Analytical Method of Two Dimensional Inverse Heat Conduction Problem using Laplace Transformation : Effect of Measuring Point Number

Abstract

An analytical method has been developed for inverse problem of two-dimensional heat conduction by using Laplace transform technique. The inverse problem is solved only for two unknown surface conditions and the other surfaces are insulated in a finite rectangular body. In actual measurement, number of measuring points in a solid is usually limited so that the number of the measured temperatures required to approximate the temperature change in it is short to obtain an approximate function with a half polynomial power series of time and the Fourier series of eigen function. In order to clear this shortage, the third order Spline method is recommended to interpolate unknown temperature at a different point from the measured temperatures and a minimal requirement of the temperature measurements is also recommended to be 8 points enough. The results calculated thereby for some representative cases show that the surface temperature and the surface heat flux can be predicted at good agreement compared with the given surface condition.