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Laminar 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 (widthlheight) ratios 0.5, 1.0 and 2.0, Rayleigh numbers 0 -2 X lo5 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 5 lo3. The behavior of the local Nusselt number for Pr = 100 compares well with the existing results for Pr -00.Des Ctudes ont CtC effectuCes sur la convection mixte laminaire dans la rtgion d'entrte thermique de canaux rectangulaires isothermes horizontaux pour des nombres de Prandtl petits et modCrCs (air) en utilisant la formulation vorticitkvitesse de 1'6quation de Navier-Stokes. Les rksultats numtriques, incluant les vecteurs vitesses transversaux, les nombres de Nusselt et les rapports des facteurs de friction locaux, sont prCsentCs pour des facteurs de forme (largeudhauteur) de 0,5, 1,0 et 2,0, des nombres de Rayleigh de 0 -2 X lo5 et des nombres de Prandtl de 0,7, 5,O et 100. On a trouvt que la force et le modtle d'kcoulement secondaire induit par les effets de convection naturelle dCpendent du nombre de Raleigh et du facteur de forme, et que I'Ccoulement secondaire entraine une augmentation importante du transfert de chaleur dans la rCgion d'entrCe. On montre que le probltme classique de Graetz est un cas limite qui s'applique uniquement lorsque Ra 5 lo3. Le comportement du nombre de Nusselt local pour Pr = 100 se compare favorablement aux rCsultats existants pour Pr -00.

Heat and mass transfer in laminar mixed convection in the thermal entrance region of horizontal square channels is investigated by using the vorticity‐velocity formulation of the Naiver‐Stokes equations. The numerical results, including the developments of temperature and concentration contours, Nuz and friction coefficient ratios, fRe / (fRe)0, are presented for an air‐water system. The effects of bottom wall temperature and the relative humidity on the momentum, heat and mass transfer in the flow are examined in detail. Results show that the influences of the evaporation of the water vapor along the wetted wall on the heat and mass transfer and the ratio fRe / (fRe)0 are rather substantial.

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Laminar mixed convection in the entrance region of shrouded arrays of heated rectangular blocks is approximated numerically for large Prandtl number fluids. The problem considered is related to the convective cooling of electronic components mounted on horizontal circuit boards. Two heating conditions are investigated; in case 1, the uniformly heated components are facing upwards and, in case 2, the heated components are facing downwards. Typical fluid streamlines and isotherms, block wall temperature distributions and local Nusselt numbers are presented. It is found that the secondary flow leads to a significant enhancement in heat transfer for cases where the block faces upwards rather than downwards.