شبیه سازی عددی انتقال حرارت جابجایی توام نانوسیال در یک محفظه شیبدار کم عمق به کمک روش شبکه بولتزمن
Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
ارش کریم پور
1
(
عضو هیئت علمی، دانشگاه آزاد اسلامی واحد نجف آباد
)
Keywords: نانوسیال, روش شبکه بولتزمن, محفظه شیبدار,
Abstract :
هدف کار حاضر بررسی جابجایی توام نانوسیال آب-مس در یک محفظه شیبدار دوبعدی کم عمق، به کمک روش شبکه بولتزمن است. از مدل شبکه 9Q2D مبتنی بر اپراتور برخورد BGK و مدل تابع توزیع انرژی گرمایی، جهت شبیه سازی دامنه ی حرارتی جریان استفاده می شود. درپوش گرم بالایی محفظه با سرعت ثابت U0 حرکت کرده و دیوار سرد پایینی نیز ثابت است. وجوه کناری محفظه عایق می باشند. اثر مقادیر مختلف زاویه شیب محفظه و کسر حجمی ذرات نانو بر خواص حرکتی و حرارتی نانوسیال در سه حالت مختلف حاکمیت جابجایی آزاد، اجباری و توام و به ازای عدد رینولدز برابر با 10 و 100، بررسی می شود. مقایسه نتایج حاصل از کار حاضر با داده های محققین پیشین نشان دهنده دقت مطلوب نتایج حاصل از مقاله حاضر است که در قالب خطوط جریان، خطوط همدما و پروفیلهای سرعت و دما ترسیم می شوند. مشاهده شد که در حالت حاکمیت جابجایی آزاد، مقدار عدد ناسلت با افزایش کسر حجمی ذرات نانو و زاویه شیب محفظه، زیادتر خواهد شد. تحقیق حاضر به خوبی بیانگر قابلیت مطلوب روش شبکه بولتزمن جهت شبیه سازی انتقال حرارت جابجایی توام نانوسیال در یک محفظه شیبدار کم عمق است.
[1] Kandlikar S, Garimella S, Li D, Colin S, King MR (2006) Heat transfer and fluid flow in minichannels and microchannels.
[2] Niu XD, Shu C, Chew YT (2007) A thermal lattice Boltzmann model with diffuse scattering boundary condition for micro thermal flows. Computers & Fluids 36: 273-281.
[3] Esfahani JA, Norouzi A (2014) Two relaxation time lattice Boltzmann model for rarefied gas flows. Physica A: Statistical Mechanics and its Applications 393: 51-61.
[4] Gad-el-Hak M (2001) Flow physics in MEMS. Rev. Mec. Ind. 2: 313-341.
[5] Nie X, Doolen GD, Chen S (2002) Lattice-Boltzmann simulation of fluid flows in MEMS. J. Stat. Phys. 107: 279-289.
[6] Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Annu. Rev. Fluid Mech. 30: 329-364.
[7] Zhou Y, Zhang R, Staroselsky I, Chen H, Kim WT, Jhon MS (2006) Simulation of micro- and nano-scale flows via the lattice Boltzmann method. Physica A: Statistical Mechanics and its Applications 362: 68-77.
[8] Karimipour A, Nezhad AH, D’Orazio A, Shirani E (2012) Investigation of the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method. Int. J. Therm. Sci. 54: 142-152.
[9] Bird G (1994) Molecular gas dynamics and the direct simulation of gas flows. Oxford University Press.
[10] Oran ES, Oh CK, Cybyk BZ (1998) Direct Simulation Mont Carlo: Recent Advances and Applications. Ann. Rev. Fluid Mech. 30: 403-441.
[11] Chen H, Chen S, Mathaaeus WM (1992) Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. Phys. Rev. A 45: 5339-5342.
[12] Tallavajhula A, Kharagpur I, Ruede U, Bartuschat D (2011) Introduction to the Lattice Boltzmann Method. 10th Indo-German Winter Academy.
[13] Bhatnagar PL, Gross EP, Krook M (1954) A model for collision process in gases. I. Small amplitude processes in charged and neutral one-component system. Phys. Rev. 94: 511-522.
[14] Succi S (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press.
[15] Chen S (2010) Lattice Boltzmann method for slip flow heat transfer in circular microtubes: Extended Graetz problem. Appl. Math. Compu. 217: 3314-3320.
[16] Chen S, Tian Z (2010) Entropy generation analysis of thermal micro-Couette flows in slip regime. Int. J. Therm. Sci. 49: 2211-2221.
[17] Lim CY, Shu C, Niu XD, Chew YT (2002) Application of lattice Boltzmann method to simulate microchannel flows. Phys. Fluids 14: 2299-2308.
[18] Shu C, Niu XD, Chew YT (2005) A Lattice Boltzmann Kinetic Model for Microflow and Heat Transfer. J. Stat. Phy. 121: 239-255.
[19] Sofonea V, Sekerka RF (2005) Boundary conditions for the upwind finite difference lattice Boltzmann model: Evidence of slip velocity in micro-channel flow. J. Comput. Phy. 207: 639-659.
[20] Zhang YH, Qin RS, Sun YH, Barber RW, Emerson DR (2005) Gas Flow in Microchannels - A Lattice Boltzmann Method Approach. J. Stat. Phy. 121: 257-267.
