Transient heat transfer measurements using thermochromic liquid crystal. Part 1: An improved technique

Accurate heat transfer measurements using thermochromic liquid crystal. Part 2: Application to a rotating disc

“…This section describes briefly the method of analysis for the transient heat transfer experiments based on the solution of Fourier's one-dimensional conduction equation for a semi-infinite substrate as described by Newton et al (2003). The one-dimensional analysis considers only the conduction in the direction normal to the surface of the wall, ignoring conduction in the transverse directions.…”

“…T aw depends on the total-temperature of the air, T a , and on the fluid dynamics (see Newton et al, 2003).…”

“…In the tests reported here, the mesh heater created an effective step-change in the air temperature, but (as discussed above) at the test section an exponential-type of behaviour (or so-called ''slow transient") was produced. Newton et al (2003) showed that the adiabatic-wall temperature, T aw , could be fitted by an exponential series of m terms. Fourier's conduction equation for a semi-infinite slab has been solved by Gillespie et al (1998) for the case where there is a simple exponential increase in the air temperature, corresponding to the case where m = 1.…”

“…Despite the thermal insulation in the upstream pipes, the air temperature at this latter location rises exponentially from its initial value towards a final steady-state temperature. A three-term exponential fit was used (see Newton et al (2003)) and the total-temperature, T a , history at the pre-swirl nozzles ( Fig. 3) can be represented by the following:…”

“…For the special case where the air temperature rises exponentially with time, Gillespie et al (1998) obtained an analytical solution of Fourier's equation. This solution was extended to an exponential-series technique by Newton et al (2003), who demonstrated that the accuracy of the simple step-change method could be brought to the more difficult case of the slow transient.…”