NUMERICAL STUDY OF MIXED CONVECTION COUPLED WITH RADIATION IN A VENTED PARTITIONED ENCLOSURE
A. Bahlaoui*, A. Raji*, M. Hasnaoui**, R. El Ayachi*, M. Naimi*,
T. Makayssi*, M. Lamsaadi*
*Faculty of Sciences and Technologies, Department of Physics, University Sultan Moulay Sliman, Team of Flows and Transfers Modeling (EMET), Laboratory of Physics and Mechanics of Materials, BP 523, Beni-Mellal, Morocco Tel.: 00212 23 48 51 12; Fax: 00212 23 48 52 01, E-mail: abderaji@fstbm.ac.ma; abderaji@yahoo.fr
"Faculty of Sciences Semlalia, Department of Physics, University Cadi Ayyad, UFR TMF, BP 2390 Marrakesh, Morocco Tel.: 00212 44 43 46 49; Fax: 00212 44 43 74 10, E-mail: hasnaoui@ucam.ac.ma
Received: 27 Sept 2007; accepted: 29 Oct 2007
The present work reports numerical results of mixed convection and surface radiation within a horizontal ventilated cavity, with an aspect ratio A = L'/H' = 2, heated from below and provided with an adiabatic partition, of a fine thickness, on the heated surface. Air, a radiatively transparent medium, is considered to be the cooling fluid. The effect of the governing parameters, which are the Reynolds number, 200 < Re < 5000, the partition position from the inlet, 0.25 < Lb < 1.75, and the emissivity of the walls, 0 < e < 0.85, on the fluid flow and heat transfer characteristics is studied in detail. The relative height of the partition, Hb = H'b/H', and the relative height of the openings, B = h'/H', are kept constant at 1/2 and 1/4 respectively.
Keywords: mixed convection, surface radiation, ventilated cavity, adiabatic partition
Organization: A teacher at the Faculty of Sciences and Technics in Beni Mellal (Morocco). Education: Doctorates in heat transfer (1994 and 2000) after attending Cadi Ayyad University. The title of the first doctorate: "Etude numérique des écoulements et des transferts de chaleur par convection dans des cavités en interaction et dans un canal de longueur finie". The title of the second thesis: "Etude numérique du phénomène de la convection mixte dans des cavités ventilées avec et sans effet de rayonnement".
Experience: Head of the physics department from 2000 to 2003.
Main range of scientific interests: Heat transfer by conduction, convection, radiation, porous media... Publications: from 2004: - Coupling between mixed convection and radiation in an inclined channel locally heated. Journal of Mechanical Engineering, 2004. - Interaction between natural convection and radiation in a square cavity heated from below. Numerical Heat Transfer, Part - A: Applications, 2004.
- Multiple steady state solutions resulting from coupling between mixed convection and radiation in an inclined. Heat and Mass Transfer, August 2005. - Combined effect of radiation and natural convection in a rectangular enclosure discreetly heated from one side. International Journal of Numerical Methods for Heat & Fluid Flow, 2006. - Multiplicité de solutions en convection naturelle couplée au rayonnement dans une cavité horizontale, Physical & Chemical News, 2006. - Mixed convection in a horizontal channel with emissive walls and partially heated from below. Numerical Heat Transfer, Part
- A: Applications, 2007. - Multiple steady state solutions for natural convection in a tilted rectangular slot containing non-Newtonian power-law fluids and subject to a transverse thermal gradient. Numerical Heat Transfer, Part - A: Applications, 2007. - Parallel flow convection in a shallow horizontal cavity filled with non-Newtonian power-law fuids and subject to horizontal and vertical uniform heat fluxes2. In press in Numerical Heat Transfer, Part - A: Applications, 2007. - Coupled natural convection and radiation in a horizontal rectangular enclosure discretely heated from below. Accepted in Numerical Heat Transfer, Part - A: Applications, 2007.
Education: A diploma of higher studies in Fluid Mechanics and Energetics (2000) of the Faculty of Sciences Semlalia, Marrakech, Morocco and a National Doctorate in Fluid Mechanics and Heat Transfer of the Faculty of Sciences and Technologies (F.S.T.), Béni-Mellal, Morocco (2006). Organization: A teacher in the F.S.T., Béni-Mellal, Morocco, during the period 2004-2007. Member of the Team of Flows and Transfers Modeling (EMET) in the F.S.T., Béni-Mellal, Morocco. The principal publications which I carried out are those cited above.
