It is shown that the equations governing the conjugate free convection boundary-layer flow on a vertical plate can be made dimensionless so as to involve only the Prandtl number. An efficient finite-difference scheme is developed to solve these equations and results are given for Pr = 0.72, 0.733 and 7.0, respectively. It is seen that an asymptotic expansion gives reliable results even at moderate values of x (dimensionless distance along the plate).