An analytical solution for the steady-state temperature distribution in a cylinder undergoing uniform heating and nonuniform cooling is presented. The method of solution is a Fourier integral transform technique. The analysis shows that the Neumann series resulting from an integral equation can be well represented by a first-order approximation when the Peclet number is large. Furthermore, it is shown that the ratio of the Biot number to the square root of the Peclet number of the cooling zones is found to play an important role in governing the thermal response of the cylinder surface. The predicted results for the circumferential temperature distribution are compared to published experimental measurements for hot rolling and also existing analytical solutions for special cases. The agreement is found to be very good. By an appropriate superposition technique, the analysis presented may be easily extended to various heat sources and convective cooling zones at different locations of the cylinder surface.

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