The heat-transfer coefficient between fluid and tube wall in turbulent flow depends upon the physical and thermal properties of the fluid. When density changes across the diameter of the tube are large (for example, when the fluid is near the critical point), the variable density can affect the transfer of momentum and heat. Equations are developed for predicting the magnitude of this effect on the heat-transfer coefficient. Deissler’s [5] expressions for the eddy diffusivity are employed in solving the equations for heat and momentum transfer. For flow in vertical tubes large density variations can also affect the heat transfer by inducing natural convection. By considering the influence of body forces on the shear stress, equations are derived to predict the effect of natural convection on the heat-transfer coefficient for turbulent flow. The results indicate that the effect is significant only for relatively high Grashof numbers and low Reynolds numbers. Such conditions may be encountered in flow of a fluid near its thermodynamic critical point. The derived equations are applied for carbon dioxide flow in the critical region under the conditions for which experimental data were measured by Bringer and Smith [2]. Because of the high Reynolds and low Grashof numbers, natural convection is not significant. However, the effect of the large density variations is found to be significant, and the predicted results agree well with the experimental data.