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Akter, Shahina, M. Ferdows, Tasveer A. Bég, O. Anwar Bég, A. Kadir, and Shuyu Sun. "Spectral relaxation computation of electroconductive nanofluid convection flow from a moving surface with radiative flux and magnetic induction." Journal of Computational Design and Engineering 8, no. 4 (2021): 1158–71. http://dx.doi.org/10.1093/jcde/qwab038.
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Abstract A theoretical model is developed for steady magnetohydrodynamic viscous flow resulting from a moving semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation and magnetic induction effects are included in addition to thermal convective boundary conditions. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The governing nonlinear boundary layer equations are converted to nonlinear ordinary differential equations by using suitable similarity transformations. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation, and linearization for solving a nonlinear system of equations. Effects of embedded parameters such as sheet velocity parameter$\lambda$, magnetic field parameter$\beta$, Prandtl number$Pr$, magnetic Prandtl number$Prm$, thermal radiation parameter$Rd$, Lewis number$Le$, Brownian motion parameter$Nb$, and thermophoresis parameter$Nt$ on velocity, induced magnetic field, temperature, and nanoparticle concentration profiles are investigated. The skin-friction results, local Nusselt number, and Sherwood number are also discussed for various values of governing physical parameters. To show the convergence rate against iteration, residual error analysis has also been performed. The flow is strongly decelerated, and magnetic induction is suppressed with greater magnetic body force parameter, whereas temperature is elevated due to extra work expended as heat in dragging the magnetic nanofluid. Temperatures are also boosted with increment in nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced with higher wall velocity, Brownian motion, and Prandtl numbers. Both hydrodynamic and magnetic boundary layer thicknesses are reduced with greater reciprocal values of the magnetic Prandtl number Prm. Nanoparticle (concentration) boundary layer thickness is boosted with higher values of thermophoresis and Prandtl number, whereas it is diminished with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing.
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Magodora, Mangwiro, Hiranmoy Mondal, and Precious Sibanda. "Dual solutions of a micropolar nanofluid flow with radiative heat mass transfer over stretching/shrinking sheet using spectral quasilinearization method." Multidiscipline Modeling in Materials and Structures 16, no. 2 (2019): 238–55. http://dx.doi.org/10.1108/mmms-01-2019-0028.
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Purpose The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching or shrinking surface. Radiation, thermophoresis and nanoparticle Brownian motion are considered. The results have attainable scientific and technological applications in systems involving stretchable materials. Design/methodology/approach The model equations governing the flow are transformed into non-linear ordinary differential equations which are then reworked into linear form using the Newton-based quasilinearization method (SQLM). Spectral collocation is then used to solve the resulting linearised system of equations. Findings The validity of the model is established using error analysis. The velocity, temperature, micro-rotation, skin friction and couple stress parameters are conferred diagrammatically and analysed in detail. Originality/value The study obtains numerical explanations for rapidly convergent solutions using the spectral quasilinearization method. Convergence of the numerical solutions was monitored using the residual error analysis. The influence of radiation, heat and mass parameters on the flow are depicted graphically and analysed. The study is an extension on the work by Zheng et al. (2012) and therefore the novelty is that the authors tend to take into account nanoparticles, Brownian motion and thermophoresis in the flow of a micropolar fluid.
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Zhu, Jing, Dan Yang, Liancun Zheng, and Xinxin Zhang. "Second-Order Slip Effects on Heat Transfer of Nanofluid with Reynolds Model of Viscosity in a Coaxial Cylinder." International Journal of Nonlinear Sciences and Numerical Simulation 16, no. 6 (2015): 285–92. http://dx.doi.org/10.1515/ijnsns-2015-0016.
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Abstract The present work makes an analysis on the effects of second-order velocity slip and temperature jump boundary conditions for third-grade nanofluid over a coaxial cylinder. In the modeling of blood-based nanofluids containing metal or metal oxide nanoparticles, the viscosity is approximated to second-order Maclaurin’s series for the first time and the effective density is handled to a combination of temperature and nanoparticles volume fraction. The governing equations are transformed into a dimensionless system of nonlinear differential equations and solved by homotopy analysis method (HAM). The accuracy and efficiency of the HAM solutions are verified by ℏ $$\hbar $$ -curves and residual error curves using package BVPh2.0. The physical interpretations are illustrated by graphs and tables. The results revealed that the Nusselt number increases with an increase of nanoparticle volume fraction. The second-order velocity slip has a significant weakened effect on the skin friction. In addition, the Brownian motion and thermophoresis movement are collaborating to increase the temperature profile.
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Zaib, A., A. J. Chamkha, M. M. Rashidi, and K. Bhattacharyya. "Impact of nanoparticles on flow of a special non-Newtonian third-grade fluid over a porous heated shrinking sheet with nonlinear radiation." Nonlinear Engineering 7, no. 2 (2018): 103–11. http://dx.doi.org/10.1515/nleng-2017-0033.
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Abstract This research peruses the characteristics of heat and mass transfern of a special non-Newtonian third-grade fluid over a porous convectively-heated shrinking sheet filled with nanoparticles. The Buongiorno model is used for the special non-Newtonian third-grade fluid that includes both the Brownian motion and the thermophoresis effects with non-linear radiation. The nonlinear system of ordinary differential equations are obtained using a suitable transformation. The converted system of equations are then numerically solved using shooting method. The numerically-obtained results for the skin friction, local Nusselt number and the local Sherwood number as well as velocity profile, temperature distribution and concentration of nanoparticle are illustrated for different physical parameters through graphs and tables. On the behalf of the whole studies, final conclusions are made and it is observed that multiple solutions are achieved for certain values of the suction parameter. Further, the non-Newtonian parameter reduces the velocity of the fluid and increases the temperature and the concentration profiles for the first solution while the reverse trend is seen for the second solution. Finally, a comparative analysis is made through previous studies in limiting cases and shown good correlation.
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Asjad, Muhammad Imran, Muhammad Zahid, Bagh Ali, and Fahd Jarad. "Unsteady MHD Williamson Fluid Flow with the Effect of Bioconvection over Permeable Stretching Sheet." Mathematical Problems in Engineering 2022 (October 3, 2022): 1–10. http://dx.doi.org/10.1155/2022/7980267.
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The unsteady flow of Williamson fluid with the effect of bioconvection in the heat and mass transfer occurring over a stretching sheet is investigated. A uniform magnetic field, thermal radiation, thermal dissipation, and chemical reactions are taken into account as additional effects. The physical problem is formulated in the form of a system of partial differential equations and solved numerically. For this purpose, similarity functions are involved to transmute these equations into corresponding ordinary differential equations. After that, the Runge-Kutta method with shooting technique is employed to evaluate the desired findings with the utilization of a MATLAB script. As a result, the effects of various physical parameters on the velocity, temperature, and nanoparticle concentration profiles as well as on the skin friction coefficient and rate of heat transfer are discussed with the aid of graphs and tables. The parameters of Brownian motion and thermophoresis are responsible for the rise in temperature and bioconvection Rayleigh number diminishes the velocity field. This study on nanofluid bioconvection has been directly applied in the pharmaceutical industry, microfluidic technology, microbial improved oil recovery, modelling oil and gas-bearing sedimentary basins, and many other fields. Further, to check the accuracy and validation of the present results, satisfactory concurrence is observed with the existing literature.
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Mohyud-din, Syed Tauseef, Umar Khan, Naveed Ahmed, and M. M. Rashidi. "Stokes’ first problem for MHD flow of Casson nanofluid." Multidiscipline Modeling in Materials and Structures 13, no. 1 (2017): 2–10. http://dx.doi.org/10.1108/mmms-03-2016-0014.
