Analysis of Heat Transfer in a Water-Cooled Thick Plate Using Solutions of the Inverse Heat Conduction Problem

This paper presents an analysis of heat transfer in a thick-walled steel plate. During the experimental studies, one surface of the plate was heated, while the other, parallel to it, was cooled with water. Based on experimental studies, a curve of the heat transfer coefficient (HTC) was obtained and used in numerical tests. The solution to the inverse heat conduction problem (IHCP) for the plate presented in this paper is based on the finite element method and variational calculus. The computational model uses the quasi-Newton BFGS algorithm. Numerical tests examined the influence of the location of the temperature measurement point and the time step on the stability and accuracy of the IHCP solution. The quality of the solution was evaluated using norms describing the average and maximum errors of the calculated boundary conditions. The analysis results in the determination of the most favorable time step for various locations of the measurement point.