Top

Journal of Applied Mathematics and Computing

Published in:

17-08-2017 | Original Research

A theoretical study of enhanced heat transfer in nanoliquids with volumetric heat source

Authors: N. Meenakshi, P. G. Siddheshwar

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2018

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

Rayleigh–Bénard convection in nanoliquids is studied in the presence of volumetric heat source. The present analytical work concerns twenty nanoliquids. Carrier liquids considered are water, ethylene glycol, engine oil and glycerine and with them five different nanoparticles considered are copper, copper oxide, silver, alumina and titania. Expression for the thermophysical properties of the nanoliquids is chosen from phenomenological laws or mixture theory. Heat source is characterized by an internal nanoliquid Rayleigh number \(R_{I_{nl}}\). Heat source adds to the energy of the system and hence an advanced onset is observed in this case compared to the problem with no heat source. In the case of heat sink, however, heat is drawn from the system leading to delay in onset. The individual effect of all the nanoparticles is to advance convection. Enhanced heat transport situation is observed in each of the nanoliquids with engine-oil-silver transporting maximum heat and water-titania the least. Additional Fourier modes are found not to have any profound effect on the results predicted by minimal modes. The connection between the Lorenz model and the Ginzburg–Landau model is clearly shown in the paper.

previous article An infeasible interior point method for the monotone SDLCP based on a transformation of the central path

next article Existence and globally exponential stability of anti periodic solution for fuzzy BAM neural networks with time delays

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Adomian, G.: A review of the decomposition method and some recent results for nonlinear equations. Comput. Math. Appl. 21, 101–127 (1991)MathSciNetCrossRefMATH

Adomian, G.: Solving Frontier Problems of Physics: The Decomposition Method, vol. 60. Springer, Berlin (2013)MATH

Agarwal, S., Bhadauria, B.S.: Convective heat transport by longitudinal rolls in dilute nanoliquids. J. Nanofluids 3, 380–390 (2014)CrossRef

Aghighi, S., Ammar, A., Metivier, C., Chinesta, F.: Parametric solution of the Rayleigh–Bénard convection model by using the PGD: Application to nanofluids. Int. J. Numer. Methods Heat Fluid Flow 25, 1252–1281 (2015)CrossRefMATH

Bergman, T.L., Incropera, F.P., Lavine, A.S.: Fundamentals of Heat and Mass Transfer. John Wiley and Sons, New York (2011)

Bhadauria, B., Siddheshwar, P.G., Singh, A.K., Gupta, V.K.: A local nonlinear stability analysis of modulated double diffusive stationary convection in a couple stress liquid. J. Appl. Fluid Mech. 9, 1255–1264 (2016)CrossRef

Bhadauria, B.S., Kiran, P.: Chaotic and oscillatory magneto-convection in a binary viscoelastic fluid under g-jitter. Int. J. Heat Mass Transf. 84, 610–624 (2015)CrossRef

Bhatia, P.K., Steiner, J.M.: Thermal instability in a viscoelastic fluid layer in hydromagnetics. J. Math. Anal. Appl. 41(2), 271–283 (1973)MathSciNetCrossRefMATH

Bianco, V., Manca, O., Nardini, S., Kambiz, V.: Heat Tansfer Enhancement with Nanofluids. CRC Press, Canada (2015)CrossRef

10.

Brinkman, H.C.: The viscosity of concentrated suspensions and solutions. J. Chem. Phys. 20, 571–571 (1952)CrossRef

11.

Buongiorno, J.: Convective transport in nanofluids. J. Heat Transf. 128, 240–250 (2005)CrossRef

12.

Chandrasekhar, S.: Hydrodynamic and Hydromagnetic Stability. Clarendon Press, Oxford (1961)MATH

13.

Choi, S.U.S.: Enhancing thermal conductivity of fluids with nanoparticles. ASME Publ. Fed 231, 99–106 (1995)

14.

Clever, R.M.: Heat transfer and stability properties of convection rolls in an internally heated fluid layer. Z. Angew. Math. Phys. 28, 585–597 (1977)CrossRefMATH

15.

