Fractional modelling of heat transfer through porous media for incompressible MHD fluid flow with laplace transform approach

Abstract

In this paper, we investigate a fractional model of an incompressible and unstable MHD viscous fluid with heat transfer pass across a porous medium. To quantify this, we used a vertical plate with a fluid connected to it. When an angled magnetic field is supplied, the plate moves in its own plane. The required nonlinear partial differential equations are used to convert the governing equations into a non-dimensional form. To find the solution of the simplified nonlinear partial differential equations, the Constant Proportional Caputo fractional derivatives are utilized. The Laplace transform techniques are used to simplify the non-dimensional governing equations of the model and the boundary conditions we discovered explicit formulations for each field. The resultant equation is solved for momentum and energy, and the solutions are given as series. The performance of velocity and temperature values are graphically plotted using MATHCAD software. In numerical simulation, the Local Skin fraction and local Nusselt number are considered and evaluated additionally. It has been concluded that the fluid’s temperature and velocity decreases by increasing the value of fractional parameter. It has also been found that the velocity and temperature increase with increasing values of$Q_0$.