The first and second laws of thermodynamics have been utilized to optimize the convective heat transfer in a packed duct with constant wail temperatures. Introducing packing into the fluid-flow passage increases the wall-to-fluid heat transfer considerably and hence reduces entropy generation due to heat transfer across: a finite temperature difference; at the same time, entropy generation due to fluid-flow friction increases. Minimization of the net entropy generation yields the criterion for system optimization. It is shown that the entropy-generation rate, a path-dependent property induced by enhancement of convective heat transfer in a packed duct, may be minimized through proper selection of operating conditions and design parameters of the system.