A method for obtaining the general solution of diffusion-induced stress problems is proposed. The method, which is an extension of the Duhamel method, includes two situations. First, the boundary condition may contain not only spatial derivatives but also time integrals of the surface temperature. Second, the solution of the diffusion equation with time-dependent surface temperature can be expressed in terms of the known solutions with the lime variation of the surface temperature as a Dirac delta function, a constant, or a power function of time. The method is applied to three simple geometries, slab, cylinder, and sphere.
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