[21] Hung YC, Ru Y (2006) A numerical study for slip flow heat transfer. Appl. Math. Compu. 173: 1246-1264.
[22] Xuan Y, Li Q, Ye M (2007) Investigations of convective heat transfer in ferrofluid microflows using lattice-Boltzmann approach. Int. J. Therm. Sci. 46: 105-111.
[23] Tian ZW, Zou C, Liu HJ, Guo ZL, Liu ZH, Zheng CG (2007) Lattice Boltzmann scheme for simulating thermal micro-flow. Physica A: Statistical Mechanics and its Applications 385: 59-68.
[24] Babovsky H (2009) A numerical model for the Boltzmann equation with applications to micro flows. Compu. Math. Appl. 58: 791-804.
[25] Chen S, Tian Z (2009) Simulation of microchannel flow using the lattice Boltzmann method. Physica A: Statistical Mechanics and its Applications 388: 4803-4810.
[26] Oztop HF, Dagtekin I (2004) Mixed convection in two-sided lid-driven differentially heated square cavity. Int. J. Heat Mass Transfer 47: 1761-1769.
[27] Karimipour A, Afrand M, Akbari M, Safaei MR (2012) Simulation of fluid flow and heat transfer in the inclined enclosure. World Academy of Science, Engineering and Technology 61: 435-440.
[28] Safaei MR, Goshayeshi HR, Razavi BS, Goodarzi M (2011) Numerical investigation of laminar and turbulent mixed convection in a shallow water-filled enclosure by various turbulence methods. Scientific Research and Essays 6: 4826-4838.
[29] Iwatsu R, Hyun JM, Kuwahara K (1993) Mixed convection in a driven cavity with a stable vertical temperature gradient. Int. J. Heat Mass Transfer 36: 1601-1608.
[30] D’Orazio A, Corcione M, Celata GP (2004) Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition. Int. J. Therm. Sci. 43: 575-586.
[31] Peng Y, Shu C, Chew YT (2003) Simplified thermal lattice Boltzmann model for incompressible thermal flows. Physical Review E 68: 026701-1-8.
[32] Jami M, Mezrhab A, Bouzidi M, Lallemand P (2007) Lattice-Boltzmann computation of natural convection in a partitioned enclosure with inclined partitions attached to its hot wall. Physica A: Statistical Mechanics and its Applications 368: 481-494.
[33] Grucelski A, Pozorski J (2012) Lattice Boltzmann simulation of fluid flow in porous media of temperature-affected geometry. J. Theo. Appl. Mech. 50: 193-214.
[34] He X, Chen S, Doolen GD (1998) A novel thermal model for the lattice Boltzmann method in incompressible limit. J. Compu. Phys. 146: 282-300.
[35] Karimipour A, Nezhad AH, D’Orazio A, Shirani E (2013) The effects of inclination angle and Prandtl number on the mixed convection in the inclined lid driven cavity using lattice Boltzmann method. J. Theo. Appl. Mech. 51: 447-462.
[36] Choi SUS (1995) Enhancing thermal conductivity of fluid with nanoparticles. Developments and Applications of Non-Newtonian Flow. ASME. FED 231/MD 66: 99-105.
[37] Oztop HF, Abu-Nada E (2008) Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. Int. J. Heat Fluid Flow 29: 1326-1336.
[38] Tiwari RK, Das MK (2007) Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transfer 50: 2002-2018.
[39] Dehnavi R, Rezvani A (2012) Numerical investigation of natural convection heat transfer of nanofluids in a C shaped cavity. Superlatti. Microstru. 52: 312-325.
[40] Arani AA, Sebdani SM, Mahmoodi M, Ardeshiri A, Aliakbari M (2012) Numerical study of mixed convection flow in a lid-driven cavity with sinusoidal heating on sidewalls using nanofluid. Superlatti. Microstru. 51: 893-911.
[41] Mahmoodi M, Hashemi SM (2012) Numerical study of natural convection of a nanofluid in C-shaped enclosures. Int. J. Therm. Sci. 55: 76-89.
[42] Oztop HF, Mobedi M, Abu-Nada E, Pop I (2012) A heatline analysis of natural convection in a square inclined enclosure filled with a CuO nanofluid under non-uniform wall heating condition. Int. J. Heat Mass Transfer 55: 5076-5086.
[43] Abouali O, Ahmadi G (2012) Computer simulations of natural convection of single phase nanofluids in simple enclosures: A critical review. Appl. Therm. Eng. 36: 1-13.
[44] Pishkar I, Ghasemi B (2012) Cooling enhancement of two fins in a horizontal channel by nanofluid mixed convection. Int. J. Therm. Sci. 59: 141-151.
[45] Karimipour A, Nezhad AH, Behzadmehr A, Alikhani S, Abedini E (2011) Periodic mixed convection of a nanofluid in a cavity with top lid sinusoidal motion. Proc. IMechE Part C: J. Mech. Eng. Sci. 225: 2149-2160.
[46] Goodarzi M, Safaei MR, Vafai K, Ahmadi G, Dahari M, Kazi SN, Jomhari N (2013) Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model. Int. J. Therm. Sci. 75: 204-220.
[47] Nemati H, Farhadi M, Sedighi K, Fattahi E, Darzi AAR (2010) Lattice Boltzmann simulation of nanofluid in lid-driven cavity. Int. Commun. Heat Mass Transfer 37: 1528-1534.
