Laminar mixed convection in the thermal entrance region of horizontal isothermal rectangular channels

Abstract

AbstractLaminar mixed convection in the thermal entrance region of horizontal isothermal rectangular channels for moderate and small Prandtl number (air) is investigated using the vorticity‐velocity formulation of the Navier‐Stokes equation. The numerical results, including the cross‐stream velocity vectors, local Nusselt numbers and local friction factor ratios are presented for the aspect (width/height) ratios 0.5, 1.0 and 2.0, Rayleigh numbers 0 ∼ 2 × 105 and Prandtl numbers 0.7, 5.0 and 100. The strength and pattern of the secondary flow induced by buoyancy effects is found to depend on the magnitude of Rayleigh number and aspect ratio, and the secondary flow leads to a significant enhancement of heat transfer in the entrance region. The classical Graetz problem is shown to be a limiting case which applies only when Ra ≤ 10.3 The behavior of the local Nusselt number for Pr = 100 compares well with the existing results for Pr → ∞.