Corcione, M.: Rayleigh–Bénard convection heat transfer in nanoparticle suspensions. Int. J. Heat Fluid Flow 32, 65–77 (2011)CrossRef

16.

Das, S.K., Putra, N., Thiesen, P., Roetzel, W.: Temperature dependence of thermal conductivity enhancement for nanofluids. J. Heat Transf. 125, 567–574 (2003)CrossRef

17.

Devi, R., Mahajan, A., et al.: Global stability for thermal convection in a couple-stress fluid. Int. Commun. Heat Mass Transf. 38, 938–942 (2011)CrossRef

18.

Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, Cambridge (2004)CrossRefMATH

19.

Elhajjar, B., Bachir, G., Mojtabi, A., Fakih, C., Charrier-Mojtabi, M.C.: Modeling of Rayleigh–Bénard natural convection heat transfer in nanofluids. Comptes Rendus Mcanique 338, 350–354 (2010)CrossRefMATH

20.

Eslamian, M., Ahmed, M., El-Dosoky, M.F., Saghir, M.Z.: Effect of thermophoresis on natural convection in a Rayleigh–Bénard cell filled with a nanofluid. Int. J. Heat Mass Transf. 81, 142–156 (2015)CrossRef

21.

Fatoorehchi, H., Abolghasemi, H.: Investigation of nonlinear problems of heat conduction in tapered cooling fins via symbolic programming. Appl. Appl. Math. 7, 717–734 (2012)MathSciNetMATH

22.

Fatoorehchi, H., Abolghasemi, H.: Approximating the minimum reflux ratio of multicomponent distillation columns based on the Adomian decomposition method. J. Taiwan Inst. Chem. Eng. 45, 880–886 (2014)CrossRef

23.

Fatoorehchi, H., Abolghasemi, H., Zarghami, R.: Analytical approximate solutions for a general nonlinear resistor-nonlinear capacitor circuit model. Appl. Math. Model. 39, 6021–6031 (2015)MathSciNetCrossRef

24.

Gaikwad, S.N., Malashetty, M.S., Prasad, K.R.: An analytical study of linear and non-linear double diffusive convection with soret and dufour effects in couple stress fluid. Int. J. Nonlinear Mech. 42, 903–913 (2007)CrossRef

25.

Garoosi, F., Bagheri, G., Talebi, F.: Numerical simulation of natural convection of nanofluids in a square cavity with several pairs of heaters and coolers (HACs) inside. Int. J. Heat Mass Transf. 67, 362–376 (2013)CrossRef

26.

Garoosi, F., Garoosi, S., Hooman, K.: Numerical simulation of natural convection and mixed convection of the nanofluid in a square cavity using Buongiorno model. Powder Tech. 268, 279–292 (2014)CrossRef

27.

Getling, A.V.: Rayleigh–Bénard Convection: Structures and Dynamics. World Scientific, Singapore (1998)CrossRefMATH

28.

Gupta, U., Sharma, G.: On Rivlin–Erickson elastico-viscous fluid heated and soluted from below in the presence of compressibility, rotation and hall currents. J. Appl. Math. Comput. 25, 51–66 (2007)MathSciNetCrossRefMATH

29.

Hamilton, R.L., Crosser, O.K.: Thermal conductivity of heterogeneous two-component systems. Ind. Eng. Chem. Fund. 1, 187–191 (1962)CrossRef

30.

Jawdat, J.M., Hashim, I., Bhadauria, B.S., Momani, S.: On onset of chaotic convection in couple-stress fluids. Math. Model. Anal. 19(3), 359–370 (2014)MathSciNetCrossRef

31.

Jawdat, J.M., Hashim, I., Momani, S.: Dynamical system analysis of thermal convection in a horizontal layer of nanofluids heated from below. Math. Probl. Eng. 2012, 1–13 (2012)MathSciNetCrossRefMATH

32.

