A model of heat transfer from a cylinder in high-speed slip flow and determination of temperature jump coefficients using hot-wires

Abstract

In small-scale, low-density or high-speed flows, the mean free path of the gas and its molecular interaction with a solid interface are key properties for the analysis of heat transfer mechanisms occurring in many flow processes ranging from micro-scale to aerospace applications. Here, we specifically examine the effects of temperature jump at the gas-solid interface on the convection from a cylinder in the high-speed slip flow regime. By employing the classical Smoluchowski temperature jump condition, we derive a simple model that explicitly predicts the heat flux (Nusselt number $\text{Nu}$) from the surface of a small heated cylinder simulating a hot-wire as a function of the Knudsen number ($\text{Kn}$) and the thermal (or energy) accommodation coefficient ($\sigma_T$) of the gas molecules interacting with the surface. The model, derived analytically and verified empirically by numerical simulations, helps clarifying coupled gas rarefaction and temperature effects on the heat transfer from a cylinder in high-speed flow. In addition, we employ the model reversely to propose a novel methodology to compute gas-surface thermal accommodation or temperature jump coefficients from hot-wire measurements.