An analysis is performed to study the effect of non-uniform slot injection (suction) into steady two-dimensional and axi-symmetric laminar boundary layers with variable viscosity and Prandtl number. Non-similar solutions have been obtained from the starting point of the streamwise co-ordinate to the exact point of separation. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation have been overcome by applying an implicit finite difference scheme with the quasi-linearization technique and an appropriate selection of finer step size along the streamwise direction. The results indicate that the separation can be delayed by non-uniform slot suction and also by moving the slot downstream but the effect of non-uniform slot injection is just the opposite. The heat transfer rate is found to depend strongly on viscous dissipation but the skin friction is little affected by it. © 2003 Elsevier Science Ltd. All rights reserved.