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Purpose The purpose of this paper is to present investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate using Buongiorno’s model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticle fraction are passively controlled on the boundary rather than actively. Design/methodology/approach The partial differential equations governing the flow are reduced to a system of non-linear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters are provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers. Findings A revised model for Stokes’ first problem in nanofluids is presented in this paper. This model considers a zero flux condition at the boundary. Governing equations after implementing the similarity transforms get converted into a system of non-linear ordinary differential equations. Numerical solution using RK-Fehlberg method is also carried out. Emerging parameters are analyzed graphically. Figures indicate a quite significant change in concentration profile due to zero flux condition at the wall. Originality/value This work can be extended for other problems involving nanofluids for the better understanding of different properties of nanofluids.
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Khan, S. U., Sabir Ali Shehzad, and N. Ali. "Analysis of bioconvection in the suspension of Maxwell nanoparticles with gyrotactic microorganisms." Multidiscipline Modeling in Materials and Structures 16, no. 4 (2019): 835–49. http://dx.doi.org/10.1108/mmms-09-2019-0177.
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Purpose An increment in energy efficiency by employing nanoparticles is a hot topic of research in present era due to its abundant implications in modern engineering and technological processes. Therefore, the current research analysis reported the viscoelastic nanofluid flow over porous oscillatory moving sheet in the presence of microorganisms. A rate-type fluid namely Maxwell fluid is employed with the addition of nanoparticles. The paper aims to discuss this issue. Design/methodology/approach First, acceptable dimensionless variables are defined to convert the system of dimensional form into the system of dimensionless forms. Later on, the self-similar solution of the boundary value problem is computed by using the homotopy analysis method. The obtained results of velocity, temperature, mass concentration and motile microorganism density profiles are interpreted through physical background. Findings The presence of both thermophoresis and Brownian motion parameters also improve the thermophysical features of non-Newtonian nanoparticles. It is also pointed out that the presence of porous medium and magnetic force enhances the nanoparticles concentration. Moreover, a weaker distribution of gyrotactic microorganism has been depicted with Peclet number and bioconvection Lewis parameter. Originality/value No such article exists in the literature yet.
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Koriko, O. K., I. L. Animasaun, M. Gnaneswara Reddy, and N. Sandeep. "Scrutinization of thermal stratification, nonlinear thermal radiation and quartic autocatalytic chemical reaction effects on the flow of three-dimensional Eyring-Powell alumina-water nanofluid." Multidiscipline Modeling in Materials and Structures 14, no. 2 (2018): 261–83. http://dx.doi.org/10.1108/mmms-08-2017-0077.
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Purpose The purpose of this paper is to scrutinize the effects of nonlinear thermal radiation and thermal stratification effects on the flow of three-dimensional Eyring-Powell 36 nm alumina-water nanofluid within the thin boundary layer in the presence of quartic autocatalytic kind of chemical reaction effects, and to unravel the effects of a magnetic field parameter, random motion of the tiny nanoparticles and volume fraction on the flow. Design/methodology/approach The chemical reaction between homogeneous (Eyring-Powell 36 nm alumina-water) bulk fluid and heterogeneous (three molecules of the catalyst at the surface) in the flow of magnetohydrodynamic three-dimensional flow is modeled as a quartic autocatalytic kind of chemical reaction. The electromagnetic radiation which occurs within the boundary layer is treated as the nonlinear form due to the fact that Taylor series expansion may not give full details of such effects within the boundary layer. With the aid of appropriate similarity variables, the nonlinear coupled system of partial differential equation which models the flow was reduced to ordinary differential equation boundary value problem. Findings A favorable agreement of the present results is obtained by comparing it for a limiting case with the published results; hence, reliable results are presented. The concentration of homogeneous bulk fluid (Eyring-Powell nanofluid) increases and decreases with ϕ and Pr, respectively. The increase in the value of magnetic field parameter causes vertical and horizontal velocities of the flow within the boundary layer to decrease significantly. The decrease in the vertical and horizontal velocities of Eyring-Powell nanofluid flow within the boundary layer is guaranteed due to an increase in the value of M. Concentration of homogeneous fluid increases, while the concentration of the heterogeneous catalyst at the wall decreases with M. Originality/value Considering the industrial applications of thermal stratification in solar engineering and polymer processing where the behavior of the flow possesses attributes of Eyring-Powell 36 nm alumina-water, this paper presents the solution of the flow problem considering 36 nm alumina nanoparticles, thermophoresis, stratification of thermal energy, Brownian motion and nonlinear thermal radiation. In addition, the aim and objectives of this paper fill such vacuum in the industry.
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Rao, A. Subba, Seela Sainath, P. Rajendra, and G. Ramu. "Mathematical Modelling of Hydromagnetic Casson non-Newtonian Nanofluid Convection Slip Flow from an Isothermal Sphere." Nonlinear Engineering 8, no. 1 (2019): 645–60. http://dx.doi.org/10.1515/nleng-2018-0016.
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Abstract In this article, the combined magnetohydrodynamic heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from an isothermal sphere surface with convective condition under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. magnetic parameter (M), Buoyancy ratio parameter (N), Casson fluid parameter (β), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr) and thermal slip (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Increasing viscoplastic (Casson) parameter decelerates the flow and also decreases thermal and nano-particle concentration. Increasing Brownian motion accelerates the flow and enhances temperatures whereas it reduces nanoparticle concentration boundary layer thickness. Increasing thermophoretic parameter increasing momentum (hydrodynamic) boundary layer thickness and nanoparticle boundary layer thickness whereas it reduces thermal boundary layer thickness. Increasing magnetohydrodynamic body force parameter decelerates the flow whereas it enhances temperature and nano-particle (species) concentrations. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.
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Jiang, Jia-Zong, Song Zhang, Lei Liu, and Bao-Min Sun. "A microscopic experimental study of nanoparticle motion for the enhancement of oxygen absorption in nanofluids." Nanotechnology Reviews 7, no. 6 (2018): 529–39. http://dx.doi.org/10.1515/ntrev-2018-0072.
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AbstractThe behavior of nanoparticle motion has a great influence on gas-liquid mass transfer. However, it has been very difficult to characterize the motion of nanoparticles from a micro view in mass transfer experiments. In this study, a novel method was proposed to investigate nanoparticle Brownian motion through the application of the total internal reflection fluorescence microscope in a self-designed sample (a quasi-static liquid micro-groove) and the mass transfer enhancement of nanoparticles. Nanoparticle movement behavior was photographed using an electron-multiplying charge coupled device, and 100 consecutive images were recorded using Micro-Manager software at a rate of 20 fps. The images were processed through the particle tracking velocimetry algorithm to calculate two-dimensional motion rates of nanoparticles caused by Brownian movement. It showed that nanoparticle loadings influenced the motion rates significantly, and the motion rates were larger with smaller particle sizes under the same operating condition. The mass transfer coefficients in the quasi-static gas-liquid mass transfer system were calculated and analyzed through microscopic measurement. Based on the above thought, three important non-dimensional numbers [Sherwood (Shp), Reynolds (Rep), and Schmidt (Scp) numbers] for mass transfer theory were studied.
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Rozora, Iryna, and Yevhenii Sheptukha. "Simulation of the fractional Brownian process with given accuracy and reliability." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 1 (2024): 147–53. http://dx.doi.org/10.17721/1812-5409.2024/1.27.
