Mixed Convection in a Vertical Heated Channel: Influence of the Aspect Ratio
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59179", author = "Ameni Mokni and Hatem Mhiri and Georges Le Palec and Philippe Bournot", title = "Mixed Convection in a Vertical Heated Channel: Influence of the Aspect Ratio", 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", volume = "3", number = "9", pages = "676-7", }
