TRANSIENT HEAT TRANSFER IN PIPES WITH TIME PERIODICALLY CHANGING BOUNDARY CONDITION

Öz

Transient heat transfer in thermal entrance region of pipes with time periodically changing surface temperature is investigated. The problem is handled in a two-regional pipe for laminar, hydrodynamically developed flow by involving fluid axial conduction. The solution is made numerically by a finite-difference method. A parametric study is done to analyse the effects of Peclet number and angular frequency on heat transfer characteristics. The results show that, considerable amount of heat is diffused back towards the upstream region by axial fluid conduction, which causes preheating the fluid prior to the heated downstream region. The heat transfer characteristics, in all axial positions, including the preheated upstream and the fully developed region, are seen to change periodically in time, similar to the periodic change of the surface temperature in the downstream region. , , , .

Anahtar Kelimeler

• Fluid axial conduction
• Time periodicaly changing boundary conduction
• Transient heat transfer
• Laminar flow heat transfer in pipe

BORULARDA ZAMANLA PERİYODİK OLARAK DEĞİŞEN SINIR ŞARTI İLE GEÇİCİ REJİM ISI TRANSFERİ

Öz

Borularda ısıl gelişme bölgesi geçici rejim ısı transferi, zamanla periyodik olarak değişen cidar dış yüzey sıcaklığı sınır şartında incelenmiştir. Problem, iki bölgeli bir boruda, hidrodinamik olarak gelişmiş laminer akış için, eksenel akışkan iletimi dikkate alınarak ele alınmış ve sonlu farklar yöntemi ile sayısal olarak çözülmüştür. Peclet sayısı ve açısal frekansın ısı transferi karakteristikleri üzerindeki etkilerini belirleyebilmek için parametrik bir çalışma yapılmıştır. Elde edilen sonuçlardan akışkan eksenel iletimi nedeniyle borunun üst akış bölgesine, akışa ters yönde önemli ölçüde ısı transfer edildiği ve bunun akışkanın borunun ısıtılan alt akış bölgesine gelmeden önce ön ısıtılmasına neden olduğu görülmüştür. Ayrıca alt akış bölgesi dış yüzey sıcaklığındaki periyodik değişime uygun olarak, tüm ısı transferi karakteristiklerinin de, ön ısıtma ve tam gelişmiş bölge de dahil olmak üzere, tüm eksenel konumlarda zamanla periyodik olarak değiştiği görülmüştür.

Anahtar Kelimeler

• Akışkan eksenel iletimi
• Zamanla periyodik olarak değişen sınır şartı
• Geçici rejimde ısı transferi

Kaynakça

1. Ateş, A., Darıcı, S. ve Bilir, Ş.,2010, Unsteady conjugated heat transfer in thick walled pipes involving two-dimensional wall ve axial fluid conduction with uniform heat flux boundary condition, International Journal of Heat and Mass Transfer, 53 (23-24), 5058-5064.
2. Altun, A. H., Bilir, Ş. ve Ateş, A., 2016, Transient conjugated heat transfer in thermally developing laminar flow in thick walled pipes and minipipes with time periodically varying Wall temperature boundary condition, International Journal of Heat and Mass Transfer,92, 63-47.
3. Aydın, O., Avcı, M., Bali, T. ve Arıcı, M.E., 2014, Conjugate heat transfer in a duct with an axially varying heat flux, International Journal of Heat and Mass Transfer, 76, 385–392.
4. Aydın, O. ve Avcı, M., 2015, Laminar forced convective slip flow in a microduct with a sinusoidally varying heat flux in axial direction, International Journal of Heat and Mass Transfer, 89, 606–612.
5. Barletta , A. ve Magyari, E., 2007, Forced convection with viscous dissipation in the thermal entrance region of a circular duct with prescribed wall heat flux, International Journal of Heat and Mass Transfer, 50, 26–35.
6. Barletta, A. ve Schio, E.R.,1999, Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux, Heat and Mass Transfer, 35, 9-16.
7. Barletta, A.ve Schio, E.R., 2000,Periodic forced convection with axial heat conduction in a circular duct, International Journal of Heat and Mass Transfer, 43, 2949-2960.
8. Barletta, A. ve Schio, E. R.,2004, Mixed convection flow in a vertical circular duct with time-periodic boundary conditions: steady-periodic regime, International Journal of Heat and Mass Transfer, 47, 3187-3195.

