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

• Published in: International journal of heat and mass transfer 2012-10, Vol.55 (21-22), p.5908-5915
• Main Authors: Pountney, Oliver, Cho, GeonHwan, Lock, Gary D, Owen, J Michael
• Format: Article
• Language: English
• Subjects: Adiabatic wall temperature; Computational fluid dynamics; Exact sciences and technology; Fluid flow; Fourier's equation; Heat transfer coefficients; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Liquid crystals; Mass transfer; Mathematical analysis; Mathematical models; Physics; Thermal instruments, apparatus and techniques; Thermochromic liquid crystal; Thermometry
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2012.06.001

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 Tad, 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 Tad could be computed from the numerical solution of Fourier’s equation. Alternatively, h and Tad could be determined analytically from a combination of the semi-infinite and steady-state solutions.