A second-order accurate finite-difference scheme based on a modification of the upwind method for the classical wave equation is proposed for transient forced convection in laminar channel flow. Stability analysis is performed, and the modified equation is established. The problem involving a step change in inlet temperature is studied for both slug and parabolic flow inside a parallel-plate duct. The accuracy of the numerical scheme is examined by comparing the results to the exact solutions available for the case of slug flow. Numerical results are presented for the average flow temperature and local Nusselt number as a function of position along the channel at different times, and the thermal wave propagation phenomena are physically interpreted.