A new method to solve non-linear inverse heat transfer problems using regression tree method

In this paper, a new method is introduced to solve the inverse problems based on the repression tree (RT). To investigate the method’s efficiency to handle the nonlinear inverse heat transfer problems, two case study problems are done in this paper; first one is estimation of the free convection heat transfer coefficient of a horizontal copper cylinder and the second is estimation of the heat transfer coefficient in the surface of a quenched copper cylinder in a fluid using the cylinder temperature history. The input data were produced by solving the direct heat transfer equations of the cylinder and Churchill-chu imperial correlation and to test the method’s sensitivity to the random errors in input data, an artificial noise with normal distribution was added to the temperature results of the direct solution. The regression tree’s results were also compared with the sequential function specification (SFS) and the artificial neural network (ANN) methods. For the first case study problem, the root-mean-square error (RMSE) of RT, SFS, and ANN methods are 0.0129, 0.1231 and 0.0217, respectively, and for the second problem 8.844, 54.09 and 71.634 are the RMSE values. The comparison shows that the presented method has a good potential to solve the nonlinear inverse heat transfer problems with low error and time lag to online estimate the unknown parameter.