A comparative study of two methods for identifying the solid-liquid interface in a cold storage system

In this article, shape identification in inverse heat conduction problems is applied to estimate the solid liquid interface in a cold storage system. The inverse algorithm consists of direct, inverse analysis, and gradient-based optimization method that iteratively estimates the unknown shape. The direct analysis used the finite-element method in the unstructured grid system to solve the direct heat conduction problem. The inverse analysis is based on recording temperature data on the outer surface of the storage capsule that calculates the objective function with calculated and measurement temperatures. The employed gradient-based optimization method is constructed using the adjoint and sensitivity equations that are used to calculate the gradient of the objective function and the optimal step size, respectively. Both the control point method (CPM) and proposed method (shape variables method) are used to estimate the unknown shape and to compare themselves. The effects of the number of sensors, grid sizes, shape scales, initial shapes, and noisy temperature data on the solution are investigated. The results show that the proposed method is more efficient in the prediction of the solid liquid interface in comparison with CPM.