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ISSN Print: 1064-2285
ISSN Online: 2162-6561
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AN EFFECTIVE ANALYTICAL METHOD IN INVERSE HEAT CONDUCTION PROBLEM WITH MEASURED TEMPERATURE TIME HISTORY AT REMOTE BOUNDARY
ABSTRACT
A hybrid analytical technique combining an exact solution method with the least squares method is applied to the boundary inverse heat conduction problem (IHCP) with measured time-varying temperatures at the remote boundary. At first, two time-varying heat flux functions were prescribed at both ends in order to derive an exact solution of the direct problem by the shifting function method instead of the integral transform. Secondly, by minimizing the least squares error between the experimental temperatures obtained from the remote boundary and the estimated temperatures generated from the exact solution, we can obtain the undetermined heat flux function at the heated end. Consequently, obtain the temperature and the heat flux distributions over the whole time and space domains. The proposed solution method avoids some troubles in traditional methods such as the inverse Laplace transform and tedious numerical schemes. One mathematical and the other experimental example are verified to depict the simplicity, efficiency, and accuracy of the method. Furthermore, the additional advantage of the methodology is that the temperature sensor can be directly set at the remote boundary without complex machining.
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