. Combined free and forced convection in a two dimensional rectangular cavity with a uniform heat source applied on the right vertical wall is studied numerically. A circular heat conducting horizontal cylinder is placed somewhere within the cavity. The present study simulates a practical system, such as a conductive material in an inert atmosphere inside a furnace with a constant flow of gas from outside. Importance is placed on the influences of the configurations and physical properties of the cavity. The development mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by employing Galerkin weighted residual finite element method. In this paper, a finite element formulation for steadystate incompressible conjugate mixed convection and conduction flow is developed. The computations are carried out for wide ranges of the governing parameters, Reynolds number (Re), Richardson number (Ri), Prandtl number (Pr) and some physical parameters. The results indicate that both the heat transfer rate from the heated wall and the dimensionless temperature in the cavity strongly depend on the governing parameters and configurations of the system studied, such as size, location, thermal conductivity of the cylinder and the location of the inflow and outflow opening. Detailed results of the interaction between forced airstreams and the buoyancy-driven flow by the heat source are demonstrated by the distributions of streamlines, isotherms and heat transfer coefficient.