Approximate Analytical Solutions for Flow of a Third-Grade Fluid Through a Parallel-Plate Channel Filled with a Porous Medium

The flow of a non-Newtonian fluid through a porous media in between two parallel plates at different temperatures is considered. The governing momentum equation of third-grade fluid with modified Darcy’s law and energy equation have been derived. Approximate analytical solutions of momentum and energy equations are obtained by using perturbation techniques. Constant viscosity, Reynold’s model viscosity, and Vogel’s model viscosity cases are treated separately. The criteria for validity of approximate solutions are derived. A numerical residual error analysis is performed for the solutions. Within the validity range, analytical and numerical solutions are in good agreement.