A detailed numerical study of heat transfer to a fluid passing through a saturated porous medium is the subject of this study. The Green's function solution method is selected in order to accomplish this task. The interesting features of this methodology are the focus of this article. As a test case, primary consideration is given to the computation of heat transfer to a fluid flowing through a circular passage with impermeable walls filled with porous materials. The analysis includes the heating / cooling effects due to a temperature change at the wall of the passage. In addition, the contributions of frictional heating are examined.