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Background. Random process theory is being used more and more in various fields of science due to the high computing power of modern computers. However, it's often important to know how much we can rely on the models we use. Methods. This paper examines the modelling of the fractional Brownian motion with given accuracy and reliability. The modelling is based on Dzhaparidze and van Zanten series representation of the fractional Brownian motion. We consider the fractional Brownian motion as an input process to a time-invariant linear system with a real-valued square-integrable impulse response function, which is defined on the finite domain. Results. We prove the theorem that gives the conditions, specifically the value of the upper limit of the summing in the model, under which the obtained model approximates fractional Brownian motion with given accuracy and reliability taking into account the response of the system. Conclusions. For the proof, we use the properties of square-Gaussian stochastic processes.
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Sharma, Niti Nipun. "Radiation model for nanoparticle: extension of classical Brownian motion concepts." Journal of Nanoparticle Research 10, no. 2 (2007): 333–40. http://dx.doi.org/10.1007/s11051-007-9256-0.
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Souayeh, Basma, and Katta Ramesh. "Numerical Scrutinization of Ternary Nanofluid Flow over an Exponentially Stretching Sheet with Gyrotactic Microorganisms." Mathematics 11, no. 4 (2023): 981. http://dx.doi.org/10.3390/math11040981.
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In the modern age, the study of nanofluids over the stretching sheet has received much attention from researchers due to its significant role in the polymer industry, for instance in the production of fibre sheets and the extrusion of molten polymers through a slit die. Due to these affordable applications, the current study focusses on the motion of metallic ternary nanofluids (Ag-Au-Cu/H2O) past an exponential stretching sheet, taking diverse effects such as gyrotactic microorganisms, activation energy, buoyancy forces and thermal radiation into consideration. The model was created with the complex system of partial differential equations. Suitable similarity transformations and non-dimensional quantities were utilized to transform the complex system of partial differential equations to a set of ordinary differential equations. The resultant system is solved with the help of Matlab software. The computational outcomes are presented through the tables and pictorial notations. It is observed from the current analysis that the nanoparticle temperature of the ternary nanofluid enhances with the enhancement of activation energy and Brownian motion parameters. For the rising values of Lewis and thermophoresis numbers there is a declination in the nanoparticle concentration distribution. The Brownian motion and radiation effects increase the microorganism profile.
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Dinarvand, Saeed, Reza Hosseini, and Ioan Pop. "Unsteady convective heat and mass transfer of a nanofluid in Howarth’s stagnation point by Buongiorno’s model." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 5 (2015): 1176–97. http://dx.doi.org/10.1108/hff-04-2014-0095.
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Purpose – The purpose of this paper is to do a comprehensive study on the unsteady general three-dimensional stagnation-point flow and heat transfer of a nanofluid by Buongiorno’s model. Design/methodology/approach – In this study, the convective transport equations include the effects of Brownian motion and thermophoresis. By introducing new similarity transformations for velocity, temperature and nanoparticle volume fraction, the basic equations governing the flow, heat and mass transfer are reduced into highly non-linear ordinary differential equations. The resulting non-linear system has been solved both analytically and numerically. Findings – The analysis shows that velocity, temperature and nanoparticle concentration profiles in the respective boundary layers depend on five parameters, namely unsteadiness parameter A, Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr and Lewis number Le. It is found that the thermal boundary layer thickens with a rise in both of the Brownian motion and the thermophoresis effects. Therefore, similar to the earlier reported results, the Nusselt number decreases as the Brownian motion and thermophoresis effects become stronger. A correlation for the Nusselt number has been developed based on a regression analysis of the data. This correlation predicts the numerical results with a maximum error of 9 percent for a usual domain of the physical parameters. Originality/value – The stagnation point flow toward a wavy cylinder (with nodal and saddle stagnation points) that a little attention has been given to it up to now. The examination of unsteadiness effect on the general three-dimensional stagnation-point flow. The application of an interesting and global model (Boungiorno’s model) for the nanofluid that incorporates the effects of Brownian motion and thermophoresis. The study of the effects of Brownian motion and thermophoresis on the nanofluid flow, heat and mass transfer characteristics. The prediction of correlation for the Nusselt number based on a regression analysis of the data. General speaking, we can tell the problem with this geometry, characteristics, the applied model, and comprehensive results, was Not studied and analyzed in literature up to now.
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Sonechkin, D. M. "Climate Dynamics as a Nonlinear Brownian Motion." International Journal of Bifurcation and Chaos 08, no. 04 (1998): 799–803. http://dx.doi.org/10.1142/s0218127498000590.
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Based on the heat balance equation of the global climate system the well-known surface air temperature time series of the Northern and Southern hemispheres were analyzed as realizations of a fractional Brownian motion. The technique of the so-called wavelet transform was used for this purpose. The technique easily admits splitting time series of interest to statistically stationary oscillations and a trend. Such temperature oscillations were extracted which include within themselves almost all differences between both hemispheric time series. As a result of subtraction of the oscillations from the primary hemispheric series a residual trend-like component was evaluated. The latter evidences a single warming trend of the global climate system that was started from the early 20th century.
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RamReddy, Ch, and Ch Venkata Rao. "Bivariate Pseudo-Spectral Local Linearisation Method for Mixed Convective Flow Over the Vertical Frustum of a Cone in a Nanofluid with Soret and Viscous Dissipation Effects." Journal of Mechanics 33, no. 5 (2017): 687–702. http://dx.doi.org/10.1017/jmech.2017.63.
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AbstractIn this investigation, we intend to present the influence of the prominent viscous dissipation and Soret effects on mixed convection heat and mass transfer over the vertical frustum of a cone in a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. In addition, the uniform wall nanoparticle condition at the surface is replaced with the zero nanoparticle mass flux condition to execute physically applicable results. The governing equations of a nanofluid flow in the dimensional form are reduced to a system of partial differential equations in the non-dimensional form by using suitable non-similarity variables and then solved by using a recently introduced spectral method named as Bivariate Pseudo-Spectral Local Linearisation Method (BPSLLM). The convergence and error analysis tests are conducted to examine the accuracy of the spectral method. To validate the method, the present numerical results are compared with the existing results in some special cases and the outcomes are observed to be in very good agreement. The effects of Brownian motion, thermophoresis, Eckert number, Soret number, nanoparticle and regular buoyancy parameters on the dimensionless surface drag, heat, nanoparticle mass and regular mass transfer rates over the vertical frustum of a cone are discussed and illustrated graphically.
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di Schio, Eugenia Rossi, Kaleem Iqbal, Paolo Valdiserri, Mohamed Bouanini, and Cesare Biserni. "Modelling the Non-Isothermal Flow of a Nanofluid in a Lid-Driven Cavity from the Perspective of Irreversibility Analysis." Defect and Diffusion Forum 439 (February 20, 2025): 13–22. https://doi.org/10.4028/p-6cjvby.
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This article examines laminar mixed convection of a nanofluid within a square cavity that contains a vertical rectangular obstacle serving as a vortex promoter. Employing Buongiorno's theory, the dimensionless governing equations are numerically solved using the finite element method to analyze the distributions of velocity, temperature, nanoparticle concentration, and entropy generation. Attention is paid to the entropy generation. Results are presented and discussed, showing that increasing the Reynolds number generates a large vortex near the obstacle, which diminishes reverse flow, enhances heat conduction, and increases entropy generation. Moreover, thermophoresis drives tiny nanoparticles from hot to cold regions, affecting heat transfer. Indeed, nanoparticle concentration decreases with higher thermophoresis (NT) and Brownian motion (NB) constraints, as these parameters are inversely related to the concentration profile.
