Numerical investigation of mixed convection from rectangular cylinders subjected to upper cross flow

Abstract

Unsteady combined natural and forced convection heat transfer from a rectangular cylinder subjected to upward cross flow is investigated numerically. The working fluids are air (Pr = 0.7) and water (Pr = 7), and the flow is laminar. The governing flow and energy equations are solved using a fractional step finite-difference scheme. The effects of the cylinder aspect ratio (a = L/D), Reynolds and Richardson numbers on the flow and heat transfer characteristics are investigated. Numerical simulations were carried out for the cylinders with aspect ratios of a = 0.5, 1, and 2, while the Richardson and Reynolds numbers varied between 0 to 10, and 100 to 200, respectively. The mean drag, mean rms lift coefficients, as well as the Strouhal number and the mean Nusselt number were computed for each simulation to determine the quantitative effects on flow and heat transfer. Steady flow is observed for Pr = 0.7, Ri = 0.5, and a = 0.5 or for Re ≥ 150 and Ri ≥ 1. For Ri = 10 and Re = 200, the flow becomes unsteady in the downstream region and trigger vortex street formation for a = 0.5, 1, and 2. Decreasing the aspect ratio, as well as increasing Reynolds number, increases the heat transfer from the cylinder. The rms lift coefficient decreases sharply at Ri < 1 for Pr = 0.7, Ri < 2 for Pr = 7 due to vortex breakdown. Further increase in the Richardson leads to a slight increase in rms lift coefficient except for Re = 200 where the sharp increase is observed due to triggered vortex formation again. For air, the increase in the mean Nusselt number in Ri = 10 case with respect to the forced convection case (Ri = 0) was 54–65% and 80–98%, respectively, for a = 0.5 and 2, while these values for water were realized as 50–68% and 53–63%, respectively. Using the computed data and nonlinear regression, the mean Nusselt number and the drag coefficients were developed.

Keywords:

• Mixed convection
• natural-forced convection
• numerical simulation
• rectangular cylinder