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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Liquid Crystals
Liquid crystals
liquid crystals
Substrates
Biot number
composite materials
Experiments
Composite materials
heat transfer coefficients
Temperature
Heat transfer coefficients
surface temperature
heat transfer
histories
Heat transfer
Fluids
temperature
fluids

Cite this

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title = "Solutions of Fourier's equation appropriate for experiments using thermochromic liquid crystal",
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.",
author = "Oliver Pountney and GeonHwan Cho and Lock, {Gary D.} and Owen, {J. Michael}",
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TY - JOUR

T1 - Solutions of Fourier's equation appropriate for experiments using thermochromic liquid crystal

AU - Pountney, Oliver

AU - Cho, GeonHwan

AU - Lock, Gary D.

AU - Owen, J. Michael

PY - 2012/10

Y1 - 2012/10

N2 - 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.

AB - 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.

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JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

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