Non-Darcian effect on mixed convection of non-Newtonian fluids along a vertical plate with variable heat flux in porous media

A nonsimilar boundary layer analysis is presented for the problem of non-Darcian mixed convection in power-law type non-Newtonian fluids along a vertical plate embedded in a fluid-saturated porous media. The surface heat flux is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter ξ and a pseudo-similarity variable η are introduced to cast the governing boundary layer equations into a system of dimensionless equations, which are solved numerically using finite difference method. The entire mixed convection regime is covered by the single nonsimilarity parameter ξ = Pe1/2x/(Pe1/2x+(Ra*x)1/(2n+1)) from pure forced convection (ξ, = 1) to pure free convection (ξ = 0). The present work examines the effects of non-Darcian flow phenomena and the variation of heat flux on mixed convection transport and demonstrates the variation in heat transfer prediction on different fluid types. It was found that the present problem depends on four parameters, namely the non-Darcian parameter Re , the mixed convection parameter ξ, the viscosity index n, and the heat flux expononant λ. The impact of these governing parameters on the surface heat transfer rate is discussed in great detail. Also represented velocity and temperature profiles are presented.