Effect of Buoyancy on Forced Convection in Vertical Regular Polygonal Ducts

Abstract

Laminar combined free and forced convection through vertical regular polygonal ducts has been studied. All fluid properties are considered constant, except variation of density in the buoyancy term. Heat flux is considered uniform in the flow direction while in the transverse direction two wall conditions have been considered; Case 1—uniform circumferential wall temperature, and Case 2—uniform circumferential heat flux. A solution by point matching method in terms of a series containing Bessel functions has been obtained. Nusselt numbers, local heat flux, local shear stress, and pressure drop have been investigated. The condition of Case 1 results in higher Nusselt number values compared to the condition of Case 2. However, these differences in Nusselt number diminish as the number of sides of the polygon are increased. In each case at higher values of the Rayleigh number, the Nusselt number is less sensitive to the number of sides. When Nusselt numbers against number of sides are considered, in Case 1, the Nusselt numbers reach asymptotic value at lower number of duct sides compared to Case 2. At low values of buoyancy effect, in Case 1, the maximum circumferential heat flux results at the centre of the wall, while at higher values of the same, the local heat flux becomes uniform over a substantial portion of the wall. Under Case 1 buoyancy effect increases the heat flux ratio at the duct corners. In three-sided polygon at higher values of the buoyancy parameter the maximum shear stress is no longer incident at the wall center. As the number of sides is increased, however, the maximum shear stress again takes place at the wall center. The Case 1 produces higher shear stress values near the wall center, while the Case 2 produces higher shear stress values near the duct corner. When the buoyancy parameter is high and the number of sides is not large, Case 2 results in higher values of pressure drop parameter compared to Case 1.