Numerical investigation of the laminar natural convection heat transfer from the equilateral triangular cluster of three horizontal spheres

Abstract

Natural convection heat transfer from the equilateral triangular cluster of three horizontal spheres in air has been investigated numerically over the range of 10≤Gr≤105. An extended model is used for the partially symmetric cluster in the three-dimensional condition, which is proposed initially by Bejan et al. (1995). The accuracy of the extended model has been validated by the single sphere. The comprehensive results consist of isothermal and streamline contours, the local drag coefficients as well as the local and average Nusselt number distributions with the different Grashof numbers. There is a thicker thermal boundary in the center clearance of the cluster due to the interaction of the three adjacent surface for all Grashof numbers, which weakens the heat transfer and deteriorates into the decreasing of local Nusselt number along the polar angle, while the negative velocity gradient has a similar effect. Then the correlation equation of the average Nusselt number in the range of 10≤Gr≤105 has been proposed. Compared with the single sphere, the average Nusselt number of the cluster changes from 64.69% to 92.45% of that of the single sphere due to the stronger buoyancy force and the larger temperature gradient with the increasing Grashof number.