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

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+۱) 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 α۱ → ۰ 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 ۲D and ۳D graphical analysis.

Keywords:

Magnetohydrodynamic (MHD) , traveling wave method , Second grade fluid , visco-elastic fluid , ۲D and ۳D graphs‎