Solutions of Fourier's equation appropriate for experiments using thermochromic liquid crystal

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Abstract

In transient heat-transfer experiments, the time to activate the thermochromic liquid crystal (TLC) can be used to evaluate h, the heat transfer coefficient. Most experimenters use the solution of Fourier's equation for a semi-infinite substrate with a step-change in the temperature of the fluid to determine h. The 'semi-infinite solution' can also be used to determine T ad, the adiabatic surface temperature, but this is an error-prone method suitable only for experiments with relatively large values of Bi, the Biot number. For Bi > 2, which covers most practical cases, more accurate results could be achieved using a composite substrate of two materials. Using TLC to determine the temperature-time history of the surface of the composite substrate, h and T ad could be computed from the numerical solution of Fourier's equation. Alternatively, h and T ad could be determined analytically from a combination of the semi-infinite and steady-state solutions.
Original languageEnglish
Pages (from-to)5908-5915
Number of pages8
JournalInternational Journal of Heat and Mass Transfer
Volume55
Issue number21-22
Early online date10 Jul 2012
DOIs
Publication statusPublished - Oct 2012

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