Investigation of the inverse problem in inclined lid-driven cavity with non-uniform heating on both side walls using the Levenberg-Marquardt algorithm

This paper employed the Levenberg-Marquardt Algorithm to solve the inverse problem of estimating non-uniform heating boundary conditions in a diagonal lid-driven cavity. The non-uniform thermal conditions on lateral walls were exponential, triangular, and sinusoidal-cosinusoidal. The finite volume method run in the Open FOAM software was used to solve the problem directly. The effect of the numbers and positions of sensors on estimation accuracy was examined for data collection, and sensitivity to noisy data was analyzed at different levels. The results showed that the proposed approach could estimate thermal boundary conditions with acceptable accuracy even when the measured data were noisy. The convergence analysis revealed that the model converged with a steep slope. This approach can be employed to determine the distribution of wall temperature in engineering uses, such as heating and cooling systems and heat transfer phenomena.