Surface Heat Flux Prediction Through Physics-Based Calibration, Part 1: Theory

A transformative methodology is presented for predicting surface heat fluxes based on interior temperature measurements. A physics-based calibration method is mathematically developed presently in the context of the linear heat equation and experimentally verified (in a later paper), indicating the...

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Bibliographic Details
Published in:Journal of thermophysics and heat transfer 2013-04, Vol.27 (2), p.189-205
Main Authors: Frankel, J. I, Keyhani, M, Elkins, B. E
Format: Article
Language:English
Subjects:
Calibration
Conduction heating
Conductive heat transfer
Diffusion theory
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Heat
Heat conduction
Heat flux
Heat transfer
Heat treatment
Mathematical analysis
Physics
Sensors
Temperature
Temperature measurement
Thermodynamics
Thermophysical properties
Three dimensional
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Summary:A transformative methodology is presented for predicting surface heat fluxes based on interior temperature measurements. A physics-based calibration method is mathematically developed presently in the context of the linear heat equation and experimentally verified (in a later paper), indicating the merit and accuracy of the approach. Sensor characterization, sensor positioning, and thermophysical properties are inherently contained without being explicitly expressed in the final mathematical expression, relating the surface heat flux to interior temperature measurements. A unified theoretical basis is presently under development that encompasses one-, two-, and three-dimensional multiregion geometries possessing orthotropic thermophysical properties. Additionally, the mathematical formalism will recover either the local surface heat flux or total surface heat transfer. This paper represents the first presentation of the concept, illustrates its genesis, and presents insight toward developing a comprehensive unified analytic treatment for inverse heat conduction by physics-based calibration. Physics-based calibration makes use of the functional operator associated with diffusion theory and does not rely on identification. The companion paper will present experimental verification of the resulting mathematical relationship using an electrical heating setup. Highly favorable results verifying the formulation are reported in the companion paper.
ISSN:0887-8722
1533-6808
DOI:10.2514/1.T3917