Natural convection heat transfer within a square porous enclosure with four heated cylinders

Abstract

The present numerical study investigates unsteady natural convection heat transfer within a square-shaped porous confinement with four heated cylinders. Simulations are performed for different cylinder spacings by arranging the cylinders along the enclosure diagonals in a rectangular array for different Darcy numbers (Da) and Rayleigh numbers (Ra). The positions of cylinders within the enclosure are limited to 0.3 ≤ S (= sH /L = sV /L) ≤ 0.6 and for each rectangular array computations were performed for 103 ≤ Ra ≤ 106 and 10−4 ≤ Da ≤ 10−2. Results reveal that conduction mode heat transfer dominates within the enclosure at Ra ≤ 104 irrespective of Da, whereas for Da = 10−3, 10−2, convective heat transfer prevails for high Ra (105, 106) values. With the increase in Ra up to Ra ≥ 105, the temperature and flow fields lose symmetry about the vertical centerline of the enclosure. For Ra = 106 and Da = 10−2 the change in time-averaged Nusselt number Nut with cylinder spacing is insignificant for all cylinders, whereas for Da = 10−3 Nut at the lower cylinders decreases slightly between S = 0.3 and 0.4 and then increases slightly up to S = 0.6.

Keywords

• Natural convection
• Cylinders
• Porous enclosure
• Rayleigh number
• Darcy number
• Nusselt number