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In this paper, the numerical results are presented by using Lie group transformations, to be more efficient and sophisticated. To solve various fluid dynamic problems numerically, we present the numerical results in a field of velocity and distribution of temperature for different parameters regarding the problem of radiative heat, a magnetohydrodynamics, and non-Newtonian viscoelasticity for the unstable flow of optically thin fluid inside a channel filled with nonuniform wall temperature and saturated porous medium, including Hartmann number, porous medium and frequency parameter, and radiation parameter, with a comparison of the corresponding flow problems for a Newtonian fluid. Moreover, the effects of the pertinent parameters on the friction coefficient of skin and local Nusselt number were discussed numerically and also illustrate that graphically.