EFFECTS OF TRANSPIRATION ON FREE-CONVECTION IN AN ANNULUS BETWEEN CONCENTRIC POROUS SPHERES

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-St okes equations of motion and the energy equation, whereby the stream-f unction and temperature are expanded in the form of power series in te rms of the Rayleigh number Ra, and injection/suction Reynolds number R e. The analytical solution is valid for small Values of Ra and Re, and all values of the Prandtl number Pr. A finite-difference solution of the governing steady-state equations of motion and energy is also prov ided. The range of validity of the analytical solution is determined b y comparison with the numerical solution. Plots of the flow patterns, velocity distributions, temperature profiles, local and overall heat t ransfer rates are presented for Pr = 0.7 and different values of Re, R a, and the radius ratio lambda. Results are shown over a range of valu es of Ra and Re such that the effects of mixed convection in the annul us can be clearly observed.