DAİRESEL BİR BORUDA ÜST KANUNU AKIŞKANININ AKIŞINDA ZORLANMIŞ TAŞINIMLA ISI TRANSFERİ

Öz

Sabit duvar ısı akısına sahip bir boruda üst kanunu akışkan akışı için boyutsuz sıcaklık, entropi üretim hızı ve Nusselt sayısı, üst kanunu indeksi, Brinkman sayısı, boyutsuz sıcaklık farkı ve grup parametrelerinin fonksiyonu olarak belirlenmiştir. Üst kanunu akışkan akışında enerji, entropi ve Nusselt sayısı için sürtünme kaynaklı enerji üretim terimini içeren bir boyutlu yaklaşık eşitlikler; terimlerin büyüklük dereceleri ve asimptotik teknikler göz önünde bulundurularak çıkarılmıştır. Hız, sıcaklık ve entropi üretimi için bir boyutlu yaklaşık eşitlikler Newton kanununa uymayan akışkan akışını için hız, sıcaklık ve entropi dağılımlarını belirlemek için analitik olarak etkin parametrelerin fonksiyonu olarak çözümlenmiştir. Akış indeksi ve Brinkman sayına bağlı Nusselt sayısı için sürtünme kaynaklı enerji üretim terimli türetilmiş eşitlik, bütün pseudo plastik ve dilatant akışkan davranışlarını kapsamaktadır. Brinkman sayısının sıcaklık, entropi üretim sayısı ve Nusselt sayısı üzerinde oldukça etkin olduğu bulunmuştur. Üs kanununu indeksinin tüm değerlerinde Nusselt sayısı, Brinkman sayısının artmasıyla üstel olarak azalmıştır.

Anahtar Kelimeler

• Entropy üretimi
• zorlanmış taşınım
• Brinkman sayısı
• üst kanunu akışkanı akışı

FORCED CONVECTION HEAT TRANSFER IN A POWER-LAW FLUID FLOW IN A CIRCULAR DUCT

Öz

The dimensionless temperature, the entropy generation rate and Nusselt number for a power-law fluid flow in a pipe with constant wall heat flux have been determined as functions of the Brinkman number, power-law index, dimensionless temperature difference and group parameters. The one-dimensional approximate equations with viscous dissipation for the energy, the entropy and the Nusselt number for a power-law fluid flow have been determined by accounting for the order of magnitude of terms and asymptotic techniques. The one-dimensional approximate equations of the velocity, the temperature and the entropy generation rate have been analytically solved to determine the velocity, the temperature and the entropy distributions in a non-Newtonian fluid flow as functions of the effective process parameters. The derived equation with viscous dissipation term for Nusselt number depending on power-law index and Brinkman number covers all types of pseudo-plastic and dilatant fluid behaviors. It has found that the Brinkman number is quite effective on the temperature, the Nusselt number and the entropy generation number. The Nusselt number has exponentially decreased with increasing Brinkman number at values of power-law index.

Anahtar Kelimeler

• Brinkman number
• entropy generation
• viscous dissipation
• power-law fluid flow

Kaynakça

1. Bejan, A., 1979, A study of entropy generation in fundamental convective heat transfer, J Heat Transf, 101, 718-725.
2. Bejan, A., 1996, Entropy generation minimization. New York, CRC Press.
3. Bejan, A., 1982, Second law analysis in heat transfer and thermal design, Adv. Heat Transfer, 15, 1-58.
4. Bird, R. B., Stewart, W. E. & Lightfoot, E. N., 2007, Transport phenomena. Revised 2nd Edition, Wiley, New York.
5. Imal, M; Ozalp, C; Yaniktepe, B; Mehdi-Rashidi, M; & Hurdogan, E., 2017, Entropy generation for a non-Newtonian shear thinning fluid with viscous heating effects. Trans. Canadian Soc. Mech. Eng., 41, 593-607.
6. Kamisli, F., 2009, Analysis of laminar flow and forced convection heat transfer in a porous medium. Transport in Porous Media, (80) 345-371.
7. Kamisli, F., 2008, Second law analysis of a disturbed flow in a thin slit with wall suction and injection, Int. J. Heat Mass transf., 51 3985-4001.
8. Kamisli, F. & Oztop, H. F., 2008, Second law analysis of 2D laminar flow of two-immiscible, incompressible viscous fluids in a channel. Heat and Mass transf., 44, 751-761.

9. Kiyasatfar, M., 2018, Convective heat transfer and entropy generation analysis of non-Newtonian power-law fluid flows in parallel-plate and circular microchannels under slip boundary conditions, Int. J. Thermal Sci., 128, 15–27.
10. Mahmud, S. & Fraser, R. A., 2006, Second law analysis of forced convection in a circular duct for non-Newtonian fluids. Energy, (31) 2226-2244.
11. Mukherjee, S., Gupta, A.K. & Chhabra, R.P., 2017, Laminar forced convection in power-law and Bingham plastic fluids in ducts of semi-circular and other cross-sections, Int. Journal Heat and Mass Transfer, 104, 112-141. Nag, P. I. K. & Kumar, N., 1989, Second law optimization of convective heat transfer through a duct with constant heat flux. Int. J. Energy Res. (13) 537-543.
12. Narusawa, U., 2001, The second law analysis of mixed convection in rectangular ducts, Heat Mass Transf., 37, 197-203.
13. Paoletti, S., Rispoli, F. & Sciubba, E., 1989, Calculation energetic loses in compact heat exchanger passages, ASME AES, 10, 21–29.
14. Sahin, A. Z., 1998, Second law analysis of laminar viscous flow through a duct subjected to constant wall temperature, J. Heat Transf., 120, 76-83.
15. Sahin, A. Z., 1998, A second law comparison for optimum shape of duct subjected to constant wall temperature and laminar flow, Heat Mass Transf., 33, 425-430.
16. Sahin, A. Z., 1999, Effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux, Heat Mass Transf., 35, 499-506.
17. Sahin, A. Z., 2014, A Simple method of determining entropy generation rate in viscous fluid flow through ducts, Arab J. Sci. Eng., 39, 1241–1249.
18. Saouli, S. & Saouli. S.A., 2009, Second law analysis of laminar non-Newtonian gravity-driven liquid film along an inclined heated plate with viscous dissipation effect, Brazilian J. Chem. Eng., 26, 407-414.
19. Sarabandi, A.H. & Moghadam, A.J., 2017, Thermal analysis of power-law fluid flow in a circular microchannel, J. Heat Transfer, 139, 1-14 (032401).
20. Shojaeian, M. & Kosar, A., 2014, Convective heat transfer and entropy generation analysis on Newtonian and non-Newtonian fluid flows between parallel-plates under slip boundary conditions, Int. J. Heat and Mass Transfer, 70, 664–673.
21. Shojaeian, M. & Kosar, A., 2016, Convective heat transfer of non-Newtonian power-law slip flows and plug flows with variable thermophysical properties in parallel-plate and circular microchannels, Int. J. Thermal Sci., 100, 155-168.