Time-accurate CFD conjugate analysis of transient measurements of the heat-transfer coefficient in a channel with pin fins

Heat-transfer coefficients (HTC) on surfaces exposed to convection environments are often measured by transient techniques such as thermochromic liquid crystal (TLC) or infrared thermography. In these techniques, the surface temperature is measured as a function of time, and that measurement is used with the exact solution for unsteady, zero-dimensional (0-D) or one-dimensional (1-D) heat conduction into a solid to calculate the local HTC. When using the 0-D or 1-D exact solutions, the transient techniques assume the HTC and the free-stream or bulk temperature characterizing the convection environment to be constants in addition to assuming the conduction into the solid to be 0-D or 1-D. In this study, computational fluid dynamics (CFD) conjugate analyses were performed to examine the errors that might be invoked by these assumptions for a problem, where the free-stream/bulk temperature and the heat-transfer coefficient vary appreciably along the surface and where conduction into the solid may not be 0-D or 1-D. The problem selected to assess these errors is flow and heat transfer in a channel lined with a staggered array of pin fins. This conjugate study uses three-dimensional (3-D) unsteady Reynolds-averaged Navier–Stokes (RANS) closed by the shear-stress transport (SST) turbulence model for the gas phase (wall functions not used) and the Fourier law for the solid phase. The errors in the transient techniques are assessed by comparing the HTC predicted by the time-accurate conjugate CFD with those predicted by the 0-D and 1-D exact solutions, where the surface temperatures needed by the exact solutions are taken from the time-accurate conjugate CFD solution. Results obtained show that the use of the 1-D exact solution for the semi-infinite wall to give reasonably accurate “transient” HTC (less than 5% relative error). Transient techniques that use the 0-D exact solution for the pin fins were found to produce large errors (up to 160% relative error) because the HTC varies appreciably about each pin fin. This study also showed that HTC measured by transient techniques could differ considerably from the HTC obtained under steady-state conditions with isothermal walls.