9. Barletta, A., Schio, E. R., Comini, G. ve P. D’Agaro, 2008, Conjugate forced convection heat transfer in a plane channel: Longitudinally periodic regime, International Journal of Thermal Sciences, b47, 43–51.
10. Barletta, A., Schio E. R., Comini, G. ve D’Agaro, P., 2009, Wall coupling effect in channel forced convection with streamwise periodic boundary heat flux variation, International Journal of Thermal Sciences, 48, 699–707.
11. Barletta, A. ve Zanchini, E., 1995, Laminar forced convection with sinusoidal wall heat flux distribution: axially periodic regime, Heat and Mass Transfer, 31, 41-48.
12. Barletta, A.ve Zanchini, E.,2003, Time-periodic laminar mixed convection in an inclined channel, International Journal of Heat and Mass Transfer, 46, 551–563.
13. Barletta, A., Zanchini, E., Lazzari, S. ve Terenzi, A., 2008, Numerical study of heat transfer from an offshore buried pipeline under steady-periodic thermal boundary conditions, Applied Thermal Engineering, 28, 1168–1176.
14. Bilir Ş., 1992, Numerical solution of Graetz problem with axial conduction, Numerical Heat Transfer, 21, 493-500.
15. Bilir Ş., 1995, Laminar flow heat transfer in pipes including two dimensional wall and fluid axial conduction, International Journal of Heat and Mass Transfer, 38(9), 1619-1625.
16. Bilir, Ş., 2002, Transient conjugated heat transfer in pipes involving two dimensional wall and axial fluid conduction, International Journal of Heat and Mass Transfer, 45 (8), 1781-1788.
17. Bilir, Ş. ve Ateş, A., 2003, Transient conjugated heat transfer in thick walled pipes with convective boundary conditions, International Journal of Heat and Mass Transfer, 46 (14), 2701-2709.
18. Conti, A., Lorenzini, G. ve Jaluria, Y., 2012, Transient conjugate heat transfer in straight microchannels, International Journal of Heat and Mass Transfer, 55, 532–7543.
19. Faghri, M. ve Sparrow, E.M., 1980, Simultaneous Wall and Fluid Axial Conduction in Laminar Pipe-Flow Heat Transfer, Journal of Heat Transfer, 102, 58-63.
20. Fourcher, B. ve Mansouri, K.,1997, An approximate analytical solution to the Graetz problem with periodic inlet temperature, Int. J. Heat and Fluid Flow,18:229-235.
21. Hildebrand, F.B., 1976, Advanced Calculus for Applications, Prentice- Hall, 170-111.
22. Hsu C.J., 1965, Heat transfer in a Round Tube with Sinusoidal Wall Heat Flux Distribution, A.I. Ch. E Journal, 11(4), 690-695. 48
23. Patankar, S.V., 1980, Numerical heat transfer and fluid flow, McGraw Hill Book Comp.
24. Patankar, S.V., Lıu, C.H., ve Sparrow, E.M., 1978, The Periodic Thermally Developed Regime in Ducts with Streamwise Periodic Wall Temperature or Heat Flux, International Journal of Heat and Mass Transfer, 21, 557-565.
25. Pearlstein, A.J., ve Dempsey, B.P., 1988, Low Peclet Number Heat Transfer in a Laminer Tube Flow Subjected to Axially Varying Wall Heat Flux, Journal of Heat Transfer, 110.3, 796-798.
26. Quaresma, J.N.N., ve Cotta R.M., 1994, Exact Solutions for Thermally Developing Tube Flow with Variable Wall Heat Flux, International Communications of Heat and Mass Transfer, 21(5): 729-742.
27. Roache, P.J., 1994, Perspective: A method for uniform reporting of grid refinement studies, Transactions of ASME Journal of Fluid Engineering, 116 (Sept), 405-413.
28. Shah, R.K. ve London, A.L., 1978, Laminar flow forced convection in ducts, Academic Press.
29. Siegel, R., 1963, Forced Convection in a Channel with Wall Heat Capacity and with Wall Heating Variable with Axial Position and Time, International Journal of Heat Mass Transfer, 6, 607-620.
30. Sparrow, E.M. ve De Farıas, F. N., 1968, Unsteady heat transfer in ducts with time-varying inlet temperature and participating walls, Int. J. Heat Mass Transfer,11, 837-853.
31. Sucec, J., 2002, Unsteady forced convection with sinusoidal duct wall generation: the conjugate heat transfer problem, International Journal of Heat and Mass Transfer, 45, 1631–1642.
32. Vedavarz, A., Kumar S. ve Moallemi M.K, 1994, Significance of non-Fourier Heat Waves in Conduction, Journal of Heat Transfer, 116, 221-224.
33. Zhu, X. W., Zhao, J. Q. ve Zhu, L., 2016, Heat transfer fluctuation in a pipe caused by axially non-uniform heat distribution, Applied Thermal Engineering, 103,314–322.
34. Zniber, K., Oubarra A. ve Lahjomri, J., 2005, Analytical Solution to the Problem of Heat Transfer in an MHD Flow Inside a Channel with Prescribed Sinusoidal Wall Heat Flux, Energy