The use of a heat transfer coefficient as a general parameter of forced convection heat transfer is shown to be unsatisfactory, and an alternative correlation making explicit allowance for pipe wall temperature variations is derived. In the derivation it is assumed that radial heat transfer in the fluid may be represented as due to an effective conductivity, and that longitudinal heat transfer is by fluid transport only. The effective conductivity and the fluid forward velocity may be arbitrary functions of radical distance. The correlation shows that the difference between wall and mean fluid temperature at any distance along the tube is composed of an entry condition term which diminishes with distance along the pipe, plus a series of terms due to temperature variations along the pipe wall. The values of the coefficients of these terms have been calculated for two ideal cases, and experimental values are being sought. Some implications of the correlation are discussed.