ISSN Online: **2379-1748**

ISBN Flash Drive: **978-1-56700-431-1**

ISBN Online: **978-1-56700-430-4**

First Thermal and Fluids Engineering Summer Conference

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

## Resumo

Accurate measurement of heat flux is important in numerous industrial 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 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). It is also assumed that the plate is insulated over the other surfaces and temperature sensors are located at the top of the plate. The number of temperature sensors has to be equal or greater than the number of unknown heat fluxes. A twodimensional 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 known values with respect to the unknown heat fluxes. Tikhonov regularization is applied to achieve a stable solution. The solution is then written in a digital filter form which allows near real-time heat flux estimation. Several numerical experiments are developed in ANSYS and used to demonstrate the validity of the proposed solution. The developed 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 the industrial processes which lead to energy and cost savings.