Natural convection heat transfer from a thin horizontal isothermal plate in air-filled rectangular enclosures

Bir izotermal plaka içeren hava dolu dikdörtgensel kapalı kutunun diğer üç kenarı yalıtılmış iken bir dikey kenarından soğutulmaktadır. Yatay olarak konumlandırılan izotermal plaka sisteme ısı girişinin tek kaynağıdır. Plaka ve soğuk duvarlar sabit sıcaklıkta muhafaza edilmektedir. Boussinesq yaklaşımı ile beraber taşınım denklemleri ve enerji denklemi SIMPLE algoritması ile kuple edilen sonlu hacim metodu (FVM) kullanılarak çözülmektedir. Sürekli rejimde, izotermal plaka yüzey alanı üzerinden ortalanan Nusselt sayısı, Rayleigh sayısı, plaka uzunluğu ve konumunun bir fonksiyonu olarak hesaplanmıştır. Rayleigh sayısı 105 ile 5×107 arasında değiştirilirken, kutu uzunluğunun %50 ve %75’ine varan iki plaka uzunluğu alternatifi göz önüne alınmıştır. Plaka kalınlığı kutu yüksekliğinin %1’i olarak sabit tutulmuştur. Plaka uzunluğu, plaka konumu ve incelik oranının (A=1 ve 2) ısı transfer karakteristikleri ve akışkan akışına etkileri incelenmiştir. Artan Rayleigh sayısı ile ısı geçiş oranı artmaktadır ve artan plaka uzunluğu ile ısı geçiş oranı (Nusselt sayısı) yaklaşık %25 azalmaktadır. Bu sayısal parametrik çalışmanın bir sonucu olarak, pratik soğutma problemlerinde kullanmak üzere, bir Nusselt sayısı bağıntısı elde edilmiştir.

Hava dolu kapalı kutular içindeki bir ince yatay izotermal plakadan doğal taşınım ile ısı geçişi

An air filled rectangular enclosure containing an isothermal plate is cooled from a lateral wall while other three sides are insulated. A horizontally situated thin isothermal plate is the sole source of heat input within the system. The plate and the cold walls are maintained at constant temperatures. The transport equations, along with the Boussinesq approximation as well as the energy equation, are solved using the finite volume method (FVM) coupled with SIMPLE algorithm. The steady state mean Nusselt number over the isothermal plate surface area is computed for each case as a function of Rayleigh number, the plate length and position. Rayleigh number is varied from 105 to 5×107 while two plate length alternatives were studied—50% and 75% of the enclosure length. The plate thickness was kept constant—1% of the enclosure height. The effects of the plate length, the plate position and the aspect ratio (A=1 and 2) on the heat transfer characteristics and the fluid flow were investigated. For increasing Rayleigh number the heat transfer rates increases, and for increasing plate length the heat transfer rate (Nusselt number) decreases by about 25%. As a result of the numerical parametric study, a correlation for the Nusselt number is obtained to be used for practical cooling problems.

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Altaç, Z. and Kurtul, Ö., Natural convection in tilted rectangular enclosures with a vertically situated hot plate inside, Applied Thermal Engineering 27, 1832– 1840, 2007.
Barozzi, G. S., Corticelli, M. A. and Nobile, E., Numerical simulation of time-dependent buoyant flows in an enclosed vertical channel, Heat and Mass Transfer 35, 89-99, 1999.
Barozzi, G. S. and Corticelli, M. A., Natural convection in cavities containing internal sources, Heat and Mass Transfer 36, 473-480, 2000.
Ben-Nakhi, A. and Chamkha, A. J., Effect of length and inclination of a thin fin on natural convection in a square enclosure, Numer Heat Transfer, Part A 50, 389- 407, 2006.
Bessaih, R. and Kadja, M., Turbulent natural convection cooling of electronic components mounted on a vertical channel, Applied Thermal Engineering 20,141-154, 2000.
Bilgen, E., Natural convection in cavities with a thin fin on the hot wall Int. J. Heat and Mass Transfer 48, 3493–3505, 2005.
Bilen, K., Yapici S., Celik C.. A Taguchi approach for investigation of heat transfer from a surface equipped with rectangular blocks. Energy Convers Manage 42, 951–961, 2001.
Comini, G., Cortella, G. and Manzan, M., A stream function-vorticity-based finite-element formulation for laminar-convection problems, Numer Heat Transfer, Part B 28, 1-22, 1995.
Dağtekin, I. and Öztop, H. F., Natural convection heat transfer by heated partitions, Int. Commun Heat Mass Transfer 28, 823-834, 2001.
Desai, C. P., Vafai, K. and Keyhani, M., On the natural convection in a cavity with a cooled top wall and multiple protruding heaters, J Electronic Packaging 117, 34-45, 1995.
El Alami, M., Najam, M., Semma, E., Oubarra, A. and Penot, F., Electronic components cooling by natural convection in horizontal channel with slots, Energy Conversion and Management 46, 2762-2772, 2005.
Frederick, R. L. and Valencia, A., Heat transfer in a square cavity with a conducting partition on its hot wall, Int. Commun. Heat Mass Transfer 16, 347-354, 1989.
Heindel, T. J., Ramadhyani, S. and Incropera, F. P., Laminar natural convection in a discretely heated cavity: I-Assessment of three-dimensional effects, ASME J Heat Transfer 117, 902-909, 1995.
Heindel, T. J., Ramadhyani, S. and Incropera, F.P., Laminar natural convection in a discretely heated cavity: II- Comparisons of experimental and theoretical results, ASME J Heat Transfer 117, 910-916, 1995.
Incropera, F.P., Convection heat transfer in electronic equipment cooling. ASME J Heat Transfer 110, 1097- 1111, 1988.
Kang, B. H. and Jaluria, Y., Natural convection heat transfer characteristics of a protruding thermal source located on horizontal and vertical surfaces, Int. J. Heat Mass Transfer 33, 1347-1357, 1990.
Le Quéré, P., Accurate solutions to the square thermally driven cavity at high Rayleigh number, Computers and Fluids 20, 29-41, 1991.
Markatos, N. C. and Pericleous, K. A., Laminar and turbulent natural convection in an enclosed cavity, Int. J. Heat Mass Transfer 5, 755-772, 1984.
Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Washington DC, 1980.
Türkoğlu, H. and Yücel, N., Natural convection heat transfer in enclosures with conducting multiple partitions and side walls, Heat and Mass Transfer 32, 1- 8, 1996.
Sun, Y. S. and Emery, A. F., Effects of wall conduction, internal heat sources and an internal baffle on natural convection in a rectangular enclosure, Int. J Heat Mass Transfer 40, 915-929, 1997.
Sathe, S. B. and Joshi, Y., Natural convection liquid cooling of substrate-mounted protrusion in a square enclosure: effects of thermophysical properties, geometric dimensions and boundary conditions, in: R.A. Wirtz, G.L. Lehmann (Eds.), Thermal Modelling and Design of Electronic Systems and Device, Vol. HTD 153, ASME (1990) 73-80.
Yücel, N. and Türkoğlu, H., Numerical analysis of laminar natural convection in enclosures with fins attached to an active wall, Heat and Mass Transfer, 33(4), 307-314, 1998.
Vahl Davis, G. D., Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Numer Method Fluids 3, 249-264, 1983.