The mixed convection boundary-layer flow on a vertical surface heated convectively is considered when a constant surface heat transfer parameter is assumed. The problem is seen to be chararterized by a mixed convection parameter . The flow and heat transfer near the leading edge correspond to forced convection solution and numerical solutions are obtained to determine how the solution then develops. The solution at large distances is obtained and this identifies a critical value of the parameter . For a solution at large distances is possible and this is approached in the numerical integrations. For the numerical solution breaks down at a finite distance along the surface with a singularity, the nature of which is discussed.