Theoretical equations have been derived for calculating heat transfer coefficients for a fluid flowing through a concentric annulus for the following two cases: (A) constant and equal heat fluxes from both walls, and (B) constant, but unequal, heat fluxes from the walls, with equal wall temperatures at a given axial position along an annular channel. In the derivations, the conditions of fully-established velocity and temperature profiles, and independence of physical properties with temperature variation across the flow channel, were assumed. The only geometrical parameter in this general case is the radius ratio r2/r1, and in the study it was varied from 1.0 to 10.0.