Conjugate forced convection in crossflow over a cylinder array with volumetric heating

Abstract

Numerical simulation of steady forced convection heat transfer in a laminar flow field over an infinite (periodic) and finite in-line array of cylinders is performed. The cylinders are arranged with a pitch to diameter ratio of two, and are heated internally with a uniform distribution of heat sources. The conjugate heat transfer problem is described by two coupled energy equations (one for the fluid, the other for the solid) and the Navier-Stokes equations. This system is solved on curvilinear coordinates via a finite-difference iterative scheme and a domain decomposition procedure. By varying the ratio of fluid-to-solid thermal conductivity (FS) between 0.01 and 100, a parametric study of heat exchange between the solid and fluid (as expressed by the Nusselt number) is reported for Reynolds numbers between 100 and 400 and Prandtl number equal to 0.71. Our results reveal that the internal heat generation case is profoundly different from that of the isothermal cylindrical array if FS is larger than unity. As FS approaches extreme values, e.g. 0.01 (or 100), the temperature field can be approximated by invoking simpler models, e.g. local thermal equilibrium (or concentric) model.