The conjugate heat transfer characteristics are studied for backward-facing step flow problem. Alternating direction implicit (ADI) method is used to find the steady state results for hydrodynamic solution using stream function-vorticity formulation. The energy equation in the fluid region and in the solid region are solved simultaneously. The conjugate effects are studied in connection with four parameters viz. Re, Pr, k and b. Effect of four parameters on local Nusselt number, interface temperature and average Nusselt number are presented in detail. The results are compared with non-conjugate case. (c) 2006 Elsevier Ltd. All rights reserved.