Natural convection of non-Newtonian fluids through permeable axisymmetric and two-dimensional bodies in a porous medium

The present work concerns the natural convection of non-Newtonian power-law fluids with or without yield stress over the permeable two-dimensional or axisymmetric bodies of arbitrary shape in a fluid-saturated porous medium. Using the fourth-order Runge-Kutta scheme method and shooting method we obtain the local non-similarity solutions. The parameters that include the dimensionless yield stress Ω, permeable constant c and power index n are studied, and the heat flux and the wall temperature are taken into consideration as variables. The local non-similarity solutions are found to be in excellent agreement with the exact solution. It is found that the results depend strongly on the values of the yield stress parameter, the wall temperature distributions, the lateral mass flux rate, and the heat flux at the boundary.