Computational Study of Non-Newtonian Thermal Convection From a Vertical Porous Plate in a Non-Darcy Porous Medium With Biot Number Effects

In this article, the nonlinear steady state boundary layer flow and heat transfer of an incompressible Eyring−Powell non-Newtonian fluid from a vertical porous plate in a non-Darcy porous medium is investigated. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a secondorder versatile, implicit finite-difference Keller box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, Eyring−Powell rheological fluid parameters (ε), the local non-Newtonian parameter based on length scale (δ), Prandtl number (Pr), Darcy number (Da), Biot number (Bi), Forchheimer parameter (Λ), and dimensionless tangential coordinate (ξ) on velocity and temperature evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. Validation with earlier Newtonian studies is presented, and excellent correlation is achieved. It is found that the velocity is reduced with increasing fluid parameter (ε) and Forchheimer parameter (Λ). But temperature is enhanced with increasing fluid parameter and Forchheimer parameter. Increasing fluid parameter δ is the local non-Newtonian parameter based on length scale x, and the Darcy parameter, Da, enhances the velocity but reduces the temperature. The increasing Biot number, Bi, is observed to enhance both velocity and temperature, and an increasing Prandtl number decreases the velocity and temperature.