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BÉG, O. ANWAR, AYESHA SOHAIL, ALI KADIR, and T. A. BÉG. "B-SPLINE COLLOCATION SIMULATION OF NON-LINEAR TRANSIENT MAGNETIC NANOBIO-TRIBOLOGICAL SQUEEZE-FILM FLOW." Journal of Mechanics in Medicine and Biology 18, no. 01 (2018): 1850007. http://dx.doi.org/10.1142/s0219519418500070.
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A mathematical model is presented for magnetized nanofluid bio-tribological squeeze-film flow between two approaching disks. The nanofluid comprises a suspension of metal oxide nanoparticles with an electrically-conducting base fluid, making the nanosuspension responsive to applied magnetic field. The governing viscous momentum, heat and species (nanoparticle) conservation equations are normalized with appropriate transformations which renders the original coupled, non-linear partial differential equation system into a more amenable ordinary differential boundary value problem. The emerging model is shown to be controlled by a number of parameters, viz nanoparticle volume fraction, squeeze number, Hartmann magnetic body force number, disk surface transpiration parameter, Brownian motion parameter, thermophoretic parameter, Prandtl number and Lewis number. Computations are conducted with a B-spline collocation numerical method. Validation with previous homotopy solutions is included. The numerical spline algorithm is shown to achieve excellent convergence and stability in non-linear bio-tribological boundary value problems. The interaction of heat and mass transfer with nanofluid velocity characteristics is explored. In particular, smaller nanoparticle (high Brownian motion parameter) suspensions are studied. The study is relevant to enhanced lubrication performance in novel bio-sensors and intelligent knee joint (orthopaedic) systems.
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Park, Suehyun, Jeongeun Song, and Jun Soo Kim. "In silico construction of a flexibility-based DNA Brownian ratchet for directional nanoparticle delivery." Science Advances 5, no. 4 (2019): eaav4943. http://dx.doi.org/10.1126/sciadv.aav4943.
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Brownian particles confined in a system with periodic and asymmetric potential can be transported in a specific direction along the potential by repetitively switching the potential on and off. Here, we propose a DNA-based Brownian ratchet for directional transport of positively charged nanoparticles in which nanoparticle delivery follows the path dictated by a single, long, double-stranded DNA. We performed Brownian dynamics simulations to prove its realization using coarse-grained models. A periodic and asymmetric potential for nanoparticle binding is constructed along a single, long, double-stranded DNA molecule by a novel strategy that uses variation in sequence-dependent DNA flexibility. Directional and processive motion of nanoparticles is achieved by changing salt concentration repetitively over several cycles to switch the asymmetric potential on and off. This work suggests that double-stranded DNA molecules with elaborately designed flexibility variation can be used as a molecule-scale guide for spatial and dynamic control of nanoparticles for future applications.
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Dang, Khyati, Vinita Makkar, and Naresh Sharma. "Radiative MHD Casson Non-Newtonian Nanofluid Slip Flow Induced by Stretching Cylinder: A Numerical Approach." Indian Journal Of Science And Technology 17, no. 38 (2024): 3993–4004. http://dx.doi.org/10.17485/ijst/v17i38.1978.
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Objectives: This article investigates the continuous magnetohydrodynamics slip flow across an extending cylinder, including heat radiation and free stream velocity. The proposed model incorporated the Brownian motion parameter and thermophoresis. Methods: Applying the similarity transformation to a system of partial differential equations yields an ordinary differential equation of first order. Since, there is the nonlinear nature of the modified equations, these ordinary differential equations are addressed by employing mathematical modeling. The shooting process has been embraced to solve changed equations by implementing the following Runge-Kutta Fehlberg method. Findings: Graphical representations are used to show how several fluid factors, such as Casson fluid parameter, free stream velocity, thermophoresis, magnetic parameter, Brownian motion parameter, heat generation parameter, Lewis number, radiation parameter, chemical reaction and curvature parameter affect concentration, temperature and velocity. Results for physical quantity of interest are also computed and reported in tabular form. The study's main findings showed that nanoparticle temperatures rise with greater Brownian motion parameter values, whereas nanoparticle concentration falls with higher heat radiation parameter values. Additionally, it is found that with rise in Lewis number rises as 0.1, 0.4, 0.7, 1.0, 1.3, heat transfer rate falls down by 21.19%. The outcomes are calculated using the MATLAB software. Novelty: This technique's validity is defended by comparing its most recent findings to previously published results and successfully meeting the convergence criteria. The present work emphasizes the analysis of free stream flow in the cylindrical area, specifically in the existence of partial slip and heat radiation, under convective circumstances. This study has significant implications for electronic devices such as processors as well as many businesses and the field of biological and medical sciences. The present investigation aims to support production businesses in achieving the desired level of quality of their products by effectively managing the transport phenomena. Keywords: Stretching cylinder, Heat radiation, Brownian motion, Thermophoresis, Non-Newtonian nanofluid, Shooting technique
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Mustafa, Meraj, and Junaid Khan. "Numerical analysis of Sakiadis flow problem considering Maxwell nanofluid." Thermal Science 21, no. 6 Part B (2017): 2747–56. http://dx.doi.org/10.2298/tsci150306001m.
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This article investigates the flow of Maxwell nanofluid over a moving plate in a calm fluid. Novel aspects of Brownian motion and thermophoresis are taken into consideration. Revised model for passive control of nanoparticle volume fraction at the plate is used in this study. The formulated differential system is solved numerically by employing shooting approach together with fourth-fifth-order-Runge-Kutta integration procedure and Newton?s method. The solutions are greatly influenced with the variation of embedded parameters which include the local Deborah number, the Brownian motion parameter, the thermophoresis parameter, the Prandtl number, and the Schmidt number. We found that the variation in velocity distribution with an increase in local Deborah number is non-monotonic. Moreover, the reduced Nusselt number has a linear and direct relationship with the local Deborah number.
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BÁRTEK, JAN, MARÍA J. GARRIDO-ATIENZA, and BOHDAN MASLOWSKI. "STOCHASTIC POROUS MEDIA EQUATION DRIVEN BY FRACTIONAL BROWNIAN MOTION." Stochastics and Dynamics 13, no. 04 (2013): 1350010. http://dx.doi.org/10.1142/s021949371350010x.
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The present work deals with stochastic porous media equation with multiplicative noise, driven by fractional Brownian motion B(H) with Hurst index H > 1/2. The stochastic integral with integrator B(H) is defined pathwise following the theory developed by Zähle [24], based on the so-called fractional derivatives. It is shown that there is a one-to-one correspondence between solutions to the stochastic equation and solutions to its deterministic counterpart. By means of this correspondence and exploiting properties of the deterministic porous media equation, the existence, uniqueness, regularity and long-time properties of the solution is established. We also prove that the solution forms a random dynamical system in an appropriate function space.
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MANNELLA, RICCARDO, PAOLO GRIGOLINI, and BRUCE J. WEST. "A DYNAMICAL APPROACH TO FRACTIONAL BROWNIAN MOTION." Fractals 02, no. 01 (1994): 81–94. http://dx.doi.org/10.1142/s0218348x94000077.
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Herein we develop a dynamical foundation for fractional Brownian motion. A clear relation is established between the asymptotic behavior of the correlation function and diffusion in a dynamical system. Then, assuming that scaling is applicable, we establish a connection between diffusion (either standard or anomalous) and the dynamical indicator known as the Hurst coefficient. We argue on the basis of numerical simulations that although we have been able to prove scaling only for "Gaussian" processes, our conclusions may well apply to a wider class of systems. On the other hand, systems exist for which scaling might not hold, so we speculate on the possible consequences of the various relations derived in the paper on such systems.
