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DOI: 10.1615/HeatTransRes.v37.i7.10
pages 571-591

Control of Free Convection Passage Across Square Cavities with Heated/Cooled Vertical Sidewalls by Manipulating "On" and "Off" Deflectors

Antonio Campo
The University of Texas at San Antonio
El Hassan Ridouane
Department of Mechanical Engineering, The University of Vermont, 33 Colchester Ave., 201 Votey Bldg., Burlington, VT 05405
Ignacio J. Benitez Sanchez
Departamento de Ingenieria de Sistemas y Automática, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain

ABSTRACT

The physical system consists of a square cavity filled with a mass of compressible air bounded by two vertical walls differentially heated and two horizontal walls insulated from the surroundings. The variable of interest is the amount of heat transferred across the cavity. To exert proper control on the amount of heat, an arrangement made with insulated deflectors in contact with the hot wall was implemented. In the two situations, an automatic controller handles three possible orientations of the deflectors. The automatic controller imparts rotation to the deflectors that gyrate around an axle that passes through their mid-point. The three possible orientations are: (1) an "on" horizontal position placed at 0°, (2) an "off" vertical position at 90° and (3) an intermediate "off" inclined position at 45°. The integration of the conservation equations was carried out with the finite volume technique. Based on numerical/experimental guidelines available for the avoidance of oscillatory regimes, the numerical calculations were limited to Rayleigh numbers ≤ 106 . A simple, reliable positioning control for the two sets of deflectors regulates the heat flow in the cooled vertical wall, keeping it below a certain value or threshold. The desired position or angle can be entered through a user interface, being transformed in a series of digital pulses by an indexer. For the case of one large deflector, the maximum heat transfer suppression is obtained at RaH = 104 , when the deflector is placed in a position of 0°. The minimal heat transfer suppression occurs at RaH = 106 when the deflector is placed at a position of 45°. For the case of two small deflectors, the maximum heat transfer suppression takes place in the RaH sub-interval 10 < RaH ≤ 106. The minimal heat transfer suppression occurs at RaH = 106. In both cases, the deflector is placed at a position of 45°.


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