Effects of transpiration on free convection in an annulus between concentric porous spheres (Q1345973)

An analysis is presented to study the effects of transpiration on free convection in an annulus between concentric porous spheres. A regular perturbation technique is applied to solve the steady-state Navier-Stokes equations of motion and the energy equation, whereby the stream-function and temperature are expanded in the form of power series in terms of the Rayleigh number \(Ra\), and injection/suction Reynolds number \(Re\). The analytical solution is valid for small values of \(Ra\) and \(Re\), and for all values of the Prandtl number \(Pr\). A finite-difference solution of the governing steady-state equations of motion and energy is also provided. The range of validity of the analytical solution is determined by comparison with the numerical solution.