Transient heat transfer measurements using thermochromic liquid crystal: lateral-conduction error

Thermochromic liquid crystal (TLC) can be used to measure the surface temperature in transient heat transfer experiments. Knowing the time at which the TLC changes colour, hence knowing the surface temperature at that time, it is possible to calculate the heat transfer coefficient, h, and the analytical one-dimensional solution of Fourier's conduction equation for a semi-infinite wall is often used for this purpose. However, the 1D solution disregards lateral variations of the surface temperature (that is, those variations parallel to the surface), which can cause a bias, or lateral-conduction error, in the calculated value of h. This paper shows how the 1D analytical solution can be used to estimate, and to provide a correction for, the error. An approximate two-dimensional analysis (which could be readily extended to three dimensions) is used to calculate the error, and a 2D finite-difference solution of Fourier's equation is used to validate the method.