اثر میدان مغناطیسی بر جابجایی آزاد سیال غیرنیوتنی در محفظه مربعی با چشمه حرارتی مرکزی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه شهرکرد، شهرکرد

2 دانشگاه شهرکرد*دانشکده فنی ومهندسی

چکیده

در این مطالعه جریان لایه‌ای تراکم ناپذیر سیال غیرنیوتنی با چشمه گرمایی مرکزی در یک محفظه برای حالت‌های بدون میدان مغناطیسی و اعمال میدان مغناطیسی یکنواخت تحت زاویه‌ای مشخص، بررسی شده است. معادلات حاکم به روش اختلاف محدود بر مبنای حجم کنترل گسسته‌سازی شده‌اند و میدان حل مسئله با استفاده از شبکه یکنواخت شبکه‌بندی شده است. این مسئله برای حالت پایدار با فرمول‌بندی ضمنی و با الگوریتم سیمپل حل شده است. در مطالعه حاضر تأثیر غیرنیوتنی بودن سیال با مدل قانون توانی با وجود میدان مغناطیسی یکنواخت، برای مقادیر شاخص توانی ۴/۱ ,۱ ,۷۵/۰  بررسی شده و نتایج به دست آمده با شرایط عدم وجود میدان مقایسه شد. با توجه به نتایج حاصل شده، می‌توان بیان کرد که اعمال میدان مغناطیسی برای شاخص‌های مختلف سیال، در رایلی‌های متفاوت رفتار یکسانی را نشان نمی‌دهد و با اعمال میدان مغناطیسی، جابجایی جریان در محفظه تقلیل می‌یابد. همچنین می‌توان گفت که با اعمال میدان مغناطیسی در محدوده  برای سیال مدل قانون توانی، افزایش عدد رایلی باعث کاهش نوسلت متوسط و برای ۱n˂ باعث افزایش نوسلت متوسط خواهد شد. برای شاخص ۱n˃ با افزایش رایلی در حضور یک میدان مغناطیسی ثابت، می‌توان جابجایی آزاد را تضعیف نمود در حالیکه این روند برای ۱n˂ با کاهش عدد رایلی رخ می‌دهد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Effects of Magnetic Field on Natural Convection of Non-Newtonian Fluid in a Square Enclosure with a Central Heat Source

نویسندگان [English]

  • Akram Jahanbakhshi 1
  • Afshin Ahmadi Nadooshan 2
1 Shahrekord University, Shahrekord
2 Mechanical Engineering Department, Shahrekord University, Shahrekord
چکیده [English]

In this study, the incompressible laminar flow of non-Newtonian fluid is studied in a cavity with a central heat source under a uniform inclined magnetic field. The governing equations are converted into nonlinear ordinary differential equations using similarity transformations and solved using finite difference based numerical methods. In the current study, the effect of non-Newtonian power-law fluid is investigated for power-law indices of 0.75, 1 and 1.4. The results are compared with the ones in which the magnetic field is not applied. It is found that the implementation of a magnetic field for different fluid indices in different Rayleigh numbers does not show similar behaviors and the results show that the magnetic field affects the convection flow, leading to a reduction in it. Also can be said that with the implementation of a magnetic field in the range of indices n ≥ 1 for power-law model fluid, increased Rayleigh number leads to reduced average Nusselt number and for n ˂ 1, the average Nusselt increases. For n ˂ 1, with increased Rayleigh number in the presence of a fixed magnetic field, free convection can be weakened while this trend for n ˂ 1 occurs with reduced Rayleigh number.

کلیدواژه‌ها [English]

