On The Solutions Of Boundary Value Problem Arising In Mixed Convection

In this article, we are interested in studying solutions of the differential equation f''' + f f'' +beta f'(f' -1) = 0 on [0, +infinity) with beta >= 1, satisfying the boundary conditions f(0) = alpha is an element of R, f'(0) = b < 0 and f'(t)->lambda as t ->+oo, where lambda is an element of {0,1}. This problem arises in the study of mixed convection adjacent to surfaces embedded in a porous medium using the boundary layer approximation.