Magnetohydrodynamic Fluctuating Free Convection Flow of Second-Grade Fluid Flow in a Porous Medium

Abstract

The article’s objective is to study the magnetohydrodynamic fluctuating free convection flow of incompressible electrically conducting viscoelastic fluid in a porous medium in the presence of a pressure gradient. The flow is between two parallel plates; the lower plate is at rest, while the upper plate moves with a free stream velocity $U\left(t\right)$ . A uniform magnetic field of strength B0 is applied transversely to the fluid motion. The dimensional governing equations and physical initial and boundary conditions are nondimensionalized by inserting appropriate dimensionless variables. Furthermore, Lighthill’s method is used to obtain exact analytical solutions for the velocity, temperature, and concentration distributions. Finally, the influences of inserted parameters are studied through plots and discussed physically. The numerical results are calculated and presented in tabular form for skin friction. It is worth mentioning that when the viscoelastic parameter ${\alpha }_1$ tends to zero, the obtained general solution is reduced to Newtonian fluid, which shows the validity and correctness of our obtained exact solutions.