Based on Fourier expansion, an analytical solution is developed for the high Prandtl number heat transfer in both fully developed laminar and turbulent non-isothermal pipe flow. Both of the mathematical expressions of the temperature distribution and the local Nusselt number have been obtained. A parametric study illustrates the characteristics of high Prandtl number heat transfer in non-isothermal pipe flow in detailed. The solutions obtained can be used for the numerical construction of the solution to the more general problems of heat transfer in the developed turbulent wall-bounded shear flows.

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