BOUNDARY ESTIMATION OF 2-D INVERSE HEAT CONDUCTION PROBLEM

Abstract

An inverse model is presented for determining the boundary estimation of two-dimensional heat conduction problem, the prior knowledge of the function is not available. This model is constructed from finite difference method of differential heat conduction equation based on that the temperature measurements are available over the problem domain. The iteration in the proposed model can be done only once and the inverse problem can be solved in a linear domain to identify the boundary condition. The linear least square method is adopted for the linear model thus iteration times can be limited to one cycle and the uniqueness of the solutions can be identified easily. For constructing numerical dicretize model FORTRON is used as programming language and output of this model is as input to another Programme made in MATLAB for linear least-square method. Results from the example confirm that proposed method is effective, only a few measuring points are sufficient to estimate the surface temperature when the measurement error are neglected. When the measurement errors are considered, more points are needed. Inverse model that is developed is implemented in an experimental model to find out the applicability of the developed model and method for inverse solution of multi-dimensional heat conduction problem. A copper slab, proper insulation with adequate heating method is proposed, accurate measurement with minimal effect of thermocouple on unknown boundary is taken carefully. For avoidance the effect of the error in the inverse solution for measuring temperature, selected points are sufficient to estimate boundary accurately. No need to consider convective heat transfer coefficient and radiation on the exposed surface to the atmosphere, to be estimated. Different configurations are selected to allocate the thermocouple for temperature measurement and results are compared with direct measurement of the unknown boundary. Results are supporting the developed model and method for inverse solution in a promising manner.