New Exact Traveling Wave Solutions for Fractional Order System ‎Describing the Second Grade Fluid through Medium with Heat ‎Transfer‎

Abstract

The aim of this paper is to determine the time-dependent MHD fractionalized three-dimensional flow of viscoelastic fluid in porous medium with heat transfer by traveling wave solution. The governing nonlinear partial differential equations are altered by utilizing the wave parameter ξ = lx + my + nz + ωtβ/Γ(β+1) into ordinary differential equations. The exact solutions are attained by applying a traveling wave method for two different cases. Here we discuss some precise cases, the solution of MHD Newtonian fluid in porosity can be obtained by substituting α1 → 0 in general solution. The impact of important governing parameters on the movement of a fluid is examined as well as the comparison of Newtonian and non-viscous fluids have been made by 2D and 3D graphical analysis.

Keywords

• magnetohydrodynamic (mhd)
• traveling wave method
• second grade fluid
• visco-elastic fluid
• 2d and 3d graphs‎