Nusselt numbers have been calculated for bilateral heat transfer to fluids flowing in annuli. The following four cases have been treated: (A) uniform and equal heat fluxes from both walls, under the condition of slug flow; (B) equal wall temperatures at the same axial location and uniform but unequal heat fluxes from the walls, under the condition of slug flow; (C) same as case (A), except flow is laminar; and (D) same as (B), except flow is laminar. In the calculations, the following assumptions were made: (a) the conditions of fully-established velocity and temperature profiles, and (b) the independence of physical properties with temperature variation across the flow channel. The Nusselt numbers, independent of Reynolds and Peclet numbers, are given as functions of the geometrical parameter, r1/r2, which varied from zero to unity, the former limit representing the case of a round pipe and the latter that of parallel plates. For case (A), the heat-transfer coefficient for the heat transferred from the inner wall becomes infinite at r1/r2 = 0.214 because the inner wall surface temperature and the bulk temperature of the flowing fluid are equal under these conditions. For case (C), this happens at r1/r2 = 0.1685. The differences in Nusselt numbers between cases (A) and (B), and between cases (C) and (D), are appreciable, attaining maxima around r1/r2 = 0.20. At r1/r2 = 1, cases (A) and (B), of course, become identical, as do cases (C) and (D). Finally, equations are given for calculating heat-transfer coefficients for each wall, for the general case where the heat fluxes from the annulus walls are uniform but not necessarily equal.