The case of heat transfer to an incompressible fluid of constant properties flowing turbulently within a pipe having constant wall temperature has been investigated analytically. Heat-transfer coefficients have been evaluated and compared to the coefficients obtained by Martinelli (1) for the same flow conditions in a pipe having a linear variation of wall temperature obtained from a constant heat-transfer rate along the pipe length. At low Prandtl numbers, such as obtained with molten metals, the ratio between the coefficients for these two cases may become as low as 0.73, with the coefficient for the constant-wall-temperature case being the smaller of the two. A simple equation of the Lyon type is indicated for the correlation of the present results.