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Gupta, Sumit, Sandeep Gupta, Nawal Kishor Jangid, Vijay kumar Singhal, Rohit Mukherjee, and Sangeeta Choudhary. "Implementation of improved Fourier's law and Fick's law for rotational flow of nanofluid over an exponentially stretching sheet." Multidiscipline Modeling in Materials and Structures 17, no. 5 (2021): 931–54. http://dx.doi.org/10.1108/mmms-08-2019-0152.
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PurposeThe purpose of the current article is to explore the rotational behavior on nanofluid flow over an exponentially stretching surface. Heat and mass flux are formulated upon Cattaneo–Christov theory.Design/methodology/approachEffect of thermophoretic, Brownian motion and thermally convective conditions is further retained. Novel boundary layer approximations are applied to transform the governing equations of continuity, momentum, energy and nanoparticle volume fraction. Convergent series solutions are obtained to manage the rotating flow with the aid of homotopy analysis method (HAM).FindingsDepending on the several dimensionless parameters including the local rotation parameter the Prandtl number Pr, the thermophoresis parameter, the Brownian motion parameter, the Lewis number Le, Biot number Bi, Deborah number in terms of heat flux relaxation parameter and Deborah number in terms of mass flux relaxation parameter with the dimensionless physical quantities are deliberated through graphs. Present results are also likened with the foregoing results in significance.Originality/valueNo such assumptions have been made for the development of analytical solution so far.
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Lu, Yingdong. "Performance Analysis of Production Systems with Correlated Demand via Diffusion Approximations." International Journal of Stochastic Analysis 2012 (December 31, 2012): 1–12. http://dx.doi.org/10.1155/2012/109417.
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We investigate the performance of a production system with correlated demand through diffusion approximation. The key performance metric under consideration is the extreme points that this system can reach. This problem is mapped to a problem of characterizing the joint probability density of a two-dimensional Brownian motion and its coordinate running maximum. To achieve this goal, we obtain the stationary distribution of a reflected Brownian motion within the positive quarter-plane, which is of independent interest, through investigating a solution of an extended Helmhotz equation.
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Sharaf, Omar Z., Ashraf N. Al-Khateeb, Dimitrios C. Kyritsis, and Eiyad Abu-Nada. "Numerical investigation of nanofluid particle migration and convective heat transfer in microchannels using an Eulerian–Lagrangian approach." Journal of Fluid Mechanics 878 (September 4, 2019): 62–97. http://dx.doi.org/10.1017/jfm.2019.606.
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An Eulerian–Lagrangian modelling approach was employed in order to investigate the flow field, heat transfer and particle distribution in nanofluid flow in a parallel-plate microchannel, with a focus on relatively low Reynolds numbers ($Re\leqslant 100$). Momentum and thermal interactions between fluid and particle phases were accounted for using a transient two-way coupling algorithm implemented within an in-house code that tracked the simultaneous evolution of the carrier and particulate phases while considering timescale differences between the two phases. The inaccuracy of assuming a homogeneous particle distribution in modelling nanofluid flow in microchannels was established. In particular, shear rate and thermophoresis were found to play a key role in the lateral migration of nanoparticles and in the formation of particle depletion and accumulation regions in the vicinity of the channel walls. At low Reynolds numbers, nanoparticle distribution near the walls was observed to gradually flatten in the streamwise direction. On the other hand, for relatively higher Reynolds numbers, higher particle non-uniformities were observed in the vicinity of the channel walls. Furthermore, it was established that convective heat transfer between channel walls and the bulk fluid can either improve or deteriorate with the addition of nanoparticles, depending on whether the flow exceeded a critical Reynolds number of enhancement. It was also established that Brownian motion and thermophoresis had a major role in nanoparticle deposition on the channel walls. In particular, Brownian motion was the main deposition mechanism for nano-sized particles, whereas due to thermophoresis, nanoparticles were repelled away from channel walls. The result of the competition between the two is that deposition gradually increased along the streamwise direction.
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Dewick, Paul R. "On Financial Distributions Modelling Methods: Application on Regression Models for Time Series." Journal of Risk and Financial Management 15, no. 10 (2022): 461. http://dx.doi.org/10.3390/jrfm15100461.
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The financial market is a complex system with chaotic behavior that can lead to wild swings within the financial system. This can drive the system into a variety of interesting phenomenon such as phase transitions, bubbles, and crashes, and so on. Of interest in financial modelling is identifying the distribution and the stylized facts of a particular time series, as the distribution and stylized facts can determine if volatility is present, resulting in financial risk and contagion. Regression modelling has been used within this study as a methodology to identify the goodness-of-fit between the original and generated time series model, which serves as a criterion for model selection. Different time series modelling methods that include the common Box–Jenkins ARIMA, ARMA-GARCH type methods, the Geometric Brownian Motion type models and Tsallis entropy based models when data size permits, can use this methodology in model selection. Determining the time series distribution and stylized facts has utility, as the distribution allows for further modelling opportunities such as bivariate regression and copula modelling, apart from the usual forecasting. Determining the distribution and stylized facts also allows for the identification of the parameters that are used within a Geometric Brownian Motion forecasting model. This study has used the Carbon Emissions Futures price between the dates of 1 May 2012 and 1 May 2022, to highlight this application of regression modelling.
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Khyati, Dang, Makkar Vinita, and Sharma Naresh. "Radiative MHD Casson Non-Newtonian Nanofluid Slip Flow Induced by Stretching Cylinder: A Numerical Approach." Indian Journal of Science and Technology 17, no. 38 (2024): 3993–4004. https://doi.org/10.17485/IJST/v17i38.1978.
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Abstract <strong>Objectives:</strong> This article investigates the continuous magnetohydrodynamics slip flow across an extending cylinder, including heat radiation and free stream velocity. The proposed model incorporated the Brownian motion parameter and thermophoresis. <strong>Methods:</strong> Applying the similarity transformation to a system of partial differential equations yields an ordinary differential equation of first order. Since, there is the nonlinear nature of the modified equations, these ordinary differential equations are addressed by employing mathematical modeling. The shooting process has been embraced to solve changed equations by implementing the following Runge-Kutta Fehlberg method. <strong>Findings:</strong> Graphical representations are used to show how several fluid factors, such as Casson fluid parameter, free stream velocity, thermophoresis, magnetic parameter, Brownian motion parameter, heat generation parameter, Lewis number, radiation parameter, chemical reaction and curvature parameter affect concentration, temperature and velocity. Results for physical quantity of interest are also computed and reported in tabular form. The study's main findings showed that nanoparticle temperatures rise with greater Brownian motion parameter values, whereas nanoparticle concentration falls with higher heat radiation parameter values. Additionally, it is found that with rise in Lewis number rises as 0.1, 0.4, 0.7, 1.0, 1.3, heat transfer rate falls down by 21.19%. The outcomes are calculated using the MATLAB software. <strong>Novelty:</strong> This technique's validity is defended by comparing its most recent findings to previously published results and successfully meeting the convergence criteria. The present work emphasizes the analysis of free stream flow in the cylindrical area, specifically in the existence of partial slip and heat radiation, under convective circumstances. This study has significant implications for electronic devices such as processors as well as many businesses and the field of biological and medical sciences. The present investigation aims to support production businesses in achieving the desired level of quality of their products by effectively managing the transport phenomena. <strong>Keywords:</strong> Stretching cylinder, Heat radiation, Brownian motion, Thermophoresis, Non-Newtonian nanofluid, Shooting technique
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APPLEBAUM, DAVID, and MICHAILINA SIAKALLI. "STOCHASTIC STABILIZATION OF DYNAMICAL SYSTEMS USING LÉVY NOISE." Stochastics and Dynamics 10, no. 04 (2010): 509–27. http://dx.doi.org/10.1142/s0219493710003066.
