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Chapter 9
Thermal Stress in a Pipe

## Excerpt

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 [17]. The stress, strain, radial displacement relationships in cylindrical coordinates are treated in detail in Reference [17]. 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:

$d2T∕dR2+(1∕R)dT∕dR=0$

If the temperatures at the inner surface, Ti, and the outer surface, To, of the pipe wall are known, Eq. (9-1) can be solved by using the following boundary conditions:

$T=TiatR=Ri$

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