بررسی تولید انتروپی در یک جریان لغزشی هیدرودینامیک مغناطیسی نانوسیال بر روی یک صفحه نفوذپذیر گسترش‌یافته

نوع مقاله: پژوهشی

نویسندگان

دانشگاه همدان

چکیده

در این مقاله قانون دوم ترمودینامیک بر روی یک صفحه نفوذپذیر گسترش‌یافته در حضور میدان مغناطیسی عمودی یکنواخت در یک جریان لغزشی نانوسیال بررسی شده است به طوری که چهار نانوذره مس ، اکسید مس ، اکسید آلومینیوم و دی اکسید تیتانیوم و همچنین آب به عنوان سیال پایه در نظر گرفته شده‌اند. معادلات تولید انتروپی، برای اولین بار در این مسئله، به صورت تابعی از گرادیان‌های سرعت و دما استخراج گردید. منحنی‌ سرعت و همچنین توزیع دما و متوسط تولید انتروپی توسط روش تحلیلی آنالیز هموتوپی به دست آمده است. با مقایسه نتایج به دست آمده و نتایج دیگر پژوهشگران مشاهده می‌شود که هم‌خوانی خوبی بین نتایج مشاهده شده است. نتایج حاصل از این مقاله، نشان می‌دهند که با کاهش پارامترهای مغناطیسی، کسر حجمی نانوذره، پارامتر مکش، عدد رینولدز، عدد برینکمن عدد هارتمن و همچنین افزایش پارامتر سرعت لغزشی، انتروپی تولید شده کاهش خواهد یافت.

کلیدواژه‌ها


عنوان مقاله [English]

Entropy Generation Analysis for an MHD Slip Nano-Fluid Flow over a Stretching Permeable Surface

نویسندگان [English]

  • Seyed Sajad jafari
  • navid Freidoonimehr
چکیده [English]

The main propose of the present article is to study the second law of thermodynamics over a stretching permeable surface in the presence of the uniform vertical magnetic field in the slip nano-fluid regime. In this study, four types of nanoparticles i.e. Copper , Copper oxide , Aluminum oxide , and Titanium dioxide and also water as the base fluid are considered. Entropy generation equations, for the first time in this problem, are derived as a function of velocity and temperature gradients. Velocity profile as well as temperature distribution and averaged entropy generation are obtained using Homotopy Analysis Method (HAM). An excellent agreement exists between the present result and the other researchers’ result. The obtained result of present study presents that by decreasing magnetic parameter, nanoparticle volume fraction parameter, suction parameter, Reynolds number, Brinkman number, and Hartmann number as well as increasing the slip velocity parameter, the generated entropy reduces.

کلیدواژه‌ها [English]

  • Second law of thermodynamics
  • Slip flow
  • Magneto-hydrodynamics flow
  • Nano-fluid
  • Homotopy Analysis Method

[1]           Zhou, D.W., (2004). “Heat transfer enhancement of copper nanofluid with acoustic cavitation”. International Journal of Heat and Mass Transfer, Vol. 47, pp. 3109-3117.

[2]           Choi, S.U.S., Eastman J.A., (1995). “Enhancing thermal conductivity of fluids with nanoparticles”. Materials Science, Vol. 231, pp. 99-105.

[3]           Eastman, J.A., Choi U.S., Li S., Soyez G., Thompson L.J., DiMelfi R.J., (1999). “Novel thermal properties of nanostructured materials”. Materials Science Forum, Vol. 312-314, pp. 629-634.

[4]           Xuan, Y., Roetzel W., (2000). “Conceptions for heat transfer correlation of nanofluids”. International Journal of Heat and Mass Transfer, Vol. 43, pp. 3701-3707.

[5]           Rashidi, M.M., Abelman S., Freidoonimehr N., (2013). “Entropy generation in steady MHD flow due to a rotating porous disk in a nanofluid”. International Journal of Heat and Mass Transfer, Vol. 62, pp. 515-525.

[6]           Liao, S.J., Beyond perturbation: introduction to the homotopy analysis method. 2004: Chapman & Hall/CRC.

[7]           Mustafa, M., Hayat T., Pop I., Asghar S., Obaidat S., (2011). “Stagnation-point flow of a nanofluid towards a stretching sheet”. International Journal of Heat and Mass Transfer, Vol. 54, pp. 5588-5594.

