Shape identification of frost formation around a refrigeration tube via adjoint-based optimization method

In this paper, the shape identification method in the Inverse Heat Conduction Problems (IHCP) is applied to estimate the shape of frost on a refrigeration tube. The inverse algorithm consists of direct, inverse analysis and gradient-based optimization method. The direct analysis used Finite Element Method (FEM) in an unstructured grid system to solve the direct heat conduction problem. The inverse analysis is based on recording temperatures data on surface of refrigeration tube that calculates the objective function. The employed gradient-based optimization method is constructed using the adjoint, sensitivity, and conjugate gradient method that are used to calculate the gradient of objective function, step size, and minimizing the objective function, respectively. The effect of shape scales and noisy temperature data are investigated. The results show that this proposed inverse algorithm is more efficient in prediction of frost formation.