Numerical Estimation of Heat Flux and Convective Heat Transfer Coefficient in a One Dimensional Rectangular Plate by Levenberg-Marquardt Method

Abstract

Background/Objectives: The objective of this paper is to simultaneously obtain heat flux and convective heat transfer coefficient for a one dimensional heat transfer problem through an inverse method. Methods/Statistical Analysis: The problem deals with a rectangular aluminium plate subjected to constant heat flux to a face, while convection and radiation occur on the opposite face. The temperature distributions with respect to space and time are calculated using full implicit “Finite Difference Method”. The geometry is simplified to a lumped system and fourth order “Runge-Kutta” is used to solve the governing equation which is then represented as a forward model. Sensitivity analysis has also been carried out in the present study. Finally, the unknown heat flux and convective heat transfer coefficient are estimated using “Levenberg- Marquardt Method” for the known temperature distribution.Findings:The two parameters discussed in the work cannot be measured and they can only be inferred by some means. As an inverse problem, Levenberg Marquardt algorithm, which is quite popular because of its gradient information, is used to estimate the unknown quantities for noisy data and also it has been proven that the method estimates with reasonable accuracy for different noise levels.Application/Improvements: Instead of using noise added surrogated data, one can perform experiments and obtain the temperature distribution which can be used as input to the inverse method. The inverse method can also be combined with probabilistic method in order to avoid getting trapped in the local minima/maxima.