Numerical modeling of thermo‐flows in a trapezoidal cavity containing different solid objects

Abstract

AbstractHeat transfer in chambers is essential in the industry as heating/cooling systems, as well as electronic equipment. This study investigates the mixed heat transfer of fluid inside a trapezoidal chamber with a hot obstacle. The variable parameters include trapezoidal side angles, Rayleigh number, surface emissivity coefficient of obstacle, heat conduction ratio, and aspect ratio of obstacle. In addition, the geometry of solid obstacles is considered rectangular and circular. The governing equations are solved numerically by a fourth‐order characteristics‐based scheme. The bottom wall of the obstacle has persistent heat flux, another wall is adiabatic and the sidelong walls of the cavity are cold, and the upper and lower walls are adiabatic. Moreover, the other walls are insulated. The results demonstrate that the mean Nusselt number of cold walls declines as the angle of side walls increases in different Rayleigh numbers. Nusselt number rises with an increment of Rayleigh number at sustained angles. Higher aspect ratios and emissivity coefficients lead to higher Nusselt numbers for various Rayleigh numbers. The results show that by increasing the angle, the Nusselt number decreases up to 50%. Also, the Nusselt number for rectangle obstacles is up to 30% more than that for a circular obstacle. The working fluid here is water, with Prandtl number 6.9.