Direct measurement of surface heat flux could be extremely challenging, if not impossible, in numerous applications. In such cases, the use of temperature measurement data from subsurface locations can facilitate the determination of surface heat flux and temperature through the solution of the inverse heat conduction problem (IHCP). Several different techniques have been developed over years for solving IHCPs, with different levels of complexity and accuracy. The filter coefficient technique has proved to be a promising approach for solving IHCPs. Inspired by the filter coefficient approach, a novel method is presented in this paper for solving one-dimensional IHCPs in a domain with temperature-dependent material properties. A test case is developed in COMSOL Multiphysics where the front side of a slab is subject to known transient heat flux and the temperature distributions within the domain are calculated through numerical simulation. The IHCP solution in the form of filter coefficients (q = FY) is defined and a genetic algorithm (GA) is used for the calculation of filter coefficients (one row of the filter matrix). The number of significant filter coefficients is determined through trial and error and the optimal number is selected for evaluating the solution. The resulting filter coefficients are then used to evaluate the surface heat flux for four different test cases and the performance of the proposed approach is assessed in detail. The results showed that the presented approach can result in finding optimal filter coefficients which can accurately estimate various types of surface heat flux profiles using temperature data from limited number of time steps and in a near real-time fashion.

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