PİMLİ ÜÇ BOYUTLU DİKDÖRTGEN KUTULARDA ISI TRANSFERİ

Abstract

Üç boyutlu gri yüzeyli dikdörtgen geometrili kutularda termal radyasyon ile doğal taşınımın etkileşimi sayısal olarak incelenmiştir. Dikdörtgen kutuda dikey karşıt izotermal duvarlar ısıtılıp soğutulurken, diğer tüm duvarlar yalıtılmıştır. Pimler sıcak duvara eklenmiştir. Katılımcı olmayan ortamda akışkanın hava (Pr=0.71) ve akışın laminer olduğu kabul edilmiştir. Boussinesq yaklaşımının kullanıldığı yoğunluk dışındaki tüm termofiziksel özelliklerinin sabit olduğu varsayılmıştır. Momentum, enerji denklemleri ve radyasyon transferi ticari CFD kodu ANSYS ile çözülmüştür. Taşınım terimlerinin ayrıklaştırılmasında ikinci dereceden ayrıklaştırma şeması, çözüm yöntemi olarak da SIMPLE algoritması ve yüzey ışınım hesabında S2S (Surface to Surface) ışınım modeli kullanılmıştır. Rayleigh sayısı (Ra), yüzey emissivitesi (ε), pim sayısı, boyutsuz pim çapları (D=d/H) ve uzunlukları (B=b/H), dikdörtgen kutunun genişlik yükseklik oranı (W/H) parametrik olarak değiştirilmiştir. Üç boyutlu kutunun, incelik oranı, W/H=0.5, 1.0 ve 2.0 olarak ele alınmıştır. Kutudaki pimlerin sayısı ise 9, 13, 17, 21 ve 25 olarak değiştirilmiştir. Rayleigh sayısı, yüzey emissivitesi, boyutsuz pim uzunlukları ve çapları, sırasıyla 103≤Ra≤106, 0.0≤ε≤1.0, 0.05≤B≤0.6, 0.025≤D≤0.1, değer aralıklarında değiştirilmiştir. Ortalama taşınım, radyasyon ve toplam Nusselt sayıları, her durum için Rayleigh sayısının bir fonksiyonu olarak hesaplanmıştır. Ayrıca ele alınan tüm durumlar için akış ve sıcaklık dağılımları verilmiş ve tartışılmıştır.

Keywords

• Üç boyutlu
• Doğal taşınım
• S2S Işınım
• Dikdörtgen kutular

HEAT TRANSFER IN THREE-DIMENSIONAL RECTANGULAR CAVITIES WITH PINS

Abstract

The interaction of natural convection with thermal radiation in three dimensional rectangular cavities with gray surfaces is studied numerically. The cavity is heated and cooled from the vertical opposing isothermal walls while all other side walls are adiabatic. The pins are placed to the active wall. The fluid is nonparticipating air (Pr=0.71), and the flow of air is assumed to be laminar. The fluid properties are taken to be constant at mean values, except for the density for which the Boussinesq approximation is employed. The governing flow, energy and the radiative transfer equations are solved by a commercial CFD code-ANSYS. The convection terms are discretized using a second order upwind scheme, and SIMPLE algorithm is adapted as the solution algorithm. The surface to surface (S2S) model is used for radiative heat transfer simulations. The Rayleigh number (Ra), the surface emissivity (ε), the number of pins, the dimensionless pin length and diameter (B=b/H and D=d/H), the slenderness of the cavity (W/H) are variable parameters of this study. The slenderness ration of W/H=0.5, 1.0 and 2.0 are considered. Enclosure with pin arrangements of 9, 13, 17, 21 and 25 are considered. The Rayleigh number, the surface emissivity, the dimensionless pin lengths and diameters are varied in the following intervals 103≤Ra≤106, 0.0≤ε≤1.0, 0.05≤B≤0.6, 0.025≤D≤0.1, respectively. The mean Nusselt numbers for convection and radiation, as well as total, were computed as a function of the Rayleigh number for each case. Also the flow and temperature distribution for some cases have been presented and discussed.

