Abstract
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 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. Plots of the flow patterns, velocity distributions, temperature profiles, local and overall heat transfer rates are presented for Pr = 0.7 and different values of Re, Ra, and the radius ratio λ. Results are shown over a range of values of Ra and Re such that the effects of mixed convection in the annulus can be clearly observed.
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