Three cases of laminar heat transfer with linear heat input in long rectangular channels have been treated by the method of orthogonal trigonometric series. The boundary conditions of the first two problems are those of laminar and slug flows with two opposite faces as secondary extended surfaces. A new fin parameter K defined as (wkm/bkf) has been shown to be the important factor in governing the Nusselt number. The third case discussed is the combined effects of free and forced-convection in vertical rectangular tubes.