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TECHNICAL PAPERS

# Numerical Investigation of the Natural Convection Flows for Low-Prandtl Fluids in Vertical Parallel-Plates Channels

[+] Author and Article Information
Antonio Campo

Department of Mechanical Engineering, The University of Vermont, Burlington, VT 05405acampo@emba.uvm.edu

Oronzio Manca

Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Università degli Studi di Napoli Real Casa dell’Annunziata, Via Roma 29, 81301 Aversa (CE), Italyoronzio.manca@unina2.it

Biagio Morrone

Dipartimento di Ingegneria Aerospaziale e Meccanica, Seconda Università degli Studi di Napoli Real Casa dell’Annunziata, Via Roma 29, 81301 Aversa (CE), Italybiagio.morrone@unina2.it

J. Appl. Mech 73(1), 96-107 (Apr 20, 2005) (12 pages) doi:10.1115/1.1991867 History: Received July 13, 2004; Revised April 20, 2005

## Abstract

Laminar natural convection of metallic fluids $(Pr⪡1)$ between vertical parallel plate channels with isoflux heating is investigated numerically in this work. The full elliptic Navier-Stokes and energy equations have been solved with the combination of the stream function and vorticity method and the finite-volume technique. An enlarged computational domain is employed to take into account the flow and thermal diffusion effects. Results are presented in terms of velocity and temperature profiles. The investigation also focuses on the flow and thermal development inside the channel; the outcomes show that fully developed flow is attained up to $Ra=103$, whereas the thermal fully developed condition is attained up to $Ra=104$. Further, correlation equations for the dimensionless induced flow rate, maximum dimensionless wall temperatures, and average Nusselt numbers as functions of the descriptive geometrical and thermal parameters covering the collection of channel Grashof numbers $1.32×103⩽Gr∕A⩽5.0×106$ and aspect ratios $5⩽A⩽15$. Comparison with experimental measurements has been presented to assess the validity of the numerical computational procedure.

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## Figures

Figure 1

(a) Sketch of the channel, (b) computational domain

Figure 2

Local Nusselt number as function of the X coordinate at Ra=104 and A=10 for several meshes

Figure 3

Local Nusselt number distribution as function of the X coordinate for several grids: (a) zoom of the inlet section of the channel X=0; (b) zoom of the exit section of the channel X=A

Figure 4

Velocity profiles as a function of Y for different node numbers at three X stations: (a) X=0.0; (b) X=A∕2; (c) X=A

Figure 5

Temperature profiles as a function of Y for different node numbers at three X stations: (a) X=0.0; (b) X=A∕2; (c) X=A

Figure 6

Wall temperature profiles as a function of X for several Ra numbers: (a) aspect ratio A=10; (b) aspect ratio A=15

Figure 7

Wall temperature profiles as a function of the normalized abscissa X∕A for Ra=104 and several channel aspect ratios A

Figure 8

Normalized velocity profiles as a function of Y for A=10 and several Ra numbers: (a) channel inlet; (b) channel exit

Figure 9

Normalized temperature profiles as a function of Y for A=10 and several Ra numbers: (a) channel inlet; (b) channel exit

Figure 10

Normalized velocity profiles as a function of Y at Ra=104 and several channel aspect ratio A: (a) channel inlet; (b) channel exit

Figure 11

Normalized temperature profiles as a function of Y at Ra=104 and several channel aspect ratio A: (a) channel inlet, (b) channel exit

Figure 12

Axial derivative of the normalized velocity U* at the centerline, Y=0.5, as a function of X

Figure 13

Local modified Nusselt numbers as a function of the axial coordinate X for different Ra values

Figure 14

Temperature isolines with A=10: (a) Ra=103, (b) Ra=106

Figure 15

Maximum wall temperatures as a function of Gr∕A and the corresponding correlation equation

Figure 16

Average Nusselt number as a function of Gr∕A and the correlation equation compared with the experimental data (25)

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