Papers by Keyword: Brownian Motion

Abstract: The onset of convection in a horizontal nanofluid layer of finite depth is a subject that can never be over-emphasized as it plays a significant role in controlling the transport phenomenon within a nanofluidic medium. This body of knowledge led to a doubtful report in 2014 by Nield and Kuznetsov concerning some obtained equations and established results. However, the accuracy of the thermal stability characteristics is strongly dependent on the used model as well as the employed methodological procedure. In this report, countable models are suggested as a better improvement of the aforementioned analysis. Either mathematical or technical point of view, it is worth concluding that the approximate analytical results elaborated by Nield and Kuznetsov can be improved properly by using the models presented herein.

Abstract: Oblique stagnation point flow of a Casson nanofluid over a heated stretching surface is examined under the influence of variable fluid properties. The impact of variable fluid properties on the flow field is examined by taking a convective boundary condition into account. Momentum, energy and concentration equations are transformed into the non-linear ordinary differential system through suitable similarity transformations and are solved analytically via Optimal Homotopy Analysis Method (OHAM). Effect of pertinent parameters on dimensionless velocity, temperature and concentration are depicted graphically. Numerical values of skin friction, Nusselt number and Sherwood number have been calculated for various parameters. The results indicate that the axial velocity decreases with an increase in variable viscosity whereas the dual impact of variable viscosity is observed on transverse velocity.

Abstract: 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.

Abstract: Dual solutions for the time-dependent flow of a Prandtl fluid containing nanoparticles along a stretching/shrinking surface are presented. The nano Prandtl fluid fills the porous stretching/shrinking surface. The Buongiorno model is employed by accounting Brownian motion and thermophoresis slip mechanisms in the analysis. The relevant nonlinear problem is treated numerically via Runge-Kutta-Fehlberg scheme. The flow profiles are scrutinized with respect to the different governing parameters. Results of this study indicate that the temperature boundary layer thickness increased due to the influence of nanoparticles.

Abstract: In this paper, we investigate the influence of non uniform heat source/sink and thermal radiation on magnetohydrodynamic flow past a slendering surface with the influence of thermophoresis and Brownian effects. The governing non-linear flow problem is solved numerically by the aid of RK based shooting method. Influence of dimensionless parameters on the velocity, temperature and concentration profiles are explored through graphical illustrations. Skin friction factor, Nusselt and Sherwood numbers are presented and discussed. Rising values of magnetic and thermophoresis parameters increase the thermal and concentration distributions. Boosting values of Brownian motion parameter enhance the Nusselt and Sherwood numbers.

Abstract: A study on the thermophoresis and Brownian moment effects on magnetohydrodynamic flow of dissipative Casson fluid over a stretching sheet is considered. The governing equations of the flow, heat and mass transfer is transformed to ordinary differential equations by using similarity transformation. Numerical solutions of these equations are obtained by using shooting technique. The influence of pertinent parameters on the velocity, temperature and concentration profiles along with friction factor, local Nusselt and Sherwood numbers are discussed and presented through graphs and tables. It is found that the heat and mass transfer rate is high in steady flow when compared to unsteady flow.

Abstract: In this paper, we investigate the combined effects of Brownian motion, thermophoresis and Cattaneo-Christov heat flux on Casson nanofluid boundary layer flow over a stretching cylinder. The governing partial differential equations (PDEs) are obtained and transformed into a system of ordinary differential equations (ODEs) by employing appropriate similarity solution. The model nonlinear boundary value problem is tackled numerically using fourth-fifth order Runge-Kutta integration scheme with shooting technique. Effects of various thermophysical parameters on the velocity, temperature and concentration profiles as well as skin friction and Sherwood number are presented graphically and discussed quantitatively. It is found that thermal relaxation parameter minimizes the temperature field and boosting the rate of heat transfer per unit volume. This heat flux conditions are very useful for thermal transport control in manufacturing and chemical industries.

Abstract: This study covers a numerical investigation of gyrotactic microorganisms contained MHD flow over a vertical plate bearing thermal radiation, thermophoresis, Brownian motion, chemical reaction and inclined magnetic field effects. With the assistance of similarity transforms, the derived governed equations are transformed as set of ODEs and solved numerically by R-K and Newton’s methods. Graphs are exhibited and explained for various parameters of interest. For engineering interest, we mainly talked about the Skin friction coefficient, reduced Sherwood, Nusselt numbers and density of motile microorganisms. We noticed a rise in the heat transfer rate of motile microorganisms for rising values of the thermophoresis and Brownian motion parameters. Increasing values of the aligned angle hikes the drag force.

Abstract: Mathematical modeling to study the effect of nonlinear thermal radiation on Casson nanofluid flow between parallel plates is established. Second order velocity slip condition is implemented at the boundary of the lower plate. An appropriate transformation is applied to alter the PDEs into ODEs and then tackled numerically by employing RKF-45. The consequence of several prevailed parameters on the Casson nanoliquid velocity components, temperature and concentration fields are portrayed graphically and deliberated in detail. Velocity component decreases near the region of lower plate while it increases along the upper plate region for magnetic and slip parameter whereas opposite behavior is obtained for the Casson parameter for the same component.

Abstract: In the framework of the generalized Kramers theory of physical and chemical kinetics the relation for the decay rate of the metastable state is obtained. The peculiarity of the system is the ratio of the potential barrier height to temperature of the system. This ratio is much less than unity. To study the process we introduce the concept of the effective square of the potential barrier. It is shown that in the limiting case the obtained relation becomes the standard formula (Kramers formula) for the decay rate.