Study Of Nonlinear Convection Research Articles

Finite Difference Simulation of Nonlinear Convection in Magnetohydrodynamic Flow in the Presence of Viscous and Joule Dissipation over an Oscillating Plate

Engineers and researchers are interested in the study of nonlinear convection, viscous dissipation, and Joule heating in various flow configurations due to their various applications in engineering processes. That is why the present study deals with the influence of nonlinear convection, viscous, and Joule dissipation of the temperature and velocity profile of incompressible fluid over a flat plate. In this study, the magnetic field acts perpendicular to the fluid flow and is supposed to be of uniform magnitude. Further, the Newtonian fluid, which is electrically conducting, passes over an infinite vertical flat plate under an oscillatory motion. The term representing the influence of the nonlinear convection phenomenon is integrated into the Navier–Stokes equation. The governing equations of the mentioned study were modeled in the form of non-linear PDEs and modified as non-dimensional equations via appropriate scaling analyses, which resulted in coupled and non-linear PDEs. For the numerical solution of the transformed non-linear PDEs, the finite difference method was applied. Finally, we present the effects of various flow parameters via graphical illustrations.

Study of nonlinear convection in a sparsely packed porous medium using spectral analysis

Nonlinear study cellular convection in a sparsely packed fluid saturated porous medium is investigated, considering the Brinkman model, using the technique of spectral analysis. It is established how the Brinkman model with free-free boundaries generalizes the study of convection in a porous medium in the sense that it yields the results tending to those of viscous and Darcy flows respectively for very small and very large values of the permeability parameter σ2. It also provides results for the transition zone (i.e. 102<σ2<103). The cross-interaction of the linear modes caused by non-linear effects are considered through the modal Rayleigh number Rγ. The possibility of the existence of steady solution with two self-excited modes in certain regions is predicted. The similarities of present analysis with and advantages over that of the power integral technique are brought out. A detailed discussion of the heat transport, with the effect of permeability thereon, is made. The theoretical values of the Nusselt number are found to be in good agreement with experimental results.