انتقال حرارت جابجایی طبیعی درون یک محفظه بسته مربعی حاوی یک پره انعطاف‏ پذیر

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد دزفول ، دزفول، ایران

2 دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد دزفول، دزفول، ایران

چکیده

در این پژوهش اثر حضور یک پره انعطاف پذیر بر روی انتقال حرارت جابه جایی طبیعی درون یک محفظه بسته مربعی بررسی شد. یک پره انعطاف پذیر نازک با زاویه انحراف 30o نسبت به محور افقی، بر روی دیواره عمودی گرم سمت چپ، درون محفظه بسته قرار گرفته است. معادلات حاکم بر جریان آرام، انتقال حرارت سیال و تغییر شکل پره انعطاف پذیر با لحاظ نمودن برهم کنش میان جریان سیال- سازه و با بهره گیری از روش شبکه متحرک لاگرانژی- اویلری ارائه شدند و سپس به شکل بی بُعد انتقال یافتند. معادلات با استفاده از روش المان محدود حل شدند و سپس صحت نتایج در مقایسه با پژوهش های معتبر پیشین ارزیابی شد. نتایج، یک بار به همراه پره انعطاف پذیر و بار دیگر با پره صلب در بازه زمانی بی بُعد صفر تا 07 / 0، در محدود اعداد رایلی 6+ 10 تا7+ 2×10 و زوایای انحراف -10o تا +40o ، درون محفظه بسته ترسیم گردید. نتایج نشان می دهند که استفاده از پره انعطاف پذیر نسبت به پره صلب باعث کاهش میزان انتقال حرارت می گردد. از سوی دیگر، استفاده از پره عایق به جای پره رسانا، سبب بروز الگوهای متفاوتی برای عدد ناسلت متوسط در طول بازه زمانی شده و تضعیف انتقال حرارت را در پی دارد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Natural Convection Heat Transfer Inside a Square Enclosure with a Flexible Fin

نویسندگان [English]

  • M. Ghalambaz 1
  • E. Jamesahar 2
  • M. Sabour 2
1 Mechanical Engineering Department, Dezful Branch, Islamic Azad University, Dezful, Iran
2 Mechanical Engineering Department, Dezful Branch, Islamic Azad University, Dezful, Iran
چکیده [English]

The present study aims to address the effect of the presence of a flexible fin on the natural convection heat transfer inside a square cavity. A flexible fin is placed on the left vertical wall by initial tilted angle 30o from the horizontal direction. An Arbitrary Lagrangian-Eulerian method for fluid-structure (fluid-flexible fin) interaction is utilized. Based on this method, the governing system of equations for laminar fluid and heat transfer is formulated into a non- dimensional form and then solved using the finite element method and then results accuracy evaluated against previous valid studies. The results are plotted for an enclosure containing a flexible fin as well as a solid fin in the non-dimensional time interval of 0 to 0.07 and in the Rayleigh number range of 106 to 2×107 and the fin tilted angle of -10° to +40°. The results show that the presence of a flexible fin deteriorates the heat transfer compared to a solid fin. In other words, using an insulated fin instead of a conductive fin makes different patterns for average Nusselt number curve in a range time and causes a reduction of the rate of heat transfer. Also, the presence of a flexible fin mounted on the hot wall especially affects the average Nusselt number in the areas above the fin location and induces oscillating heat transfer patterns.

کلیدواژه‌ها [English]

