Laminar natural convection heat transfer and air flow in three-dimensional rectangular enclosures with pin arrays attached to hot wall

In this study, laminar natural convection heat transfer in 3D rectangular air filled enclosures, with pins attached to the active wall, is studied numerically. Two cases of rectangular enclosures are considered: H/L = 1 and H/L = 2. The enclosure is heated from a lateral wall and is cooled from the opposite lateral wall while the other walls of the enclosure are insulated. A number of isothermal cylindrical pins are attached to the interior of the hot wall in various arrangements to enhance the heat transfer. Three-dimensional steady-state continuity, Navier–Stokes and energy equations, along with the Boussinesq approximation, are solved. The dimensionless pin diameters and the pin lengths considered in this study are d/H = 0.025, 0.050 and 0.1, and b/H = 0.1, 0.2 and 0.3, respectively. The number of pins of 2, 4, 5, 6, 8, 9 and 10 are arranged as staggered and in-line (horizontal and vertical) configurations. As the pin diameter, pin length and the number of pins are varied, the air flow pattern and the temperature field are obtained for each case for the Rayleigh numbers ranging from 105 to 107. Also for each case, the mean Nusselt numbers over the cold surface are computed and compared with those of bare enclosure. The Nusselt Number Ratio with respect to the enclosure without pins increases with pin length, pin number and for tall enclosures. Using long pins could result in as much as 34% increase in the Nusselt number ratio.