The analysis of the conjugate conduction and mixed convection heat transfer in a downward facing channel constituted by two non-isothermal extended surfaces, a base and an adiabatic shroud is numerically performed. The effect of fin conductivity, Grashof number, dimensionless clearance (C*) and dimensionless inter fin spacing (S*) is carried out through the evolution of the temperature, heat transfer and fluid flow fields. Computed results reveal that buoyancy induced cross-stream flow enhances flow by-pass through the clearance, especially for higher fin spacing. Moreover, it reveals that isothermal surface (infinite conductivity) leads to a significant overprediction of heat transfer as high as 134%, especially at lower fin spacing (S* = 0.1). In addition, enhancing dimensionless fin conductance parameter by 200%, an increase of heat transfer as good as 62% is noted for S* = 0.1. At higher fin spacing (S* = 0.3 and 0.5), effect of Grashof number on heat transfer found to be more profound at higher Grashof number (>10(5)). Zero clearance turns out to be the superior configuration. (C) 2014 Elsevier Ltd. All rights reserved.