The analyses of Poppendiek and Palmer for laminar and turbulent flow between parallel plates with uniform internal heat generation have been extended to the case of internal heat generation decreasing parabolically with distance from the wall. It is shown that the effect of this nonuniformity is to increase the temperature of the wall with respect to the bulk temperature. Thus, the wall cooling required to maintain a given wall temperature is greater with the nonuniform than with the uniform internal heat generation.