An analytical study was carried out to determine the effects of the degree of eccentricity of the two circles of an annulus on both local and average heat-transfer coefficients for turbulent flow of liquid metals. The study was based on the conditions of 1) heat transfer to or from the inner wall only, 2) uniform heat flux, and 3) fully developed temperature and velocity profiles. The scope of the investigation is indicated the following ranges of parameters studied: Reynolds number, 5 × 104 to 106 Peclet number, 368 to 8000 Ratio of outer to inner radius, 1.0 to 4.0 Eccentricity, up to 70% of maximum displacement. The results showed that eccentricity can have very great effects on both the local and average heat-transfer coefficients and consequently on the circumferential temperature variations around the annulus walls. At a radius ratio of 1.5 and a Peclet number of 1700, for example, the average coefficient was found to decrease 67 and 93%, when the eccentricity was increased from 0.0 to 0.30 and from 0.0 to 0.70, respectively. Under these conditions, the ratios of total circumferential temperature difference to the difference between the average inner-wall temperature and the stream bulk temperature were found to be 3.20 and 3.55, respectively.