Stochastic Analysis of Temperature Distribution in a Solid With Random Heat Conductivity

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Abstract
Stochastic temperature distribution in a solid medium with random heat conductivity is investigated by the method of perturbation. The intrinsic randomness of the thermal conductivity k(x) is considered to be a distribution function with random amplitude in the solid, and several typical stochastic processes are considered in the numerical examples. The formulation used in the present analysis describes a situation that the statistical orders of the random response of the system are the same as those of the intrinsic random excitations, which is characteristic for the problem with extrinsic randomness. The maximum standard deviation of the temperature distribution from the mean value in the solid medium reveals the amount of unexpected energy experienced by the solid continuum, which should be carefully inspected in the thermal-failure design of structures with intrinsic randomness.

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