Heat flux and temperature determination in a cylindrical element with the use of Finite Volume Finite Element Method

Abstract

This paper presents a method to determine the local heat flux and temperature distribution on a thick cylindrical surface through the solution of an inverse heat conduction problem (IHCP). In particular, the method is developed for cases when traditional measurements cannot be performed due to difficulties in accessing the surface; a common situation in engineering and research practice. In particular, inverse methods are sensitive to measurement errors, for example, those caused by a mispositioned temperature sensor on a solid body. Hence, this paper proposes a method that is insensitive to, and can accurately be used, even in presence of these errors. The proposed method lowers the error in the local heat flux and temperature determination hence making the inverse methods more reliable.The proposed method is based on the finite element-finite volume method (FEMFVM) approach. It is tested using measurement data obtained on a laboratory stand. The measurements are performed using thermocouples installed inside a solid cylindrical wall.The method is tested and compared to other numerical methods, including the finite volume method (FVM) and the finite element method (FEM). Extensive additional calculations are carried out to evaluate the impact of random measurement errors on the accuracy of the proposed method.The calculation results prove that the new method is suitable and useful in the case of complex geometrical shapes and enables accurate determination of parameters such as the heat flux, and the outer surface temperature.