Atesmen, M. Kemal. "Thermal Stress in a Pipe." Everyday Heat Transfer Problems: Sensitivities to Governing Variables. Ed. M. Kemal Atesmen. ASME Press, 2009.
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Thermal stresses generated by temperature variations in the wall of a pipe have been studied extensively in Reference by Timoshenko, S. and J. N. Goodier . The stress, strain, radial displacement relationships in cylindrical coordinates are treated in detail in Reference . To calculate the thermal stresses in a pipe wall, the temperature distribution in the pipe wall has to be known. The temperature distribution in the radial direction, R, can be obtained from a steady-state, one-dimensional heat conduction equation in cylindrical coordinates. By assuming constant thermophysical properties and no heat sources in the pipe wall, the heat conduction equation for the temperature distribution, T, is:
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