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Research Papers: Natural and Mixed Convection

A Numerical Study of Developing Buoyancy-Assisted Mixed Convection With Spatially Periodic Wall Heating

[+] Author and Article Information
Chris D. Dritselis

Mechanical Engineering Department, University of Thessaly, Pedion Areos, Volos 38334, Greece e-mail: dritseli@mie.uth.gr

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 26, 2016; final manuscript received February 13, 2017; published online April 19, 2017. Assoc. Editor: Dr. Antonio Barletta.

J. Heat Transfer 139(8), 082502 (Apr 19, 2017) (8 pages) Paper No: HT-16-1605; doi: 10.1115/1.4036088 History: Received September 26, 2016; Revised February 13, 2017

The validity of a parabolic model for simulating the developing buoyancy-assisted mixed convection flow in a vertical channel with spatially periodic wall temperature is verified by a full elliptic model of the momentum and energy equations. A detailed assessment of the effects of the grid resolution, the Richardson number, the Reynolds number, and the preheating zone is presented through extensive comparisons of the velocity and temperature fields and spatial variations of pressure and local heat fluxes at the walls yielded by both models. The parabolic model is capable of reproducing the flow modification into a pattern consisting of a recirculating zone with increasing Richardson number, capturing adequately the main trends of the flow and heat transfer results. For certain combinations of the relevant nondimensional parameters, the solutions of the parabolic model agree reasonably well with those of the elliptic model from a quantitative point of view. In all the cases examined here, the computational time needed by the parabolic model is significantly smaller than that of the elliptic model.

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Figures

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Fig. 1

Flow configuration

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Fig. 2

Predictions of the flow field based on the parabolic ((a), (c), and (e)) and elliptic ((b), (d), and (f)) models for Ri = 3 ((a) and (b)), 4 ((c) and (d)), and 5 ((e) and (f)) at Re = 250

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Fig. 3

Predictions of the temperature field near the heating zone based on the parabolic (a) and elliptic (b) models for Ri = 5 at Re = 250

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Fig. 4

Variation of U velocity in the vertical direction (a) and wall-normal distributions of U (b) predicted by the parabolic and elliptic models at Re = 250 and Ri = 5

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Fig. 5

Variation of pressure in the vertical direction predicted by the parabolic and elliptic models for various values of the Richardson number at Re = 250

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Fig. 6

Variation of local heat flux at the hotter left wall Q1 and the colder right wall Q2 in the vertical direction predicted by the parabolic and elliptic models at Re = 250 and Ri = 5

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Fig. 7

Variation of U velocity component in the vertical direction predicted by the parabolic and elliptic models for various values of the Reynolds number at Ri = 5

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Fig. 8

Variation of local heat fluxes at the left Q1 and right wall Q2 in the vertical direction predicted by the parabolic and elliptic models for various values of the Reynolds number at Ri = 5. The values of Q2 are shifted downward by −20.

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Fig. 9

Wall-normal distributions of U and Θ at the beginning of the heating zone at X = 0 predicted by the parabolic and elliptic models with a preheating zone of L(a) = 5

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