A survey of the developments in heat transfer studies of non-linear inelastic as well as elastic fluids in tubes is given. Experimental findings concerning heat transfer enhancement characteristics of viscoelastic aqueous polymer solutions are very significant. Specifically, it is reported that heat transfer results for viscoelastic aqueous polymer solutions are drastically higher than those found for water in laminar flow in rectangular ducts. A number of investigators suggested that the high experimental heat transfer values were due to secondary flows resulting from the elasticity of the fluids. In this context recent results concerning the fully developed thermal field in constant pressure gradient driven laminar flow of a class of viscoelastic fluids characterized by single mode, non-affine constitutive equations in straight pipes of arbitrary contour ∂D is reviewed. Heat transfer enhancement due to shear-thinning is identified together with the enhancement due to the inherent elasticity of the fluid. The latter is the result of secondary flows in the cross-section. Increasingly large enhancements are computed with increasing elasticity of the fluid as compared to its Newtonian counterpart. Large enhancements are possible even with dilute fluids. Isotherms for the temperature field are presented and discussed for several non-circular contours such as the ellipse and the equilateral triangle together with heat transfer behavior in terms of the Nusselt number Nu.

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