Analytic solution for heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects

An analytic approximate solution is presented for the natural convective dissipative heat transfer of an incompressible, third grade, non-Newtonian fluid flowing past an infinite porous plate embedded in a Darcy–Forchheimer porous medium. The mathematical model is developed in an (x,y)(x,y) coordinate system. Using a set of transformations, the momentum equation is rendered one-dimensional and a partly linearized heat conservation equation is derived. The viscoelastic formulation presented by Akyildiz [Akyildiz FT. A note on the flow of a third grade between heated parallel plates. Int J Non-Linear Mech 2001;36:349–52] is adopted, which generates lateral mass and viscoelastic terms in the heat conservation equation, as well as in the momentum equation. A number of special cases of the general transformed model are discussed. A homotopy analysis method (HAM) is implemented to solve, with appropriate boundary conditions, the coupled third-order, second degree ordinary differential equation for momentum and the second-order, fourth degree heat conservation equation.