Estimation of Time-Varying Heat Source for One-Dimensional Heat Conduction by Conjugate Gradient Method

Abstract

Inverse analysis using Conjugate Gradient (CGM) with adjoint problem is carried out for estimating time-varying heat source in one-dimensional heat conduction. Three types of source terms are considered: constant, linearly increasing, and linearly decreasing. The direct problem is first solved with actual heat source values and temperature data is obtained for the domain. The inverse problem is then solved for the estimation of heat source using few of these temperature data. In actual practice, temperatures are measured experimentally and hence contain measurement errors. Therefore, the random error have been added in the temperature data for simulating temperature readings taken from experiments. The direct problem, inverse problem, sensitivity problem, and adjoint problem equations are discretized by Finite volume method (FVM) and solved by developing MATLAB code. For constant and linear source, the estimated source values have the same behavior with actual source values but for linearly decreasing source, there is large deviation of estimated values from actual values.