Assuming a background flow of velocity U = U(x) in the axial direction x of a circular cylinder with surface temperature distribution T (w) = T (w) (x) in a saturated porous medium, for the temperature boundary layer occurring on the cylinder three exactly solvable cases are identified. The functions {U(x), T (w) (x)} associated with these cases are given explicitly, and the corresponding exact solutions are expressed in terms of the modified Bessel function K (0) (z), the incomplete Gamma function I" (a, z) and the confluent hypergeometric function U(a, b, z), respectively. The correlation between the Nusselt number and the P,clet number as well as the curvature effects on the heat transfer are discussed in all these cases in detail. Some "universal" features of the exponential surface temperature distribution are also pointed out.