  • Laminar natural convection heat transfer
  • Flexible fin
  • Fluid-Structure Interaction
  • Arbitrary Lagrangian-Eulerian method
  • Moving mesh
[1] M. Al-Arabi, B. Sakr, Natural convection heat transfer from inclined isothermal plates, International journal of heat and mass transfer, 31(3) (1988) 559-566.
[2] H. Buchberg, I. Catton, D. Edwards, Natural convection in enclosed spaces—a review of application to solar energy collection, Journal of Heat Transfer, 98(2) (1976) 182-188.
[3] D.R. Pangavhane, R. Sawhney, P. Sarsavadia, Design, development and performance testing of a new natural convection solar dryer, Energy, 27(6) (2002) 579-590.
[4] H.B. Awbi, A. Hatton, Natural convection from heated room surfaces, Energy and buildings, 30(3) (1999) 233-244.
[5] S.W. Frey Jr, M.I. Herson, Natural convection cooling system for electronic components, in, Google Patents, 1985.
[6] Kuehne, I., van der Linden, A., Seidel, J., Schreiter, M., Fromme, L. and Frey, A., 2011, October. Fluid-Structure Interaction Modeling for an Optimized Design of a Piezoelectric Energy Harvesting MEMS Generator. In Proceedings of the COMSOL Users Conference.
[7] B. Ganapol, Analytical Benchmarks for Nuclear Engineering Applications,Case Studies in Neutron Transport Theory. Organisation for Economic Co-operation and Development, (2008).
[8] J.K. Shultis, R.E. Faw, Fundamentals of Nuclear Science and Engineering, Third Edition, CRC press, 2016.
[9] G. de Vahl Davis, Natural convection of air in a square cavity: a bench mark numerical solution, International Journal for numerical methods in fluids, 3(3) (1983) 249-264.
[10] Q.-H. Deng, G.-F. Tang, Numerical visualization of mass and heat transport for conjugate natural convection/heat conduction by streamline and heatline, International Journal of Heat and Mass Transfer, 45(11) (2002) 2373-2385.
[11] D. Kaminski, C. Prakash, Conjugate natural convection in a square enclosure: effect of conduction in one of the vertical walls, International Journal of Heat and Mass Transfer, 29(12) (1986) 1979-1988.
[12] M. Sathiyamoorthy, A. J. Chamkha, Analysis of natural convection in a square cavity with a thin partition for linearly heated side walls, International Journal of Numerical Methods for Heat & Fluid Flow, 24(5) (2014) 1057-1072.
[13] Laminar natural convection heat transfer in a differentially heated square cavity due to a thin fin on the hot wall, Journal of Heat Transfer, 125(4) (2003) 624-634.
[14] A. Ben-Nakhi, A.J. Chamkha, Conjugate natural convection in a square enclosure with inclined thin fin of arbitrary length, International journal of thermal sciences, 46(5) (2007) 467-478.
[15] A. Elatar, M.A. Teamah, M.A. Hassab, Numerical study of laminar natural convection inside square enclosure with single horizontal fin, International Journal of Thermal Sciences, 99 (2016) 41-51
[16] B. Alshuraiaan, K. Khanafer, The effect of the position of the heated thin porous fin on the laminar natural convection heat transfer in a differentially heated cavity, International Communications in Heat and Mass Transfer, 78 (2016) 190-199.
[17] M. Toda, S. Osaka, Vibrational fan using the piezoelectric polymer PVF 2, Proceedings of the IEEE, 67(8) (1979) 1171-1173.
[18] T. Acikalin, S.M. Wait, S.V. Garimella, A. Raman, Experimental investigation of the thermal performance of piezoelectric fans, Heat Transfer Engineering, 25(1) (2004) 4-14.
[19] U. Küttler, W.A. Wall, Fixed-point fluid–structure interaction solvers with dynamic relaxation, Computational Mechanics, 43(1) (2008) 61-72
[20] W.S. Fu, W.J. Shieh, A study of thermal convection in an enclosure induced simultaneously by gravity and vibration, International Journal of Heat and Mass Transfer, 35(7) (1992) 1695-1710.
[21] F. Xu, J.C. Patterson, C. Lei, Heat transfer through coupled thermal boundary layers induced by a suddenly generated temperature difference, International Journal of Heat and Mass Transfer, 52(21-22) (2009) 4.4975-966.
[22] X. Shi, J. Khodadadi, Fluid flow and heat transfer in a lid-driven cavity due to an oscillatory thin fin: transient behavior, in: ASME 2004 Heat Transfer/Fluids Engineering Summer Conference, American Society of Mechanical Engineers, 2004, pp. 413-421.
[23] E. Jamesahar, M. Ghalambaz, A.J. Chamkha, Fluid–solid interaction in natural convection heat transfer in a square cavity with a perfectly thermal-conductive flexible diagonal partition, International Journal of Heat and Mass Transfer, 100 (2016) 303-319.
[24] M. Ghalambaz, E. Jamesahar, M.A. Ismael, A.J. Chamkha, Fluid-structure interaction study of natural convection heat transfer over a flexible oscillating fin in a square cavity, International Journal of Thermal Sciences, 111 (2017) 256-273.
[25] H.-J. Bungartz, M. Schäfer, Fluid-structure interaction: modelling, simulation, optimisation, Springer Science & Business Media, 2006.
[26] G.T. Mase, G.E. Mase, Continuum mechanics for engineers, CRC press, 1999.
[27] J.F. Wendt, Computational fluid dynamics: an introduction, Springer Science & Business Media, 2008.
[28] J. Hron, S. Turek, A monolithic FEM/multigrid solver for an ALE formulation of fluid-structure interaction with applications in biomechanics, in: Fluid-structure interaction, Springer, 2006, pp. 146-170.
[29] C.W. Hirt, A.A. Amsden, J. Cook, An arbitrary Lagrangian-Eulerian computing method for all flow speeds, Journal of computational physics, 14(3) (1974) 227-253.
[30] T.J. Hughes, W.K. Liu, T.K. Zimmermann, Lagrangian-Eulerian finite element formulation for incompressible viscous flows, Computer methods in applied mechanics and engineering, 29(3) (1981) 329-349.
[31] J. Donea, S. Giuliani, J.-P. Halleux, An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions, Computer methods in applied mechanics and engineering, 33(1-3) (1982) 689-723.
[32] J. Donea, A. Huerta, Finite element methods for flow problems, John Wiley & Sons, 2003.
[33] J. Donea, A. Huerta, J.-P. Ponthot, A. Rodriguez-Ferran, Encyclopedia of Computational Mechanics Vol. 1: Fundamentals., Chapter 14: Arbitrary Lagrangian-Eulerian Methods, in, Wiley & Sons, 2004.
[34] B.M. Froehle, High-order discontinuous Galerkin fluid-structure interaction methods, UC Berkeley, 2013.
[35] T. Basak, S. Roy, A. Balakrishnan, Effects of thermal boundary conditions on natural convection flows within a square cavity, International Journal of Heat and Mass Transfer, 49(23-24) (2006) 4525-4535.
[36] S. Shao, E.Y. Lo, Incompressible SPH method for simulating Newtonian and non-Newtonian flows with a free surface, Advances in water resources, 26(7) (2003) 787-800.
[37] F. Sun, Investigations of smoothed particle hydrodynamics method for fluid-rigid body interactions, University of Southampton, 2013.
[38] A.C. Hindmarsh, P.N. Brown, K.E. Grant, S.L. Lee, R. Serban, D.E. Shumaker, C.S. Woodward, SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers, ACM Transactions on Mathematical Software (TOMS), 31(3) (2005) 363-396.