A technique for analyzing two-dimensional thermal fields in hollow cylinders is presented when the cylinders are assembled of a number of perfectly connected coaxial layers made of dissimilar materials exhibiting arbi...
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A technique for analyzing two-dimensional thermal fields in hollow cylinders is presented when the cylinders are assembled of a number of perfectly connected coaxial layers made of dissimilar materials exhibiting arbitrarily continuous radial variation of their thermophysical properties. Making use of the direct integration method allows for reducing the original heat conduction equation with stepwise variable coefficients to the integral equations of the second kind with solution constructed through the resolvent-kernel technique in the form of explicit dependences on the applied thermal loading on the inner and outer circumferences of the cylinders and the internal heat sources. This approach allows for constructing a solution from the "single-solid" standpoint and thus is efficient for an arbitrary number of layers exhibiting inhomogeneous properties. On the other hand, the application of this technique does not involve the generalized-derivative apparatus typical for the use of single -solid methods. The applicability of the proposed solution for the verification of homogenization models for stratified cylinders is demonstrated by the considered case studies.
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