A Global Time Treatment for Inverse Heat Conduction Problems

Abstract

A new global time treatment is proposed and demonstrated for inverse heat conduction problems. This exposition illustrates the methodology by carefully and meticulously investigating the classic Beck’s problem. It is shown that accurate and stable numerical results occur without resorting to any stabilizing scheme beyond the implementation of a global basis representation for the temperature distribution. As a global time method the entire space-time domain is resolved in a simultaneous fashion. The approach is also extendable to multidimensional and multiprobe situations without difficulty. In direct problems the method has been successively applied to initial value problems, Volterra integral equations, and parabolic and hyperbolic partial and integro-partial differential equations.

Global space–time multiquadric method for inverse heat conduction problem

“…The first test problem of one-dimensional IHCP is the classical Beck's problem [4], in which a triangular surface heat flux q(t) is imposed at x = 0 as…”

“…However, in many practical situations, not all the necessary conditions are available due to incomplete understanding of the physical process, or technical difficulties associated with direct measurement. And thus the IHCP problems arise, which may involve the estimation of the system geometry [1], the thermal properties [2], the boundary conditions [3][4][5] and the initial temperature distribution [6][7][8] with the assistance of auxiliary temperature measurements. These problems are inherently ill-posed so that small input errors in the measured data may produce arbitrarily large deviations in the results [9,10].…”

Inverse Process Analysis for the Acquisition of Thermophysical Data

“…A well-designed experiment removes the need for a complicated inverse analysis. It should be noted that several inverse heat conduction codes based on the method of Frankel and Keyhani [23], Green's functions [24], and space marching [25] were prepared and tested for this project. However, owing to the highly ill-posed nature of inverse heat conduction, data processing [26] is required in order to arrive at a high-quality surface heat flux prediction.…”

Reduction of Thermographic Phosphors Data to Heat Rates

“…Frankel and Keyhani [1997] suggested the use of temperature derivatives to stabilize the inverse heat conduction solution. Since then, numerous conference proceed-…”

“…Frankel and Keyhani [1997] suggested the use of temperature derivatives to stabilize the inverse heat conduction solution. Since then, numerous conference proceed-ings that identify the utility of heating rate measurement devices have appeared Keyhani, 1999, Frankel andOsborne, 2003, e.g.].…”