This paper presents a steady measurement technique based on thermochromic liquid crystals (TLC) that can be used for study of conjugate heat transfer. In contrast to the more commonly used transient thermochromic liquid crystal technique, this technique requires steady-state experiments, and eliminates some of the limitations of the transient version at the cost of measurements or knowledge of thermal conditions all surfaces and increased computations for data reduction. This technique requires that thermal boundary conditions be known or measured on all internal or external surfaces of the test block. All surfaces that are exposed to external air flow are coated with a broad-bandwidth TLC. The thermal boundary conditions are then sent to a steady conduction solver that involves the boundary element method (BEM) and an inverse problem approach (BEM/IP). This combined BEM/IP approach minimizes the effects of random experimental error in measured data and calculates surface heat flux, from which the intended convective heat flux coefficients can then be calculated. The technique is applied to a prismatic stainless steel block exposed to warm air flows on three sides — an arrangement that has been used often to simulate flow through a blade tip gap. It is found that an in-situ pixel-by-pixel calibration of TLC hue vs temperature is needed in order to obtain reasonable accuracy. A calibration-curve-fit uncertainty of better than 0.4°C (at 95% confidence level) was obtained in this process. In the actual experiments, conjugate heat transfer was set up by passing cold water through three cooling channels that span the test block. Once the experiments are completed and the TLC colors are converted to surface temperature distributions, the BEM/IP approach is used to obtain surface heat flux distributions, and then distribution of heat transfer coefficients.

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