Keywords

• Three-dimensional
• Natural convection
• S2S Radiation
• Rectangular cavities

References

1. Akiyama M., and Chong Q.P., 1997, Numerical analysis of natural convection with surface radiation in a square enclosure, Numer. Heat Tr. A-Appl, 32, 419-433.
2. Alessio M.E., and Kuminski D.A., 1989, Natural convection and radiation heat transfer from an array of inclined pin fins, J. Heat Transf., 111(1), 197-199.
3. Balaji C., and Venkateshan S.P., 1993, Interaction of surface radiation with free convection in a square cavity, Int. J. Heat Fluid Fl., 14(3), 260-267.
4. Balaji C., and Venkateshan S.P., 1994, Correlations for free convection and surface radiation in a square cavity, Int. J. Heat Fluid Fl., 15(3), 249-251.
5. Ben-Nakhi A., and Chamkha A.J., 2006, Effect of length and inclination of a thin fin on natural convection in a square enclosure, Numer. Heat Tr. A-Appl, 50, 381-399.
6. Bocu Z., and Altaç Z., 2011, Laminar natural convection heat transfer and air flow in three-dimensional rectangular enclosures with pin arrays attached to hot wall, Appl. Therm. Eng., 31, 3189-3195.
7. Bouali H., Mezrhab A., Amaoui H., and Bouzidi M., 2006, Radiation-natural convection heat transfer in an inclined rectangular enclosure, Int. J. Therm. Sci., 45, 553-566.
8. Colomer G., Costa M., Consul R., and Oliva A., 2004, Three dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method, Int. J. Heat Mass Tran., 47, 257-269.

9. Da Silva A.K., and Gosselin L., 2005, On the thermal performance of an internally finned three dimensional cubic enclosure in natural convection, Int. J. Heat Mass Tran., 44, 540-546.
10. Das, D., Dwivedi, A., and Verma, S.P., 2018, Performance of heated pin fin arrangement in a rectangular cavity-An experimental approach, J. Mech. Sci. Technol., 32(4), 1897-1903.
11. Dogan M., Sivrioglu M., and Yılmaz O., 2014, Numerical analysis of natural convection and radiation heat transfer from various shaped thin fin-arrays placed on a horizontal plate-a conjugate analysis, Energ. Convers. Manage., 77, 78-88. 49
12. Frederick R.L., and Moraga S.G., 2007, Three-dimensional natural convection in finned cubical enclosures, Int. J. Heat Fluid Fl., 28, 289-298.
13. Kuznetsov G.V., and Sheremet M.A., 2009, Conjugate natural convection with radiation in an enclosure, Int. J. Heat Mass Tran., 52, 2215-2223.
14. Martyushev S.G., and Sheremet M.A., 2014, Conjugate natural convection combined with surface thermal radiation in a three-dimensional enclosure with a heat source, Int. J. Heat Mass Tran., 73, 340-353.
15. Mezrhab A., and Bchir L., 1998, Radiation-natural convection interactions in partitioned cavities, Int. J. Numer. Method H., 8, 781-799.
16. Rabhi M., Bouali H., and Mezrhab A., 2008, Radiation-natural convection heat transfer in inclined rectangular enclosures with multiple partitions, Energ. Convers. Manage., 49, 1228-1236.
17. Ramesh N., and Venkateshan S.P., 1999, Effect of surface radiation on natural convection in a square enclosure, J. Thermophys. Heat Tr., 13(3), 299-301.
18. Rammohan Rao V., and Venkateshan S.P., 1996, Experimental study of free convection and radiation in horizontal fin arrays, Int. J. Heat Mass Tran., 39(4), 779-789.
19. Sahray D., Shmueli H., Ziskind G., and Letan R., 2010, Study and optimization of horizontal-base pin-fin heat sinks in natural convection and radiation, J. Heat Transf., 132(1), 012503-012503-13.
20. Saravanan S., and Sivaraj C., 2015, Combined natural convection and thermal radiation in a square cavity with a nonuniformly heated plate, Computer & Fluids, 117, 125-138.
21. Sen S., and Sarkar A., 1995, Effects of variable property and surface radiation on laminar natural convection in a square enclosure, Int. J. Numer. Method H., 5, 615-627.
22. Sertkaya A.A., Bilir S., and Kargıcı S., 2011, Experimental investigation of the effects of orientation angle on heat transfer performance of pin-finned surfaces in natural convection, Energy, 36, 1513-1517.
23. Sharma A.K., Velusamy K., Balaji C., and Venkateshan S.P., 2007, Conjugate turbulent natural convection with surface radiation in air filled rectangular enclosures, Int. J. Heat Mass Tran., 50, 625-639.
24. Sparrow E.M., and Vemuri S.B., 1985, Natural convection/radiation heat transfer from highly populated pin fin arrays, J. Heat Transf .,107(1), 190-197.
25. Tric E., Labrosse G., and Betrouni M., 2000, A first incursion into the 3D structure of natural convection of air in a differentially heated cubic cavity, from accurate numerical simulations, Int. J. Heat Mass Tran., 43, 4043-4056.
26. Vivek V., Sharma A.K., and Balaji C., 2012, Interaction effects between laminar natural convection and surface radiation in tilted square and shallow enclosures, Int. J. Therm. Sci., 60, 70-84.
27. Zografos A.I., and Sunderland J.E., 1990, Natural convection from pin