Abdelghani Raji
Ahmed Bahlaoui
HI
131
Nomenclature
A - aspect ratio of the cavity (= L' / H') B - relative height of the openings (= h'/ H') cv - convection
Fj - view factor from St surface to Sj one g - acceleration due to gravity, m/s2 h - height of the openings, m H - height of the cavity, m Hb - relative height of the partition (= H'b / H')
I - dimensionless irradiation (= I'/oT' 4) J - dimensionless radiosity (= J'/oT'4) L ' - length of the cavity, m
Lb - dimensionless x-direction distance of the partition from the inlet (= L'b / H')
Nr - convection-radiation interaction parameter (= oT'4 / q')
Nu - average Nusselt number
Pr - Prandtl number (= v /a)
q' - imposed wall heat flux, W/m2
Qr - dimensionless radiative heat flux (= Q'r /oT'4)
Ra - Rayleigh number (= g p q'H'4/avA,)
rd - radiation
Re - Reynolds number (= u'H' / v)
t - dimensionless time (= t'u'0 /H')
T - dimensionless fluid temperature (= A(T' - T')/ q' H')
T/- dimensional fluid temperature, K
T - dimensionless mean temperature
Tmax - dimensionless maximum temperature
T' - common temperature of the left vertical cold wall and
imposed flow, K
T0 - dimensionless reference temperature (= AT' / q' H') u0 - velocity of the imposed flow, m/s (u, v) - dimensionless horizontal and vertical velocities (=(uv')/ u0)
(x, y) - dimensionless coordinates (= (x', y') / H')
Greek symbols
a - thermal diffusivity of fluid, m2/s P - thermal expansion coefficient of fluid, 1/K At - dimensionless time step e - walls emissivity
A - thermal conductivity of fluid, W/(K-m) v - kinematic viscosity of fluid, m2/s Q - dimensionless vorticity (= fl' H' / u0) T - dimensionless stream function (= ^'/u'0 H') o - Stefan-Boltzman constant (= 5.67-10-8 W/m2-K4)
Subscripts and Superscripts
' - cold temperature H - heated wall max - maximum value min - minimum value ' - dimensional variable
Introduction
Mixed convection heat transfer in ventilated systems continues to be a fertile area of research, due to the interest of the phenomenon in many technological processes, such as the design of solar collectors, thermal design of buildings, air conditioning and recently the cooling of electronic circuit boards. In the literature, numerous analytical, numerical and experimental studies dealing with mixed convection in ventilated geometries have been reported without radiation effect. The effect of the latter can be neglected in the case of configurations with non emissive or weakly emissive boundaries which is not the case in general since the contribution of radiation to the overall heat transfer could be significant. In the absence of radiation, mixed convection in a square enclosure provided with a partially dividing partition was studied numerically by Hsu et al. [1], How and Hsu [2] and Hsu and Wang [3]. Results of the simulations indicate that the heat transfer and flow structure are strongly dependent on the height, the conductivity ratio and the location of the conducting baffles. Laminar mixed convection in a two-dimensional enclosure with assisting and opposing flows was studied numerically by Raji and Hasnaoui in the case of a cavity uniformly heated from one or two side walls [4-6]. The obtained results show that the Re-Ra plane can be divided in regions corresponding to the dominance of the forced convection or to the mixed convection regime where the heat transfer is maximum. Recently, mixed convection from a flush-mounted uniform heat sources in a rectangular enclosure with openings was numerically investigated by Bhoite et al [7]. and Saha et al. [8]. In the case of ventilated cavities, the numerical study, conducted by Raji and Hasnaoui [9] on combined mixed convection and radiation, showed that the contribution of radiation could be important even though the cooling fluid is transparent to radiation. The neglected effect of thermal radiation is mainly justified by the fact that the heat transfer is especially ensured by mixed or forced convection. However, moderate temperature differences give rise to significant radiation effects and the fact of neglecting their contribution becomes non realistic. The main objective of the present study consists of examining the effect of the Reynolds number, Re, the horizontal position of partition, Lb, and the emissivity of the walls, e, on flow and thermal fields. Variations, versus the main controlling parameters, of maximum and mean temperatures are also explored.
Problem formulation
The configuration under study, together with the system of coordinates is depicted in Fig. 1. It consists of a ventilated rectangular cavity. The bottom wall is uniformly heated with a constant heat flux and provided with a vertical adiabatic baffle. The upper horizontal and right vertical walls are considered insulated, while the
International Scientific Journal for Alternative Energy and Ecology № 6 (62) 2008
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left side of the cavity is cooled with a constant temperature. The system is submitted to an imposed flow of ambient air through an opening located on the lower part of left vertical wall. The forced flow leaves the cavity through an outflow opening placed on the higher part of the right vertical wall. The inner surfaces, in contact with the fluid, are assumed to be gray, diffuse emitters and reflectors of radiation with identical emissivities. The fluid properties are evaluated at a mean temperature and the airflow is assumed to be, two-dimensional, laminar, incompressible and obeying the Boussinesq approximation. Under these assumptions, the dimensionless governing equations, w
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