The coupled conduction and convection heat transfer from the protruding heat source in a vertical channel is numerically investigated. Conjugate solution of the two-dimensional energy equation is obtained for the incompressible air flow over the rectangular block with local heat source. It was found that several recirculation zones and separation bubble near the block were related to Re and Gr. And the results show that fractions of the heat transfer through each of the block face, maximum temperature of the block and the relative effect of each parameter on the maximum temperature and heat transfer.