The effects of suction/blowing and viscous dissipation on the steady non-linear viscous flow and heat transfer over a horizontal shrinking permeable surface of variable temperature or heat flux with a power-law velocity is numerically studied. The results complete those recently reported by Cortell [10] to the case of a shrinking surface. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of multiple solutions. Two cases are considered, namely prescribed surface temperature (PST) and prescribed heat flux (PHF). Dual and triple solutions are found to exist for certain parameters. (C) 2012 Elsevier Ltd. All rights reserved.