Sd. Gulwadi et Af. Elkouh, EFFECTS OF TRANSPIRATION ON FREE-CONVECTION IN AN ANNULUS BETWEEN CONCENTRIC POROUS SPHERES, Journal of engineering mathematics, 28(6), 1994, pp. 483-499
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.