A Periodic-Transient Method for High-Resolution Heat Transfer Measurement on Two-Dimensional Curved Surfaces

Measurement of heat transfer distribution is frequently required in engineering. However, some heat transfer techniques are not able to measure accurately on two-dimensional curved surfaces. In this field, periodic-transient measurement methods are advantageous. This paper describes the development of a periodic-transient technique for high-resolution heat transfer measurement and its application to multiple air-jet cooling of a concave solar receiver window. In contrast to other measurement techniques, the periodic-transient technique requires neither homogenous heating nor quantitative measurement of surface or fluid temperatures. The heat transfer coefficient is determined by periodically heating the substrate and evaluating the phase shift between the heat flux penetrating the substrate and the resulting temperature response. Equations for a hollow-sphere and flat-plate substrates are derived. The curved window surface is periodically heated by a simple device with standard light bulbs. A procedure for taking the transient heating characteristic into consideration is described. The distribution of surface temperature fluctuation is measured nonintrusively by thermography. For the sample application of air-jet cooling, a detailed uncertainty estimation is presented. The relative measurement uncertainty of the local, convective heat transfer coefficient ranges from $−2.4%$ to $+14.1%$ for $h=10W∕(m2K)$ and from $−2.3%$ to $+9.7%$ for $h=200W∕(m2K)$⁠. The uncertainty of the spatially averaged heat transfer coefficient lies between $+2.0%$ and $+9.8%$ for $hm=10W∕(m2K)$ and between $+0.7%$ and $+6.7%$ for $hm=200W∕(m2K)$⁠. The periodic-transient method described complements established techniques for high-resolution heat transfer measurements on two-dimensional curved surfaces.