Estimation of transient boundary flux for a developing flow in a parallel plate channel

Abstract

Purpose -The purpose of this paper is to develop a numerical model for estimating the unknown boundary heat flux in a parallel plate channel for the case of a hydrodynamically and thermally developing laminar flow. Design/methodology/approach -The conjugate gradient method (CGM) is used to solve the inverse problem. The momentum equations are solved using an in-house computational fluid dynamics (CFD) source code. The energy equations along with the adjoint and sensitivity equations are solved using the finite volume method.Findings -The effects of number of measurements, distribution of measurements and functional form of unknown flux on the accuracy of estimations are investigated in this work. The prediction of boundary flux by the present algorithm is found to be quite reasonable. Originality/value -It is noticed from the literature review that study of inverse problem with hydrodynamically developing flow has not received sufficient attention despite its practical importance. In the present work, a hydrodynamically and thermally developing flow between two parallel plates is considered and unknown transient boundary heat flux at the upper plate of a parallel plate channel is estimated using CGM.

Calculation of Heat Flux Across the Hot Surface of Continuous Casting Mold Through Two-Dimensional Inverse Heat Conduction Problem

“…The difference could attribute to the thermocouples arrangement in computed domain, as the accuracy of 2D-IHCP is not only affected by the algorithm but also determined by the number of thermocouples and their locations. [25,35,37] Generally, the more measurements taken and closer to the boundary of conditions, the more precise of the recovered results would be.…”

“…[19,30,31] The reason for CGM algorithm to be used here to solve the 2D-IHCP is because it is one of the most effective techniques for the inverse problem and has been successfully applied in many studies. [32][33][34][35][36][37] The merits of CGM are as follows: (1) it does not need to determine the regularization parameter, and (2) it is very convenient to be extended from one case to other similar cases. This study would be conducted in the following way: first, the 2D-IHCP model was built based on the responding temperatures detected from two columns of the thermocouples that embedded in the mold wall, where the responding temperatures measured by the first column of thermocouples (close to the mold hot face) were used for minimizing the objective function of inverse calculation, and the other ones were used as the boundary condition instead of estimating the heat transfer coefficient by convection of the water coolant, which is similar to other mold simulator experiments.…”