  • Non- Newtonian fluid
  • Power-law model
  • Magnetic field
  • Natural convection
[1] A. Kasaeipoor, B. Ghasemi, A. Raisi, Magnetic field effect on nanofluid water-cu natural convection in an inclined T shape cavity, Modares Mechanical Engineering, 14(12) (2014) 179-189 (In Persian).
[2] M. Lamsaadi, M. Naimi, M. Hasnaoui, Natural convection heat transfer in shallow horizontal rectangular enclosures uniformly heated from the side and filled with non-Newtonian power law fluids, Energy conversion and Management, 47(15) (2006) 2535-2551.
[3] M. Lamsaadi, M. Naimi, M. Hasnaoui, M. Mamou, Natural convection in a tilted rectangular slot containing Non-Newtonian Power-Law fluids and subject to a longitudinal thermal gradient, Numerical Heat Transfer, Part A: Applications, 50(6) (2006) 561-583.
[4] Z. Alloui, P. Vasseur, Natural convection of Carreau–Yasuda non-Newtonian fluids in a vertical cavity heated from the sides, International Journal of Heat and Mass Transfer, 84 (2015) 912-924.
[5] A. Raisi, The influence of a pair constant temperature baffles on power-law fluids natural convection in a square enclosure, Modares Mechanical Engineering, 15(11) (2016) 215-224.
[6] B. Ghasemi, S. Aminossadati, A. Raisi, Magnetic field effect on natural convection in a nanofluid-filled square enclosure, International Journal of Thermal Sciences, 50(9) (2011) 1748-1756.
[7] D. Picchi, P. Poesio, A. Ullmann, N. Brauner, Characteristics of stratified flows of Newtonian/non-Newtonian shear-thinning fluids, International Journal of Multiphase Flow, 97 (2017) 109-133.
[8] J. Raza, A. M. Rohni, Z. Omar, Rheology of micropolar fluid in a channel with changing walls: Investigation of multiple solutions, Journal of Molecular Liquids, 223 (2016) 890-902.
[9] A. Mahmoudi, I. Mejri, M. A. Abbassi, A. Omri, Lattice Boltzmann simulation of MHD natural convection in a nanofluid-filled cavity with linear temperature distribution, Powder Technology, 256 (2014) 257-271.
[10] H. Aminfar, M. Mohammadpourfard, Y. N. Kahnamouei, A 3D numerical simulation of mixed convection of a magnetic nanofluid in the presence of non-uniform magnetic field in a vertical tube using two phase mixture model, Journal of Magnetism and Magnetic Materials, 323(15) (2011) 1963-1972.
[11] H. Mozayyeni, A. Rahimi, Mixed convection in cylindrical annulus with rotating outer cylinder and constant magnetic field with an effect in the radial direction, Scientia Iranica, 19(1) (2012) 91-105.
[12] O. Mahian, H. F. Oztop, I. Pop, S. Mahmud, S. Wongwises, Design of a vertical annulus with MHD flow using entropy generation analysis, Thermal Science, 17(4) (2013).
[13] P. Hatzikonstantinou, P. Vafeas, A general theoretical model for the magnetohydrodynamic flow of micropolar magnetic fluids. Application to Stokes flow, Mathematical Methods in the Applied Sciences, 33(2) (2010) 233-248.
[14] H. Yamaguchi, X.-R. Zhang, X.-D. Niu, K. Yoshikawa, Thermomagnetic natural convection of thermo-sensitive magnetic fluids in cubic cavity with heat generating object inside, Journal of Magnetism and Magnetic Materials, 322(6) (2010) 698-704.
[15] M. Lajvardi, J. Moghimi-Rad, I. Hadi, A. Gavili, T. D. Isfahani, F. Zabihi, J. Sabbaghzadeh, Experimental investigation for enhanced ferrofluid heat transfer under magnetic field effect, Journal of Magnetism and Magnetic Materials, 322(21) (2010) 3508-3513.
[16] M. Sheikholeslami, H. Sajjadi, A. A. Delouei, M. Atashafrooz, Z. Li, Magnetic force and radiation influences on nanofluid transportation through a permeable media considering Al2 O3 nanoparticles, Journal of Thermal Analysis and Calorimetry, 136(6) (2019) 2477-2485.
[17] M. Atashafrooz, M. Sheikholeslami, H. Sajjadi, A. A. Delouei, Interaction effects of an inclined magnetic field and nanofluid on forced convection heat transfer and flow irreversibility in a duct with an abrupt contraction, Journal of Magnetism and Magnetic Materials, 478 (2019) 216-226.
[18] H. Sajjadi, A. A. Delouei, M. Atashafrooz, M. Sheikholeslami, Double MRT Lattice Boltzmann simulation of 3-D MHD natural convection in a cubic cavity with sinusoidal temperature distribution utilizing nanofluid, International Journal of Heat and Mass Transfer, 126 (2018) 489-503.
[19] H. Sajjadi, A. A. Delouei, M. Sheikholeslami, M. Atashafrooz, S. Succi, Simulation of three dimensional MHD natural convection using double MRT Lattice Boltzmann method, Physica A: Statistical Mechanics and its Applications, 515 (2019) 474-496.
[20] A. Kasaeipoor, B. Ghasemi, S. Aminossadati, Convection of Cu-water nanofluid in a vented T-shaped cavity in the presence of magnetic field, International Journal of Thermal Sciences, 94 (2015) 50-60.
[21] D. L. Pyle, P. J. Fryer, C. D. Reilly, Chemical engineering for the food industry: Springer Science & Business Media, 2012.
[22] J. Pittman, J. Richardson, C. Sherrard, An experimental study of heat transfer by laminar natural convection between an electrically-heated vertical plate and both Newtonian and non-Newtonian fluids, International Journal of Heat and Mass Transfer, 42(4) (1999) 657-671.
[23] A.-M. Ghenaatian, A. Raisi, B. Ghasemi, Natural Convection Heat Transfer in an Inclined Square Enclosure Filled with Nanofluid in the Presence of Magnetic Field, Tabriz Mechanical Engineering Journal, 76(3) (2015) 155-165 (In Persian).
[24] Y. Dong, Q. Zhai, Natural convection study in an enclosure with different aspect ratios, International Journal of Modern Physics C, 18(12) (2007) 1903-1923.
[25] M. Hortmann, M. Perić, G. Scheuerer, Finite volume multigrid prediction of laminar natural convection: bench-mark solutions, International journal for numerical methods in fluids, 11(2) (1990) 189-207.