Fluid flow and heat transfer in a plate-fin and tube heat exchanger were studied, using a fundamental model consisting of a pair of parallel plates and a square cylinder passing perpendicularly through the plates, which simulated plate-fins and a tube, respectively. The analytical results were reported about the heat transfer in a laminar region for Reynolds number R_e=200 and Prandtl number P_r=0.71. Heat transfer characteristics under a constant wall heat flux condition were show in terms of distributions of temperatures and local Nusselt numbers, and the heat transfer mechanism was investigated in detail.