PARAMETER IDENTIFICATION IN TWO-DIMENSIONAL FINS USING THE BOUNDARY ELEMENT METHOD

Abstract

The identification of the ratio of the convective heat transfer coefficient and the thermal conductivity of two-dimensional polygonal fins on square and hexagonal (equilateral-triangular) pitches and the equivalent radial rectangular fin from a single additional boundary or internal temperature measurement is investigated. This problem is motivated by the facilities available at the University of Manchester, which at the moment make possible only a single temperature measurement, and is approached by combining the boundary element method (BEM) with a constrained nonlinear minimization technique. The accuracy, convergence, and stability of the proposed numerical method with respect to the level of noise added into the temperature measurement are carefully analyzed. The inaccuracy in the numerical results obtained using the combined BEM–constrained nonlinear minimization technique is around three and nine times less than the level of noise added into the extra temperature measurements located in the domain and on the boundary, respectively. The sensitivity analysis with respect to the location of the extra temperature measurement suggests that more accurate numerical approximates for the ratio of the convective heat transfer coefficient and the thermal conductivity of the fins investigated are retrieved for one additional boundary temperature measurement than for one extra internal temperature measurement. Furthermore, the BEM–constrained nonlinear minimization technique is also robust with respect to the initial guess for the minimization process. In addition, the inaccuracy in the prediction of the average of the space-dependent coefficient for only one additional internal or boundary temperature measurement ranges from 5.33% to 25.35%.