, the porosity and Richardson number values lead to reducing the heat transfer rate of mixed convection flow in a porous medium. Originality/value A comparison between Darcy–Brinkman–Forchheimer model and Darcy–Brinkman model is discussed and analyzed. The authors finally conclude that the Darcy–Brinkman model overestimates the heat transfer rate.

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Mureithi, Eunice W., and James P. Denier. "Absolute-convective instability of mixed forced-free convection boundary layers." Fluid Dynamics Research 42, no. 5 (2010): 055506. http://dx.doi.org/10.1088/0169-5983/42/5/055506.

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Choudhury, Rita, and Sajal Kumar Das. "Mixed Convective Visco-Elastic MHD Flow with Ohmic Heating." International Journal of Computer Applications 68, no. 10 (2013): 7–13. http://dx.doi.org/10.5120/11613-7004.

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Hayat, Tasawar, Ikram Ullah, Ahmed Al-Saedi, and Bashir Ahmad. "Mixed convective radiative flow of vicoelastic liquid subject to space dependent internal heat source and chemical reaction." Thermal Science 23, no. 6 Part B (2019): 3843–53. http://dx.doi.org/10.2298/tsci171229287h.

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Present study addresses Soret and Dufour effects in mixed convection MHD flow of viscoelastic liquid with chemical reaction. Flow induced by an exponential stretching sheet is addressed in the presence of magnetic field. Energy expression is modelled by exponential space dependent internal heat source, thermal radiation, and convective condition. Relevant problems are modelled by employing boundary-layer concept. The partial differential systems are reduced to ordinary differential systems, and problem is solved by homotopic technique. Physical insight of results is arranged by graphs and tables.

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Chen, Shu-Hua, and Yuh-Lang Lin. "Effects of Moist Froude Number and CAPE on a Conditionally Unstable Flow over a Mesoscale Mountain Ridge." Journal of the Atmospheric Sciences 62, no. 2 (2005): 331–50. http://dx.doi.org/10.1175/jas-3380.1.

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Abstract In this study, idealized simulations are performed for a conditionally unstable flow over a two-dimensional mountain ridge in order to investigate the propagation and types of cloud precipitation systems controlled by the unsaturated moist Froude number (Fw) and the convective available potential energy (CAPE). A two-dimensional moist flow regime diagram, based on Fw and CAPE, is proposed for a conditionally unstable flow passing over a two-dimensional mesoscale mountain ridge. The characteristics of these flow regimes are 1) regime I: flow with an upstream-propagating convective system and an early, slowly moving convective system over the mountain; 2) regime II: flow with a long-lasting orographic convective system over the mountain peak, upslope, or lee slope; 3) regime III: flow with an orographic convective or mixed convective and stratiform precipitation system over the mountain and a downstream-propagating convective system; and 4) regime IV: flow with an orographic stratiform precipitation system over the mountain and possibly a downstream-propagating cloud system. Note that the fourth regime was not included in the flow regimes proposed by Chu and Lin and Chen and Lin. The propagation of the convective systems is explained by the orographic blocking and density current forcing associated with the cold-air outflow produced by evaporative cooling acting against the basic flow, which then determines the propagation and cloud types of the simulated precipitation systems.

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Chaturvedi, S. K., T. O. Mohieldin, and G. C. Huang. "Mixed Laminar Convection in Trombe Wall Channels." Journal of Solar Energy Engineering 110, no. 1 (1988): 31–37. http://dx.doi.org/10.1115/1.3268234.

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The two-dimensional, steady, combined forced and natural convection in a vertical channel is investigated for the laminar regime. To simulate the Trombe wall channel geometry properly, horizontal inlet and exit segments have been added to the vertical channel. The vertical walls of the channel are maintained at constant but different temperatures while the horizontal walls are insulated. A finite difference method using up-wind differencing for the nonlinear convective terms, and central differencing for the second order derivatives, is employed to solve the governing differential equations for the mass, momentum, and energy balances. The solution is obtained for stream function, vorticity, and temperature as the dependent variables by an iterative technique known as successive substitution with overrelaxation. The flow and temperature patterns in the channel are obtained for Reynolds numbers and Grashof numbers ranging from 25 to 100 and 10,000 to 1,000,000, respectively. Both local and overall heat transfer coefficients are computed for the channel aspect ratio varying from 5 to 15. For a given value of Grashof number, as the Reynolds number is increased, the flow patterns in the vertical channel exhibit a change from natural convection like flow patterns in which a large recirculating region is formed in the vertical part of the channel, to a forced flow type pattern. This is also the case with isotherms. The size of the recirculating region in the channel increases with increasing value of Gr/Re2. At low Reynolds number, the stream function, and isotherms are qualitatively similar to those reported for the natural convection in rectangular slots.

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D’Alessio, S. J. D. "Using boundary-layer coordinates to compute unsteady laminar two-dimensional viscous and convective flows." AIP Advances 12, no. 9 (2022): 095019. http://dx.doi.org/10.1063/5.0107995.

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In this paper, the use of boundary-layer coordinates to compute various unsteady laminar two-dimensional viscous flows is discussed. Three illustrative examples are provided, including flow around a corner, free convective flow from a heated corner, and mixed convective vortex flow. A numerical solution procedure to solve the transformed equations is also outlined. Various results and comparisons are presented and discussed. Good agreement is found with well-known documented studies.

