Numerical Estimation of Interfacial Heat Flux Using Inverse Heat Conduction Method

Abstract

Heat dissipation at the interface of mold and casting plays an important role to reduce the casting defects and for the production of better castings. Therefore, the study of interfacial heat transfer during solidification of castings is of utmost significance. This paper focuses on the numerical estimation of heat flux at the inner surface of a hollow cylinder by using the ‘inverse heat conduction’ method. The ‘inverse heat conduction’ method involves the estimation of boundary conditions from the knowledge of transient temperature distribution inside a heat-conducting body. In the present work, one-dimensional heat transfer in the radial direction of the cylinder is considered assuming insulation at the top and bottom. Conjugate gradient method with adjoint problem has been employed to solve the inverse problem of transient heat flux estimation. Inputs to the inverse problem are one-dimensional transient simulated temperature data within the cylinder. Simulated data are generated by solving the direct problem for four test functions of heat flux, viz., cosine, triangular, polynomial and step function. Random error terms having zero mean and two different standard deviation values are used to form simulated data. The estimated results have been compared with the exact values used to generate the simulated data. The estimated results are found to be in good match with the exact one for all the test functions with some deviations at the sharp corners. This proves the worth of the inverse method for the estimation of transient interfacial heat flux during metal casting.