Mixed Convection in a Vertical Heated Channel: Influence of the Aspect Ratio

Authors: Ameni Mokni , Hatem Mhiri , Georges Le Palec , Philippe Bournot

Abstract:

In mechanical and environmental engineering, mixed convection is a frequently encountered thermal fluid phenomenon which exists in atmospheric environment, urban canopy flows, ocean currents, gas turbines, heat exchangers, and computer chip cooling systems etc... . This paper deals with a numerical investigation of mixed convection in a vertical heated channel. This flow results from the mixing of the up-going fluid along walls of the channel with the one issued from a flat nozzle located in its entry section. The fluiddynamic and heat-transfer characteristics of vented vertical channels are investigated for constant heat-flux boundary conditions, a Rayleigh number equal to 2.57 1010, for two jet Reynolds number Re=3 103 and 2104 and the aspect ratio in the 8-20 range. The system of governing equations is solved with a finite volumes method and an implicit scheme. The obtained results show that the turbulence and the jet-wall interaction activate the heat transfer, as does the drive of ambient air by the jet. For low Reynolds number Re=3 103, the increase of the aspect Ratio enhances the heat transfer of about 3%, however; for Re=2 104, the heat transfer enhancement is of about 12%. The numerical velocity, pressure and temperature fields are post-processed to compute the quantities of engineering interest such as the induced mass flow rate, and average Nusselt number, in terms of Rayleigh, Reynolds numbers and dimensionless geometric parameters are presented.

Keywords: Aspect Ratio, Channel, Jet, Mixed convection

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1074633

References:

[1] W. Elenbaas, Heat Dissipation of Parallel Plates by Free convection, Physica, vol. 9, n┬░ 1, pp.1-28, 1942
[2] J.R. Bodoia and J.F. Osterle, The Development of Free Convection Between Heated Vertical Plates, J. of Heat Transfer , Trans. ASME, Series C, vol. 84, n┬░1, pp.40-44, 1962.
[3] S.J. Kim, S.W. Lee, Air Cooling Technology for Electronic Equipment, CRC Press, Boca Raton, FL, 1996.
[4] A. Bejan, Shape and Structure from Engineering to Nature, Cambridge University Press, New York, 2000.
[5] G.A. Ledezma, A. Bejan, Optimal geometric arrangement of staggered vertical plates in natural convection, ASME J. Heat Transfer 119 pp. 700-708,1997.
[6] S. Sathe, B. Sammakia, A review of recent developments in some practical aspects of air-cooled electronic packages, ASME J. Heat Transfer 120 pp. 830-839,1998.
[7] A. Bejan, A.K. da Silva, S. Lorente, Maximal heat transfer density in vertical morphing channels with natural convection, Numer. Heat Transfer A 45, pp. 135-152, 2004.
[8] A. Auletta, O.Manca, B. Morrone, V. Naso, Heat transfer enhancement by the chimney effect in a vertical isoflux channel, Int. J. Heat Mass Transfer 44 pp. 4345-4357, 2001.
[9] A.K. da Silva, L. Gosselin, Optimal geometry of L- and C-shaped channels for maximum heat transfer rate in natural convection, Int. J. Heat Mass Transfer 48 pp. 609-620, 2005
[10] A. Andreozzi, A. Campo, O. Manca, Compounded natural convection enhancement in a vertical parallel-plate channel, Int. J. Thermal Sciences 47 (6) (2008) 742-748.
[11] Hugot G., Etude de la convection naturelle laminaire entre deux plaques planes verticales parallèles et isothermes, Entropie 46 pp. 55-66. 1972
[12] M.Miyamoto, Y. Katoh, J. Kurima, H. Saki, Turbulent free convection heat transfer from vertical parallel plates. in Heat Transfer, eds C. L. Tien, V. P.Carey and J. K. Ferrell, Vol. 4. Hemisphere, Washington, DC, pp. 1593- l598. 1986
[13] A. Auletta, O. Manca, Heat and fluid flow resulting from the chimney effect in a symmetrically heated vertical channel with adiabatic extensions, International Journal of Thermal Sciences 41 pp. 1101-1111. 2002.
[14] A. Andreozzi, B. Buonomo, O.Manca, Thermal management of a symmetrically heated channel-chimney system, International Journal of Thermal Sciences,48, pp. 475-487, 2009.
[15] J.R. Dyer , The Development of Laminar Natural convective Flow in a Vertical Uniform Heat Flux Duct, Int. J. Heat Mass Transfer, vol.18, pp.1455-1465, 1975.
[16] C.F. Hess and C.W. Miller, Natural Convection in a Vertical Cylinder subject to Constant Heat Flux, Int. J. Heat Mass Transfer, vol. 22, pp.421-430, 1979.
[17] A. Bar-Cohen and W.M. Rohsnow, Thermally Optimum Spacing of Vertical Natural Convection Cooled, Parallel Plates, J. Heat Transfer, vol.116, pp.116-123, 1984.
[18] F. Marcondes and C.R. Maliska, Treatment of the Inlet Boundary Conditions in Natural Convection Flows on open Ended Channels, Numerical Heat Transfer, Part B, vol.35 ,pp.317-345, 1999.
[19] A. Auletta, O.Manca, B. Morrone, V. Naso, Heat transfer enhancement by the chimney effect in a vertical isoflux channel. Int. J. Heat Mass Transfer 44 pp. 4345-4357, 2001.
[20] Y. Asako, H. Nakamura,M. Faghri, Natural convection in a vertical heated tube attached to a thermally insulated chimney of a different diameter. ASME J. Heat Transfer, pp.112 : 790-795,1990.
[21] A.G. Straatman, J.D. Tarasuk, J.M. Floryan, Heat transfer enhancement from a vertical, isothermal channel generated by the chimney effect,. ASME J. Heat Transfer.115 pp. 395-402, 1993.
[22] A. Andreozzi, B. Buonomo, O. Manca, Numerical study of natural convection in vertical channels with adiabatic extensions downstream,. Numer. Heat Transfer A (47):pp.1-22, 2005.
[23] G.A. Shahin, J.M. Floryan, Heat transfer enhancement generated by the chimney effect in systems of vertical channel. ASME J. Heat Transfer, 121: pp.230-232, 1999.
[24] F.Penot, A.M.Dalbert, convection naturelle mixte et forcée dans un thermosiphon vertical chauffé ├á flux constant,. International Journal of Heat and Mass Transfer 26 (11) pp.1639-1647, 1983.
[25] M. Najam, M. El Almi, M. Hasnaoui, A. Amahamid, Etude numérique de la convection mixte dans une cavité en forme de T soumis ├á un flux de chaleur constant et ventilé par le bas ├á l-aide d- un jet d-air vertical,. Compte Rendu de Mécanique, 330 pp. 461-467 , 2002.