Mixed Convection Heat Transfer from Semi-circular Cylinders in a Vertical Channel

Abstract

The flow and heat transfer characteristics of mixed convection heat transfer from semi-circular cylinders under various confinements and configurations have been studied in the current work. Initially, a semi-circular cylinder was placed symmetrically in a vertical channel. The confinement ratio (0.2 ≤ β ≤ 0.8), Reynolds number (1 ≤ Re ≤ 50), Prandtl number (0.7 ≤ Pr ≤ 50), and Richardson number (0 ≤ Ri ≤ 2) are taken as the governing parameters. Further, two semi-circular cylinders (in tandem) were kept symmetrically in the vertical channel, keeping β = 0.2, to study the effect of the cylinder spacing ratio (1 ≤ yC ≤ 6) on mixed convection heat transfer. All other governing parameters varied in the same ranges as in the case of the single cylinder. The FVM (Finite Volume Method) based CFD simulator (ANSYS Fluent) was used to solve the relevant governing equations along with specified boundary conditions. The two-dimensional, steady, laminar approximation was used to obtain the solutions. The solutions for equations of momentum and energy were achieved employing an upwind scheme of second-order with the SIMPLE technique for pressure-velocity coupling. The Gauss-Siedel method, in combination with the multi-grid method, was used to converge the iterative solutions. The obtained results are presented as streamline profiles, isotherm profiles, distributions of pressure coefficient (CP) and local Nussel number (Nu), drag coefficient (CD) and average Nusselt number (Nuavg), etc. For the single-cylinder case, CD values show a positive dependence on β and negative dependence on Re. However, CD values are increased with Ri for a rise in β upto 0.33. Beyond this β value, the Ri value had no significant effect on CD due to the domination of inertial forces at high confinement. The rise in β, Re, and Pr values increases the Nuavg value. However, due to the aiding buoyancy, Ri has a mixed impact on the Nuavg value. A substantial increase of 100% in Nuavg value at Re = 50, Pr = 50 and Ri = 2 is observed with an increase in β from 0.2 to 0.8. Further, in the case of tandem cylinders, the drag coefficients for upstream (C1) and downstream (C2) cylinders (CD1 and CD2, respectively) decrease with Re and increase with Ri. The increase in yC shows a substantial rise in CD2 values at low Ri compared to high Ri values. A hike in Re and Pr values shows improvement in the average Nusselt numbers of C1 and C2 cylinders (Nuavg1 and Nuavg2, respectively). At a high value of Re = 50, Nuavg2 significantly increased with yC. For yC > 3, the Nuavg2 increased with an elevation in Ri. A maximum percent enhancement in Nuavg1 with the rise in yC value is found as 23% at Re = 1 and Pr = 0.7, whereas a maximum percent improvement of 134% in the Nuavg2 value is seen due to the rise in yC at Re = 50, Pr = 50 and Ri = 2. Overall, a complex interplay of governing parameters has been observed in the flow and thermal characteristics in both cases of mixed convection.