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

Abstract

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.

Onset of secondary flow and enhancement of heat transfer in horizontal convergent and divergent channels heated from below

“…From the review of literature, it appears that the results obtained for the critical Rayleigh number for the initiation of the plume, the number of plume produced and the heat transfer characteristic between the experiments with water and the ones with air are different. Numerical studies were also performed to study the occurrence and the structure of the secondary flow and the enhancement of heat transfer in both the developing and fully developed regions [17][18][19][20][21][22][23]. The trends obtained in general are consistent with the experimental observations.…”

Combined buoyancy effects of thermal and mass diffusion on laminar forced convection in the thermal entrance region of horizontal square channels

“…To check further the adequacy of the numerical scheme described above, the limiting results of mixed convection heat transfer were obtained and were contrasted with those of Lin and Chou (1989). It is clearly seen in Table 2 that the maximum deviation in Nu, is less than 3 % .…”

“…with a uniform wall heat flux. Lin et al (1988b) investigated laminar mixed convection heat transfer in shrouded arrays of heated rectangular blocks, and Lin and Chou (1989) examined buoyancy effects on forced convection in the thermal entrance region of horizontal isothermal channels. Several experimental studies of mixed convection flow in the thermal entrance or combined entry regions of horizontal parallel plate channels have been well undertaken (Hwang and Liu, 1976;Incropera et al, 1987;Kamotani et al, 1979;Maughan and Incropera, 1987).…”

Combined heat and mass transfer for laminar flow of moist air in a 3D rectangular duct: CFD simulation and validation with experimental data

“…They assumed constant heat flux at the walls with different aspect ratios and showed that the secondary velocity induced due to buoyancy force significantly enhances the heat transfer process and reduces the thermal entrance length. Without the restriction of large Prandtl number, there are detailed numerical studies of mixed convective heat transfer in the entrance region of a horizontal rectangular channel by Abou-Ellai and Morcos [24], Incropera and Schutt [25], Mahaney et al [26], Lin and Chou [27] and Lin et al [28].…”

“…There are a lot of research works on the determination of heat and mass transfer coefficients considering the effect of buoyancy forces and a large share of it belongs to the internal flows . Whereas some of the works consider only heat transfer [9][10][11][12][13][14][15][24][25][26][27][28] to quantify Nusselt number, many of them treat simultaneous heat and mass transfer [16][17][18][19][20][21][22][23]29,30] to determine Nusselt and Sherwood numbers together. Most of the works in the literature present numerical data and correlations [9][10][11][12][13][16][17][18][19][20][21][22][24][25][26][27][28]30] with only a few presenting experimental data and correlations [14,15,23,29].…”