[8]           Abbas, Z., Wang Y., Hayat T., Oberlack M., (2010). “Mixed convection in the stagnation-point flow of a Maxwell fluid towards a vertical stretching surface”. Nonlinear Analysis: Real World Applications, Vol. 11, pp. 3218-3228.

[9]           Rashidi, M.M., Ali M., Freidoonimehr N., Nazari F., (2013). “Parametric analysis and optimization of entropy generation in unsteady MHD flow over a stretching rotating disk using artificial neural network and particle swarm optimization algorithm”. Energy, Vol. 55, pp. 497-510.

[10]         Rashidi, M.M., Freidoonimehr N., Hosseini A., Bég O.A., Hung T.K., (2014). “Homotopy simulation of nanofluid dynamics from a non-linearly stretching isothermal permeable sheet with transpiration”. Meccanica, Vol. 49, pp. 469-482.

[11]         Bejan, A., (1980). “Second law analysis in heat transfer”. Energy, Vol. 5, pp. 720-732.

[12]         Çengel, Y.A., Boles M.A., Thermodynamics: an engineering approach. 2006: McGraw-Hill Higher Education.

[13]         Bejan, A., Second-Law Analysis in Heat Transfer and Thermal Design, in Advances in Heat Transfer, P.H. James, F.I. Thomas, Editors. 1982, Elsevier. p. 1-58.

[14]         Bejan, A., Entropy generation minimization: the method of thermodynamic optimization of finite-size systems and finite-time processes. 1996: CRC Press.

[15]         Bejan, A., (1979). “A Study of Entropy Generation in Fundamental Convective Heat Transfer”. Journal of Heat Transfer, Vol. 101, pp. 718-725.

[16]         Ibáñez, G., Cuevas S., López de Haro M., (2006). “Optimization of a magnetohydrodynamic flow based on the entropy generation minimization method”. International Communications in Heat and Mass Transfer, Vol. 33, pp. 295-301.

[17]         Arikoglu, A., Ozkol I., Komurgoz G., (2008). “Effect of slip on entropy generation in a single rotating disk in MHD flow”. Applied Energy, Vol. 85, pp. 1225-1236.

[18]         Aïboud, S., Saouli S., (2010). “Second Law Analysis of Viscoelastic Fluid over a Stretching Sheet Subject to a Transverse Magnetic Field with Heat and Mass Transfer”. Entropy, Vol. 12, pp. 1867-1884.

[19]         Brinkman, H.C., (1952). “The viscosity of concentrated suspensions and solutions”. The Journal of Chemical Physics, Vol. 20, pp. 571-571.

[20]         Oztop, H.F., Abu-Nada E., (2008). “Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids”. International Journal of Heat and Fluid Flow, Vol. 29, pp. 1326-1336.

[21]         Aïboud, S., Saouli S., (2010). “Entropy analysis for viscoelastic magnetohydrodynamic flow over a stretching surface”. International Journal of Non-Linear Mechanics, Vol. 45, pp. 482-489.

[22]         Liao, S.J., (2004). “On the homotopy analysis method for nonlinear problems”. Applied Mathematics and Computation, Vol. 147, pp. 499-513.

[23]         Liao, S., (2004). “On the homotopy analysis method for nonlinear problems”. Applied Mathematics and Computation, Vol. 147, pp. 499-513.

[24]         Ali, M.E., (1994). “Heat transfer characteristics of a continuous stretching surface”. Wärme - und Stoffübertragung, Vol. 29, pp. 227-234.

[25]         Ishak, A., Nazar R., Pop I., (2009). “Boundary layer flow and heat transfer over an unsteady stretching vertical surface”. Meccanica, Vol. 44, pp. 369-375.

[26]         Grubka, L.J., Bobba K.M., (1985). “Heat Transfer Characteristics of a Continuous, Stretching Surface With Variable Temperature”. Journal of Heat Transfer, Vol. 107, pp. 248-250.

[27]         Mahdy, A., (2012). “Unsteady mixed convection boundary layer flow and heat transfer of nanofluids due to stretching sheet”. Nuclear Engineering and Design, Vol. 249, pp. 248-255.

[28]         Bachok, N., Ishak A., Pop I., (2012). “Flow and heat transfer characteristics on a moving plate in a nanofluid”. International Journal of Heat and Mass Transfer, Vol. 55, pp. 642-648.