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Ahmad, Shafiq, Sohail Nadeem, and Aysha Rehman. "Mathematical Analysis of Thermal Energy Distribution in a Hybridized Mixed Convective Flow." Journal of Nanofluids 10, no. 2 (2021): 222–31. http://dx.doi.org/10.1166/jon.2021.1778.

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The mixed convective flow of hybrid nanofluid (SWCNT-MWCNT/EG) containing micropolar fluid past a Riga surface embedded in porous medium is explored in detail throughout this study. In the momentum equation, the Darcy Forchheimer effect is used. The heat transfer phenomenon is exploited with viscous dissipation and thermal stratification over a non-Fourier heat flux model. PDEs are transformed into the necessary governing equations using transformations. The numerical results of non-linear governing equations are collected using Matlab function bvp4c. Graphical representations of the effects of relevant parameters on velocity, skin friction, and temperature are shown. The comparison of simple nanofluid and hybrid nanofluid is discussed in graphs. The temperature field is higher for hybrid nanofluid than simple nanofluid when solid volume fraction enhances. With increasing solid volume fraction, porosity parameter, and mixed convection parameter, the axial friction factor rises. The momentum boundary layer is inversely proportional to the slip parameter, Hartman number, variable viscosity and the porosity parameter.

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Mashkour, Mahmoud A. "Analysis of transient mixed convection in a horizontal channel partially heated from below." Eastern-European Journal of Enterprise Technologies 4, no. 8(112) (2021): 16–22. http://dx.doi.org/10.15587/1729-4061.2021.238649.

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The heat convection phenomenon has been investigated numerically (mathematically) for a channel located horizontally and partially heated at a uniform heat flux with forced and free heat convection. The investigated horizontal channel with a fluid inlet and the enclosure was exposed to the heat source from the bottom while the channel upper side was kept with a constant temperature equal to fluid outlet temperature. Transient, laminar, incompressible and mixed convective flow is assumed within the channel. Therefore, the flow field is estimated using Navier Stokes equations, which involves the Boussinesq approximation. While the temperature field is calculated using the standard energy model, where, Re, Pr, Ri are Reynolds number, Prandtl number, and Richardson number, respectively. Reynolds number (Re) was changed during the test from 1 to 50 (1, 10, 25, and 50) for each case study, Richardson (Ri) number was changed during the test from 1 to 25 (1, 5, 10, 15, 20, and, 25). The average Nusselt number (Nuav) increases exponentially with the Reynold number for each Richardson number and the local Nusselt number (NuI) rises in the heating point. Then gradually stabilized until reaching the endpoint of the channel while the local Nusselt number increases with a decrease in the Reynolds number over there. In addition, the streamlines and isotherms patterns in case of the very low value of the Reynolds number indicate very low convective heat transfer with all values of Richardson number. Furthermore, near the heat source, the fluid flow rate rise increases the convection heat transfer that clarified the Nusselt number behavior with Reynolds number indicating that maximum Nu No. are 6, 12, 27 and 31 for Re No. 1, 10, 25 and 50, respectively

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Chin, Y., C. F. Ma, X. Q. Gu, and L. Xu. "Mixed Convective Heat Transfer From a Simulated Microchip to Liquid Flows in a Horizontal Rectangular Channel." Journal of Electronic Packaging 113, no. 3 (1991): 309–12. http://dx.doi.org/10.1115/1.2905411.

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Mixed convection from a small heater (5mm × 5mm) to liquid flows in a horizontal rectangular channel is investigated experimentally. The results of three cases in which the buoyancy is normal to the liquid flow directions — hot surface facing upward, facing downward and vertically attached to one wall of the channel — are presented. Correlations are also provided to predict the mixed convective effects in the range 100 < ReL < 4000. The results demonstrated that both the Reynolds number ReL and the modified Rayleigh number RaL* pronouncedly dominate the heat transfer process. In all of the above cases, heat transfer was enhanced over that of forced convection.

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Kang, B. H., Y. Jaluria, and S. S. Tewari. "Mixed Convection Transport From an Isolated Heat Source Module on a Horizontal Plate." Journal of Heat Transfer 112, no. 3 (1990): 653–61. http://dx.doi.org/10.1115/1.2910437.

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An experimental study of the mixed convective heat transfer from an isolated source of finite thickness, located on a horizontal surface in an externally induced forced flow, has been carried out. This problem is of particular interest in the cooling of electronic components and also in the thermal transport associated with various manufacturing systems, such as ovens and furnaces. The temperature distribution in the flow as well as the surface temperature variation are studied in detail. The dependence of the heat transfer rate on the mixed convection parameter and on the thickness of the heated element or source, particularly in the vicinity of the source, is investigated. The results obtained indicate that the heat transfer rate and fluid flow characteristics vary strongly with the mixed convection variables. The transition from a natural convection dominated flow to a forced convection dominated flow is studied experimentally and the basic characteristics of the two regimes determined. This transition has a strong influence on the temperature of the surface and on the heat transfer rate. As expected, the forced convection dominated flow is seen to be significantly more effective in the cooling of a heat dissipating component than a natural convection dominated flow. The location of the maximum temperature on the module surface, which corresponds to the minimum local heat transfer coefficient, is determined and discussed in terms of the underlying physical mechanisms. The results obtained are also compared with these for an element of negligible thickness and the effect of a significant module thickness on the transport is determined. Several other important aspects of fundamental and applied interest are studied in this investigation.

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