A Principal Component Analysis and neural network based non-iterative method for inverse conjugate natural convection

Inverse Heat Transfer Problems (IHTP) are characterized by estimation of unknown quantities by utilizing any given information of the system. In this study, the inverse problem of estimation of boundary heat flux for a given temperature distribution on the walls of a two dimensional square cavity with a finite wall thickness is considered. A non-iterative method is applied utilizing Artificial Neural Network (ANN) and Principal Component Analysis (PCA) to estimate the parameters that define the boundary heat flux. The forward model is numerically solved with Fluent 6.3 for known values of a linearly varying boundary heat flux and the temperature distribution thus obtained is utilized to train the ANN for the inverse model. A parametric study is carried out to determine the effect of the thermal conductivity of the top and bottom walls on the flow and temperature distribution in the cavity. PCA analysis is carried out to reduce the dimensions of the input data set for the inverse model. These reduced dimensions are used to train the network and due to low dimensionality of the input, the effort required to train the network is considerably less. The trained networks are finally used to estimate boundary heat flux for any desired temperature distribution on the top and bottom walls. Additionally, covariance analysis is carried out in order to estimate the required number of temperatures during an experiment, on the top and bottom walls for the prediction of heat flux with a reasonable accuracy. The inverse model with covariance analysis is compared with the inverse model with PCA and both the methods are found to be equally potent.