SIMILARITY SOLUTIONS IN FREE-CONVECTION BOUNDARY-LAYER FLOWS ADJACENTTO VERTICAL PERMEABLE SURFACES IN POROUS-MEDIA .1. PRESCRIBED SURFACE-TEMPERATURE

The equation which governs the similarity solution for free convection boundary-layer flow along a vertical permeable surface is considered in some detail. The solution is seen to depend on the power-law expone nt m and mass transfer parameter gamma. The range of existence of solu tion is considered first. It is shown that for fluid injection (gamma > 0) a solution exists for m > -1/2, independen of gamma, whereas for fluid withdrawal (gamma ( 0), the solution exists for m > m(0) (gamma) , where m(0) --> -1/2 as gamma --> 0 and m(0) --> -1 as \gamma\ --> in finity. Solutions for large mass transfer rates are then obtained. The solution for fluid withdrawal has the same form for all m > -1, where as for fluid injection the form of the asymptotic solution depends on the value of m. A solution valid for large m is then derived. Here it is seen that the form of solution is different in the three cases gamm a > 0, gamma = 0 and gamma < 0.