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We investigate the perturbation of the nonlinear differential equation [Formula: see text] by random noise terms consisting of Brownian motion and an independent Poisson random measure. We find conditions under which the perturbed system is almost surely exponentially stable and estimate the corresponding Lyapunov exponents.
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Ahmad, I., M. R. Jagwal, and M. Sajid. "Numerical Simulation of Non-Axisymmetric Homann's Stagnation-Point Flow of Nanofluid." Journal of Nanofluids 9, no. 1 (2020): 47–55. http://dx.doi.org/10.1166/jon.2020.1725.
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This paper addresses numerical results for nanofluid near Homann's non-axisymmetric stagnation-point flow. The nanofluids model shows Brownian motion and thermophoresis effects. Recently, Weidman modify the Homann's stagnation-point problem to non-axisymmetric on rigid surface by superposing additional periodic terms to outer potential flow. The numerical results for couple differential system are obtained by means of shooting method. The solution is achieved for diverse values of involved parameter and ratio γ = b/a (b is shear and a is strain rate), which ranges from (–∞, ∞). The distributions for shear stresses, heat and mass transfer rate, temperature and nanoparticle concentration compared to their large- asymptotic behaviors also presented. For nanofluids, properties may vary considerably near solid boundary due to thermophoresis and Brownian motion of the fluid particles. These effects can result in decreasing viscosity within the boundary layer for heated fluids, thus leading to heat transfer enhancement.
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Nazia, S., B. Seshaiah, P. Sreedevi, and P. Sudarsana Reddy. "Non-Newtonian Electrically Conducting Nano Fluid Heat and Mass Transfer Analysis Over a Vertical Cone with Convective Boundary Condition." Journal of Nanofluids 12, no. 4 (2023): 967–77. http://dx.doi.org/10.1166/jon.2023.1980.
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Electrically conducting, thermally radiative non-Newtonian Nano fluid heat and mass transfer features over a vertical permeable cone with chemical reaction and convective boundary condition is numerically scrutinized in this article. The system of transformed mathematical equations are numerically solved by utilizing the most efficient Finite element method. Brownian motion, Magnetic field, Lewis number, Biot number, Chemical reaction, Buoyancy ratio, Suction/Injection, Prandtl number, Thermal radiation parameters influence on Nanoparticle volume fraction, temperature and velocity scatterings is evaluated and the outcomes are plotted through graphs. Furthermore, the non-dimensional rates of concentration and heat transfer values are also premeditated. The temperature of the Nano fluid amplifies with rising values of Brownian motion parameter and this augmentation is more in non-Newtonian case than the Newtonian case. Addition of Convective boundary condition into the liquid flow intensifies the rates of heat transfer of non-Newtonian nanoliquid.
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Zhao, Chaofeng, Zhibo Zhai, and Qinghui Du. "Optimal control of stochastic system with Fractional Brownian Motion." Mathematical Biosciences and Engineering 18, no. 5 (2021): 5625–34. http://dx.doi.org/10.3934/mbe.2021284.
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Asselborn, S. A., E. S. Zatsepin, D. S. Isakov, A. M. Gerasimov, D. G. Pikhulya, and Yu V. Miklyaev. "ILLUMINATION SYSTEM FOR SUB-DIFFRACTION RESOLUTION MICROSCOPY." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 3 (2022): 68–78. http://dx.doi.org/10.14529/mmph220308.
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Illumination scheme for superresolution microscopy is developed. The scheme accomplishes dark filed illumination with a laser light source including spatial coherence suppression. The scheme allows to observe nanoparticles with a size smaller than 50 nm. This is necessary to get higher resolution in the previously proposed method of superresolution microscopy (Near field Optical Random Microscopy – NORM). This method is based on real-time video processing of a nanoparticles Brownian motion those are located near the object surface. The method of vertical coordinate measurement is demonstrated. This method is based on astigmatic nanoparticle imaging. Three-dimensional distributions of suspended nanoparticles are obtained. Vertical resolution better than 200 nm and lateral resolution better than 100 nm are demonstrated.
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Ali, Mohammad, and Md Abdul Alim. "Influence of Slip Parameter, Viscous Dissipation and Joule Heating Effect on Boundary Layer Flow and Heat Transfer Over a Power-Law Stretching Wedge-Shaped Surface with the Correlation Coefficient and Multiple Regressions." International Journal of Applied Mechanics and Engineering 27, no. 2 (2022): 1–21. http://dx.doi.org/10.2478/ijame-2022-0016.
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Abstract The influence of slip parameter, viscous dissipation, and Joule heating parameter on MHD boundary layer nanofluid flow over a permeable wedge-shaped surface was analysed. The PDEs and the associated boundary conditions were transformed to a set of non-similar ODEs and the obtained system of equations was solved numerically with the help of the spectral quasi-linearization method (SQLM) by applying suitable software. This method helps to identify the accuracy and convergence of the present problem. The current numerical results were compared with previously published work and are found to be similar. The fluid velocity, fluid temperature, and nanoparticle concentration within the boundary layer region for various values of the parameters such as the slip effect, magnetic strength, Prandtl number, Lewis number, stretching ratio, viscous dissipation, suction, Brownian motion, Joule heating, heat generation, and thermophoresis are studied. It is observed that the Brownian motion, Joule heating, viscous dissipation, and thermophoresis lead to decreases in the heat and mass transfer rate. The skin friction coefficient enhances with slip, magnetic, permeability, and suction parameters, but reduces with the Brownian motion, wedge angle, and stretching ratio parameters whereas there is no effect of mixed convection, thermophoresis, heat generation parameters, the Prandtl and Eckert number.
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Simpson, D. J. W., and R. Kuske. "The positive occupation time of Brownian motion with two-valued drift and asymptotic dynamics of sliding motion with noise." Stochastics and Dynamics 14, no. 04 (2014): 1450010. http://dx.doi.org/10.1142/s0219493714500105.
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We derive the probability density function of the positive occupation time of one-dimensional Brownian motion with two-valued drift. Long time asymptotics of the density are also computed. We use the result to describe the transitional probability density function of a general N-dimensional system of stochastic differential equations representing stochastically perturbed sliding motion of a discontinuous, piecewise-smooth vector field on short time frames. A description of the density at larger times is obtained via an asymptotic expansion of the Fokker-Planck equation.
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Narahari, Marneni, Suresh Kumar Raju Soorapuraju, Rajashekhar Pendyala, and Ioan Pop. "Transient two-dimensional natural convection flow of a nanofluid past an isothermal vertical plate using Buongiorno’s model." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 1 (2017): 23–47. http://dx.doi.org/10.1108/hff-09-2015-0394.
