Forced convection flow of viscous dissipative power-law fluids in a plane duct, part 1. hydrodynamically and thermally fully developed flow

Bu çalışmada, sabit termofiziksel özelliklere sahip power-law akışkanın düzlemsel kanal içerisindeki laminer zorlanmış taşınımı, viskoz yayılım etkileri dahil edilerek, analiz edilmiştir. Çalışmanın bu bölümünde, birinci hidrodinamik ve termal açıdan tam gelişmiş akış incelenmektedir. Sabit ısı akısı (H1 sınır koşulu) ve sabit yüzey sıcaklığı(T sınır koşulu) olmak üzere iki farklı termal sınır koşulu ele alınmıştır. Power-law indeksi ve Brinkman sayısının sıcaklık dağılımı ve Nusselt sayısı üzerindeki etkisi, T ve H1 sınır koşullarında, sıcak ve soğuk cidar durumları için analitik olarak belirlenmiştir. Nu-Br-n davranışlarında süreksizlikler gözlenmiş ve bu süreksizlikler enerji dengesi açısından tartışılmıştır.

Bir düzlemsel kanal içerisindeki viskoz yayılımlı power-law akışkanların zorlanmış taşınım akışı Kısım 1. hidrodinamik ve termal olarak tam gelişmiş akış

In this study, an analysis of laminar forced convection in a plane duct for a power-law fluid with constant thermophysical properties is performed by taking the viscous dissipation into account. This part of the study, Part 1, examines both hydrodynamically and thermally fully developed flow case. Two different thermal boundary conditions are considered: the constant heat flux (H1 boundary condition) and the constant wall temperature (T boundary condition). The combined and interactive influences of the power-law index and the Brinkman number on temperature distribution and the Nusselt numbers are analytically determined both for the wall heating and cooling cases at T and H1 boundary conditions. Singularities are observed in Nu-Br-n behaviors and these are discussed in terms of the energy balance.

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Aydın, O. and Avcı, M., Viscous dissipation effects on the heat transfer in a Poiseuille flow, Applied Energy 83, 495-512, 2006.
Barletta, A. and Rossi di Schio, E., Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux, Heat and Mass Transfer 35, 9-16, 1999.
Barletta, A. and Zanchini, E., Forced convection in the thermal entrance region of a circular duct with slug flow and viscous dissipation, Int. J. Heat Mass Transfer 40, 1181-1190, 1997.
Barletta, A., Fully developed laminar forced convection in circular ducts for power-law fluids with viscous dissipation, Int. J. Heat Mass Transfer 40, 15-26, 1997.
Basu, T. and Roy, D. N., Laminar heat transfer in a tube with viscous dissipation, Int. J. Heat Mass Transfer 28, 699-701, 1985.
Brinkman, H. C., Heat effects in capillary flow, Appl. Sci. Res. A2, 120-124, 1951.
Cotta, R. M. and Özışık, M. N., Laminar forced convection to non-Newtonian fluids in ducts with prescribed wall heat flux, Int. Comm. Heat Mass Transfer 13, 325-34, 1986.
Dang, V. D., Heat transfer of a power-law fluid at low Peclet number flow, J. Heat Transfer 105, 542-549, 1983.
Hartnett, J. P. and Cho, Y. I., Non-Newtonian Fluids, In Handbook of Heat Transfer (edited by W.M. Rohsenow, J.P. Hartnett, Y.I. Cho), McGraw Hill, New York, 1998.
Irvine, T. F. and Karni, J., Non-Newtonian Fluid Flow and Heat Transfer, In Handbook of Single-Phase Convective Heat Transfer (Edited by S. Kakaç, R.K. Shah, W. Aung), Wiley, New York, 1987, Chap. 20.
Khatyr, R., Ouldhadda, D. and Il Idrissi, A., Viscous dissipation effects on the asymptotic behavior of laminar forced convection for Bingham plastics in circular ducts, Int. J. Heat Mass Transfer 46, 589-598, 2003.
Lawal, A. and Mujumdar, A. S., The effects of viscous dissipation on heat transfer to power law fluids in arbitrary cross-sectional ducts, Warme Stoffübertragung 27, 437-446, 1992.
Lin, T. F., Hawks, K. H. and Leidenfrost, W., Analysis of viscous dissipation effect on the thermal entrance heat transfer in laminar pipe flows with convective boundary conditions, Warme und Stoffübertragung 17, 97-105, 1983.
Liou, C. T. and Wang, F. S., Solutions to the extended Graetz problem for a power-law fluid with viscous dissipation and different entrance boundary conditions, Numer. Heat Transfer A 17, 91-108, 1990.
Min T., Yoo J. Y. and Choi H., Laminar convective heat transfer of a Bingham plastic in a circular pipe-I. Analytical approach – thermally fully developed flow and thermally developing flow (the Graetz problem extended), Int. J. Heat Mass Transfer 40, 3025-3037, 1997.
Oosthuizen, P. H. and Naylor, D., Introduction to Convective Heat Transfer Analysis, McGraw-Hill, New York, 1999.
Ou, W. J. and Cheng, K.C., Viscous dissipation effects in the entrance region heat transfer in pipes with uniform heat flux Appl. Sci. Res. 28, 289-301, 1973.
Pinho, F. T. and Oliveira, P. J., Analysis of forced convection in pipes and channels with the simplified Phan-Thien-Tanner fluid, Int. J. Heat Mass Transfer 43, 2273-2287, 2000.
Shah, R. K. and London A. L., Advances in Heat Transfer (suppl. 1), Academic Press, New York, 1978.
Tyagi, V.P., Laminar forced convection of a dissipative fluid in a channel, J. Heat Transfer 88, 161-169, 1996.
Vradis, G. C., Dougher J. and Kumar, S., Entrance pipe flow and heat transfer for a Bingham plastic, Int. J. Heat Mass Transfer 36, 543-552, 1993.
Zanchini, E., Effect of viscous dissipation on the asymptotic behavior of laminar forced convection in circular tubes, Int. J. Heat Mass Transfer 40, 169-178, 1997.