Inverse boundary problem for estimating the boundary conditions of a radiant enclosure using the measurement of temperature on a solid object within the enclosure

Abstract

Paper presented at the 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, 19-21 July, 2010.

In this paper, we present an inverse analysis to estimate the thermal boundary conditions over a two-dimensional radiant enclosure from the knowledge of the measured temperatures for some points on a solid object within the enclosure. The conduction heat transfer in the solid object and the radiative heat transfer between the surface elements of the enclosure are formulated by the finite volume method and the net radiative method, respectively. The resultant set of noulinear equations, including the energy equation for the solid object, the energy conservation along the boundary surface of the solid object, and the radiative exchange between surface elements of the radiant enclosure, are solved by the Newton's method The inverse method for estimation of boundary conditions over the radiant enclosure surface is solved by the conjugate gradient method through minimizing an objective function which is expressed as the sum of square residuals between measured and estimated temperatures for some sampling points on the solid object The performance of the present technique of inverse analysis is evaluated by several numerical experiments, and the effects of some parameters, such as the number and the positions of sensors, and the measurement errors over the accuracy of the inverse solution are investigated. The results show that the temperature profile over the wall of the radiant enclosure can be recovered accurately, even for sharp gradient profiles and noisy input data.