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Purpose The purpose of this paper is to present a numerical investigation of the transient two-dimensional natural convective boundary-layer flow of a nanofluid past an isothermal vertical plate by incorporating the effects of Brownian motion and thermophoresis in the mathematical model. Design/methodology/approach The problem is formulated using the Oberbeck–Boussinesq and the standard boundary-layer approximations. The governing coupled non-linear partial differential equations for conservation of mass, momentum, thermal energy and nanoparticle volume fraction have been solved by using an efficient implicit finite-difference scheme of the Crank–Nicolson type, which is stable and convergent. Numerical computations are performed and the results for velocity, temperature and nanoparticle volume fraction are presented in graphs at different values of system parameters such as Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number, Lewis number and dimensionless time. The results for local and average skin-friction and Nusselt number are also presented graphically and discussed thoroughly. Findings It is found that the velocity, temperature and nanoparticle volume fraction profiles enhance with respect to time and attain steady-state values as time progresses. The local Nusselt number is found to decrease with increasing thermophoresis parameter, while it increases slightly with increasing Brownian motion parameter. To validate the present numerical results, the steady-state local Nusselt number results for the limiting case of a regular fluid have been compared with the existing well-known results at different Prandtl numbers, and the results are found to be in an excellent agreement. Research limitations/implications The present analysis is limited to the transient laminar natural convection flow of a nanofluid past an isothermal semi-infinite vertical plate in the absence of viscous dissipation and thermal radiation. The unsteady natural convection flow of a nanofluid will be investigated for various physical conditions in a future work. Practical implications Unsteady flow devices offer potential performance improvements as compared with their steady-state counterparts, and the flow fields in the unsteady flow devices are typically transient in nature. The present study provides very useful information for heat transfer engineers to understand the heat transfer enhancement with the nanofluid flows. The present results have immediate relevance in cooling technologies. Originality/value The present research work is relatively original and illustrates the transient nature of the natural convective nanofluid boundary-layer flow in the presence of Brownian motion and thermophoresis.
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LIU, YONG, and HUAIZHONG ZHAO. "REPRESENTATION OF PATHWISE STATIONARY SOLUTIONS OF STOCHASTIC BURGERS' EQUATIONS." Stochastics and Dynamics 09, no. 04 (2009): 613–34. http://dx.doi.org/10.1142/s0219493709002798.
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In this paper, we show that the stationary solution u(t, ω) of the differentiable random dynamical system U: ℝ+ × L2[0, 1] × Ω → L2[0, 1] generated by the stochastic Burgers' equation with large viscosity, denoted by ν, driven by a Brownian motion in L2[0, 1], is given by: u(t, ω) = U(t, Y(ω), ω) = Y(θ(t, ω)), where Y(ω) can be represented by the following integral equation: [Formula: see text] Here θ is the group of P-preserving ergodic transformations on the canonical probability space [Formula: see text] such that θ(t, ω)(s) = W(t + s) - W(t), where W is the L2[0, 1]-valued Brownian motion on the probability space [Formula: see text], Tν is the linear operator semigroup on L2[0, 1] generated by νΔ.
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Hymavathi, D., M. Ramachandru, M. Chenna Krishna Reddy, and N. Kishan. "Heat Generation and Thermal Radiation Effects on Magneto Hydrodynamics Non Newtonian Casson Nanofluid with Gyro Tactic Microorganisms Over a Plate, Stagnation and Wedge Through Porous Media." Journal of Nanofluids 12, no. 6 (2023): 1463–74. http://dx.doi.org/10.1166/jon.2023.1933.
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The numerical interventions of two dimensional steady flow of MHD Non-Newtonian nanofluids containing the gyro-tactic microorganisms through porous media over a plate, wedge, and stagnation point are highlighted in this paper. Mainly the Peclet number, bioconvection, Brownian motion, thermophoresis, and heat generation impacts are addressed to consolidate thermal and nanofluid concentration conservative equations with passively controlled boundary conditions for three different geometrical conditions of flow over a plate, wedge, and stagnation point. By considering the impacts of the varying pertinent parameters, namely thermophoresis, Brownian motion, Prandtl number, heat generation, chemical reaction, bio convectional and magnetic parameters, results are analysed graphically for the momentum, temperature, nanoparticle volume fractions, and the density of motile microorganisms profile, as well as the local Nusselt and motile microorganism numbers. Relevant similarity transformations are used to obtain the system of ordinary differential equations and the equations are solved numerically by using Bvp4c via MATLAB based on the shooting technique.
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GARRIDO-ATIENZA, M. J., B. MASLOWSKI, and B. SCHMALFUß. "RANDOM ATTRACTORS FOR STOCHASTIC EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION." International Journal of Bifurcation and Chaos 20, no. 09 (2010): 2761–82. http://dx.doi.org/10.1142/s0218127410027349.
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In this paper, the asymptotic behavior of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is studied. In particular, it is shown that the corresponding solutions generate a random dynamical system for which the existence and uniqueness of a random attractor is proved.
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Vinita, Parveen Kumar, and Vikas Poply. "Mathematical Modelling of Magnetohydrodynamic Nanofluid Flow with Chemically Reactive Species and Outer Velocity Towards Stretching Cylinder." Journal of Nanofluids 12, no. 4 (2023): 1067–73. http://dx.doi.org/10.1166/jon.2023.1951.
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This article investigate the impact of magnetohydrodynamic nanofluid past a stretching cylinder with chemical reactive species. The momentum, energy and concentration equations are represented by a set of partial differential equations which are moulded into a system of ordinary differential equations using mathematical modelling of the physical problem. After adopting the Runge Kutta Fehlberg approach, the moulded equations are solved using the shooting procedure. To study the effects of various fluid parameters, a parametric analysis was performed. Brownian motion and thermophoresis were investigated in the appealing pattern. The effects of important fluid characteristics, such as outer velocity, chemical reaction, thermophoresis, Lewis number, Brownian motion on concentration, temperature, and velocity have been investigated and shown in graphically and tabulated forms. The core findings of this work is that concentration of the nanofluid decreasing with more reacting species and rate of heat transfer is significantly controlled by outer velocity parameter and magnetic parameter which is very useful in manufacturing processes.
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Chang, Ho, Kuan Lin Tsai, and Tsing Tshih Tsung. "A Study on Dynamic Stability of the Fe3O4 Magnetorheological Fluid." Materials Science Forum 561-565 (October 2007): 2175–78. http://dx.doi.org/10.4028/www.scientific.net/msf.561-565.2175.
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In this paper investigates the dynamic stability of Fe3O4 magnetorheological fluid produced by Submerged Arc Nanoparticle Synthesis System which our team has modified, that is, the dynamic stability of magnetic microparticle in Brownian motion. Through this modified system, parameters such as the exact peak current, the time of discharge and off time, and voltage can be preset. The results of the experiment show that the Fe3O4 magnetorheological fluid produced by the modified submerged arc nanoparticle synthesis system has wt 20% and vol 1% surfactants after being mixed with water. After being placed aside for one day and 15 days respectively, the average diameters of the two nanofluid measured with particle size analyzer and TEM are both 40nm. Furthermore, after analyzed through Brookhaven ZetaPlus the zeta potential of the two nanofluid both reach 40mv, which proves that the magnetic nanofluid show superior performance of suspension.
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Jamali, Vida, Cory Hargus, Assaf Ben-Moshe, et al. "Anomalous nanoparticle surface diffusion in LCTEM is revealed by deep learning-assisted analysis." Proceedings of the National Academy of Sciences 118, no. 10 (2021): e2017616118. http://dx.doi.org/10.1073/pnas.2017616118.
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The motion of nanoparticles near surfaces is of fundamental importance in physics, biology, and chemistry. Liquid cell transmission electron microscopy (LCTEM) is a promising technique for studying motion of nanoparticles with high spatial resolution. Yet, the lack of understanding of how the electron beam of the microscope affects the particle motion has held back advancement in using LCTEM for in situ single nanoparticle and macromolecule tracking at interfaces. Here, we experimentally studied the motion of a model system of gold nanoparticles dispersed in water and moving adjacent to the silicon nitride membrane of a commercial LC in a broad range of electron beam dose rates. We find that the nanoparticles exhibit anomalous diffusive behavior modulated by the electron beam dose rate. We characterized the anomalous diffusion of nanoparticles in LCTEM using a convolutional deep neural-network model and canonical statistical tests. The results demonstrate that the nanoparticle motion is governed by fractional Brownian motion at low dose rates, resembling diffusion in a viscoelastic medium, and continuous-time random walk at high dose rates, resembling diffusion on an energy landscape with pinning sites. Both behaviors can be explained by the presence of silanol molecular species on the surface of the silicon nitride membrane and the ionic species in solution formed by radiolysis of water in presence of the electron beam.
