Comparison of analytical and superposition solutions of the transient liquid crystal technique

The transient liquid crystal technique has been widely used in heat transfer measurement and, due to the nature of the transient test, the mainstream temperature changes over time. In many previous studies, the change of mainstream temperature was assumed as a series of step changes and Duhamel's superposition theorem was applied to evaluate the heat transfer coefficient. In this paper, the error in calculating the heat transfer coefficient by the series-of-step-changes assumption with Duhamel's superposition theorem is discussed and the analytical solution for the curve-fitted mainstream temperature with nth-order polynomials is presented. The solution using the series of step changes showed a high dependency on the size of the time step, thus on the sampling ratio of the mainstream temperature measurement, and higher error was induced for the higher heat transfer coefficient. It is recommended that the size of time step in the series of step changes should be minimized and that the use of an analytical solution would be a better choice in the transient liquid crystal test. It is expected that the presented analytical solution for the curve-fitted mainstream temperature with polynomials could be applied to many slow transient liquid crystal tests.