Real Time Solution for Inverse Heat Conduction Problems in a Two- Dimensional Plate with Multiple Heat Fluxes at the Surface

Abstract

Abstract Heat flux measurement is essential in several industrial applications. While direct measurement of heat flux is not a simple task and sometimes is not even possible, measuring temperature is much easier and viable in a variety of applications. Heat flux estimation using temperature measurement data requires solving inverse heat conduction problems (IHCP’s). In the present paper, a real-time solution for a two-dimensional inverse heat conduction problem is presented. It is assumed that multiple unknown heat fluxes are applied at the bottom of a plate (y = 0) and the plate is insulated over other surfaces. Temperature sensors are located at the top of the plate. The number of temperature sensors has to be equal to or greater than the number of unknown heat fluxes. A two-dimensional inverse heat conduction problem with multiple unknowns needs to be solved in order to estimate the heat fluxes using temperature measurement data. A solution is developed based on minimization of sum of the squares of the errors between the estimated temperatures and measured values with respect to the unknown heat fluxes. Tikhonov regularization is applied to overcome the ill-posedness of the problem and achieve a stable solution. The solution is then written in a digital filter form which allows near real-time heat flux estimation. Two numerical experiments are developed using ANSYS to demonstrate the performance of the proposed solution. The presented solution can be used to calculate heat fluxes in a near real-time fashion in variety of applications including metal quenching. Real-time and accurate measurement of heat flux improves controllability of numerous industrial processes which lead to energy and cost savings.