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Hayashi, Terutake, Yuki Ishizaki, Masaki Michihata, Yasuhiro Takaya, and Shin-ichi Tanaka. "Study on Nanoparticle Sizing Using Fluorescent Polarization Method with DNA Fluorescent Probe." International Journal of Automation Technology 9, no. 5 (2015): 534–40. http://dx.doi.org/10.20965/ijat.2015.p0534.
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Fluorescent polarization methods are used to detect complementary base pairing of DNA in biological fields. These methods work by measuring the rotational diffusion coefficient of Brownian motion of the fluorescent particles in solution. The rotational diffusion coefficient corresponds to the inverse third power of diameter according to the Debye-Stokes-Einstein equation for nanoparticles as hard spheres. We develop a novel method to measure the rotational diffusion coefficient using a fluorescent probe with a DNA spacer connected to a gold nanoparticle. We studied the physical characteristics of this probe to verify the feasibility of the proposed method. The rotational diffusion coefficients of gold nanoparticles with diameters ranging between 5–20 nm were measured using this developed system. In this manuscript we describe a novel fluorescent polarization method for nanoparticle sizing using a fluorescent DNA probe.
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Shapochkina, Irina V., Nastassia D. Savina, Elena M. Zaytseva, Viktor M. Rozenbaum, Maria I. Ikim, and Aleksander S. Bugaev. "Adiabatic Brownian motor with a stepwise potential perturbed by a dichotomous harmonic sygnal." Journal of the Belarusian State University. Physics, no. 2 (May 21, 2021): 71–80. http://dx.doi.org/10.33581/2520-2243-2021-2-71-80.
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We obtained an analytical expression for the average motion velocity of an adiabatic Brownian motor (ratchet), which operates due to small dichotomous spatially harmonic fluctuations of a stepwise potential. The symmetry properties of the average velocity as a functional of the stationary and fluctuating components of the nanoparticle potential energy are revealed, and the ranges of values of the system parameters that ensure the rightward and leftward motion of the motor are determined. We showed that the average motor velocity is a non-monotonic function of the stepwise potential height. For a singular (infinitely high and narrow) potential barrier, the average velocity depends non-monotonically on the «power» of this barrier (the barrier width multiplied by the exponent of the ratio of the barrier height to the thermal energy). The article continues the further development of theoretical methods of symmetry analysis by applying the general approaches proposed by the authors to specific motor systems.
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Wang, Huarui, Jianqi Shen, and Xiaoshu Cai. "Online measurement of nanoparticle size distribution in flowing Brownian motion system using laser diode self-mixing interferometry." Applied Physics B 120, no. 1 (2015): 129–39. http://dx.doi.org/10.1007/s00340-015-6113-1.
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Sykes, Edward A., Qin Dai, Christopher D. Sarsons, et al. "Tailoring nanoparticle designs to target cancer based on tumor pathophysiology." Proceedings of the National Academy of Sciences 113, no. 9 (2016): E1142—E1151. http://dx.doi.org/10.1073/pnas.1521265113.
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Nanoparticles can provide significant improvements in the diagnosis and treatment of cancer. How nanoparticle size, shape, and surface chemistry can affect their accumulation, retention, and penetration in tumors remains heavily investigated, because such findings provide guiding principles for engineering optimal nanosystems for tumor targeting. Currently, the experimental focus has been on particle design and not the biological system. Here, we varied tumor volume to determine whether cancer pathophysiology can influence tumor accumulation and penetration of different sized nanoparticles. Monte Carlo simulations were also used to model the process of nanoparticle accumulation. We discovered that changes in pathophysiology associated with tumor volume can selectively change tumor uptake of nanoparticles of varying size. We further determine that nanoparticle retention within tumors depends on the frequency of interaction of particles with the perivascular extracellular matrix for smaller nanoparticles, whereas transport of larger nanomaterials is dominated by Brownian motion. These results reveal that nanoparticles can potentially be personalized according to a patient’s disease state to achieve optimal diagnostic and therapeutic outcomes.
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KOTELENEZ, PETER M. "FROM DISCRETE DETERMINISTIC DYNAMICS TO BROWNIAN MOTIONS." Stochastics and Dynamics 05, no. 03 (2005): 343–84. http://dx.doi.org/10.1142/s0219493705001511.
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Two types of point particles, large and small, with state space ℝd are considered, where d ≥ 2 and "large" and "small" refer to different masses. The small particles move deterministically with very large initial velocities. They transfer their momenta to the large particles through a smooth mean field interaction which completely determines the motion of the large particles. The joint dynamics is described in a spacetime lattice by an Euler scheme for coupled oscillators with a friction term for the large particles. This lattice defines the mesoscale for the system. A scaling limit leads to a replacement of the mesoscale by the macroscale as follows: The very large initial velocities are assumed to be independent and they let a small particle interact with a large particle only for a short time, after which the particle escapes to infinity and new particles start interacting with the large particles. Thus, the initial spatial independence of the small particles causes independence in the time increments of the velocities of the large particles. Therefore, as the friction of the large particles and the speed of the small particles tend to infinity in this scaling limit, the positions of the large particles become the positions of spatially correlated Brownian motions whose correlations can be computed from the interaction force. A similar result holds for a system without friction, where the velocities of the large particles become spatially correlated Brownian motions.
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BESALÚ, MIREIA, and DAVID NUALART. "ESTIMATES FOR THE SOLUTION TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY A FRACTIONAL BROWNIAN MOTION WITH HURST PARAMETER H ∈ (⅓, ½)." Stochastics and Dynamics 11, no. 02n03 (2011): 243–63. http://dx.doi.org/10.1142/s0219493711003267.
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In this paper we establish precise estimates for the supremum norm for the solution of a dynamical system driven by a Hölder continuous function of order between ⅓ and ½ using the techniques of fractional calculus. As an application we deduce the existence of moments for the solutions to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(⅓, ½) and we obtain an estimate for the supremum norm of the Malliavin derivative.
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Kiran Kumar, R. V. M. S. S., and S. V. K. Varma. "MHD Boundary Layer Flow of Nanofluid Through a Porous Medium Over a Stretching Sheet with Variable Wall Thickness: Using Cattaneo–Christov Heat Flux Model." Journal of Theoretical and Applied Mechanics 48, no. 2 (2018): 72–92. http://dx.doi.org/10.2478/jtam-2018-0011.
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Abstract The hydromagnetic nanofluid flow over a stretching sheet in a porous medium with variable wall thickness in the presence of Brownian motion and thermophoresis is investigated. The heat transfer characteristics with variable conductivity are explored by using Cattaneo-Christov heat flux model. The governing non-linear ordinary differential equations are solved by using boundary value problem default solver in MATLAB bvp4c package. The impact of various important flow parameters on velocity, temperature and nanoparticle concentration as well as the friction factor coefficient and the rate of heat and mass transfer coefficients are presented and discussed through graphs and tables. It is found that the fluid velocity is accelerated with an increase in wall thickness parameter for n > 1, while the reverse trend is observed for n < 1.
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Tóth, Árpád, Dániel Bánky, and Vince Grolmusz. "Mathematical modelling and computer simulation of Brownian motion and hybridisation of nanoparticle–bioprobe–polymer complexes in the low concentration limit." Molecular Simulation 38, no. 1 (2012): 66–71. http://dx.doi.org/10.1080/08927022.2011.602217.
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