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 plate and a square cylinder passing perpendicularly through the plates, which simulated plate-fins and a tube, respectively. The analytical results were reported for the heat transfer in a laminar region for Reynolds number R_e=200 and Prandtl number R_r=0.71. Heat transfer characteristics under the constant wall heat flux condition were shown in terms of distributions of temperatures and local Nusselt numbers, and the heat transfer mechanism was investigated in detail.