Annals of the Assembly for International Heat Transfer Conference 13

ISBN 1-56700-225-0 / CD 1-56700-226-9

Year 2006

P. L. Woodfield
Dept. of Mechanical Engineering, Saga University, 1 Honjo Saga City, Saga 840-8502, Japan

Masanori Monde
Department of Mechanical Engineering, Saga University, 1 Honjo Saga City, Saga 840-8502, Japan

Yuichi Mitsutake
Department of Mechanical Engineering, Saga University, 1 Honjo Saga City, Saga 840-8502, Japan

The accuracy of an analytical solution to a two-dimensional inverse heat conduction problem is investigated by comparison with analytical results for a moving heat source on the surface. This provides a rigorous test case with direct relevance to quenching experiments. Accurate predictions are obtained for the peak heat flux provided the width of the heat source is larger than the sensor spacing. By discussing the inverse problem in terms of Fourier components it is demonstrated that the high frequency modes in both time and space are responsible for non-uniqueness of the solution. This observation suggests that no inverse solution can correctly resolve higher frequency components beyond certain limits in either time or space. Simple relations are derived in order to estimate the minimum wavelength and time period that can be resolved for a given experimental set up, assuming a certain level of uncertainty. In addition, the formulation of the analytical inverse solution and implementation procedure is such that questionable high frequency components are damped strongly. It is proposed that the inverse solution should be understood as representing an average over a short period of time and a short distance in space. By numerical simulation it is demonstrated that this is a useful and practical interpretation for the present inverse solution if the heat source moves slowly.

CND-05 pages DOI: 10.1615/IHTC13.p27.50 Download article

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