Laminar mixed convection over an isothermal vertical plate has been modeled with first-order momentum and thermal discontinuities at the wall. Local non-similarity transformations, using two non-similarity variables, have been applied to study the mixed convection boundary layer problem. Numerical solutions were obtained for varying conditions in assisting flow based on the three-equation model. Non-similar velocity and temperature distributions within the boundary layer have been presented. Results are also presented for the effect of non-continuum upon wall slip velocity, temperature jump, wall shear stress and boundary layer thickness in both gaseous and liquid flows for Gr(x)/Re-x(2) varying from 0.0001 to 8.0. (C) 2009 Elsevier Ltd. All rights reserved.