New Heat Flux-Temperature Integral Relationships: Mathematical Developments based on Integral Transforms and Integral Equation Regularization
by
Jay I. Frankel
Mechanical, Aerospace and Biomedical Engineering Department, University of Tennessee, Knoxville, TN (USA) 37996-2210

Recent re-formulations involving one-, two-, and three-dimensional heat conduction, have demonstrated the importance of understanding heating rate (dT/dt, in degrees Celsius per second) for determining internal and surface heat fluxes in transient situations in a highly accurate manner. These physical problems are mathematically ill-posed since measurement noise is strongly amplified in the re-construction of the heat flux. This mathematically obtained insight strongly encourages the development of a new class of rate-based sensors and requires rethinking on the proper choice of digital filters. Using integral transforms or Green’s function with integral equation regularization (Abel type), we will develop a family of integral relationships between temperature and heat flux that can be used in practice. Thus, the time history of temperature (or its temporal derivative) will be used to acquire the heat flux. This is in contrast to conventional means based on Fourier’s law involving a spatial derivative.

Date received: January 30, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caub-35.