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

摘要

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.