Kakac, S., Pramuanjaroenkij, A.: Review of convective heat transfer enhancement with nanofluids. Int. J. Heat Mass Transf. 52, 3187–3196 (2009)CrossRefMATH

33.

Khanafer, K., Vafai, K., Lightstone, M.: Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transf. 46, 3639–3653 (2003)CrossRefMATH

34.

Kim, J., Choi, C.K., Kang, Y.T., Kim, M.G.: Effects of thermodiffusion and nanoparticles on convective instabilities in binary nanofluids. Nanoscale Microscale Thermophys. Eng. 10, 29–39 (2006)CrossRef

35.

Kim, J., Kang, Y.T., Choi, C.K.: Analysis of convective instability and heat transfer characteristics of nanofluids. Phys. Fluids 16, 2395–2401 (2004)CrossRefMATH

36.

Kim, J., Kang, Y.T., Choi, C.K.: Soret and dufour effects on convective instabilities in binary nanofluids for absorption application. Int. J. Refrig. 30, 323–328 (2007)CrossRef

37.

Krishnamurti, R.: Convection induced by selective absorption of radiation: A laboratory model of conditional instability. Dyn. Atmos. Oceans 27, 367–382 (1998)CrossRef

38.

Lorenz, E.N.: Deterministic nonperiodic flow. J. Atmos. Sci. 20(2), 130–141 (1963)CrossRefMATH

39.

Magyari, E.: Comment on the homogeneous nanofluid models applied to convective heat transfer problems. Acta Mech. 222, 381–385 (2011)CrossRefMATH

40.

Malashetty, M.S., Gaikwad, S.N., Swamy, M.: An analytical study of linear and non-linear double diffusive convection with soret effect in couple stress liquids. Int. J. Therm. Sci. 45, 897–907 (2006)CrossRef

41.

McKenzie, D.P., Roberts, J.M., Weiss, N.O.: Convection in the Earth’s mantle: Towards a numerical simulation. J. Fluid Mech. 62, 465–538 (1974)CrossRefMATH

42.

Narayana, M., Sibanda, P., Siddheshwar, P.G., Jayalatha, G.: Linear and nonlinear stability analysis of binary viscoelastic fluid convection. Appl. Math. Model. 37, 8162–8178 (2013)MathSciNetCrossRef

43.

Nield, D.A., Kuznetsov, A.V.: The onset of convection in a horizontal nanofluid layer of finite depth. Eur. J. Mech. B/Fluids 29, 217–223 (2010)MathSciNetCrossRefMATH

44.

Nield, D.A., Kuznetsov, A.V.: The onset of convection in an internally heated nanofluid layer. J. Heat Transf. 136(1), 014501 (2014)CrossRef

45.

Park, H.M.: Rayleigh–Bénard convection of nanofluids based on the pseudo-single-phase continuum model. Int. J. Therm. Sci. 90, 267–278 (2015)CrossRef

46.

Payne, L.E., Straughan, B.: Critical Rayleigh numbers for oscillatory and nonlinear convection in an isotropic thermomicropolar fluid. Int. J. Eng. Sci. 27, 827–836 (1989)CrossRefMATH

47.

Platten, J.K., Legros, J.C.: Convection in Liquids. Springer, Berlin (2012)MATH

48.

Putra, N., Roetzel, W., Das, S.K.: Natural convection of nano-fluids. Heat Mass Transf. 39, 775–784 (2003)CrossRefMATH

49.

Riahi, N., Hsui, A.T.: Nonlinear double-diffusive convection with local heat and solute sources. Int. J. Eng. Sci. 24, 529–544 (1986)MathSciNetCrossRefMATH

50.

Roberts, P.H.: Convection in horizontal layers with internal heat generation. J. Fluid Mech. 30, 33–49 (1967)CrossRef

51.

Rudraiah, N., Siddheshwar, P.G.: Effect of non-uniform basic temperature gradient on the onset of Marangoni convection in a fluid with suspended particles. Aerosp. Sci. Tech. 4, 517–523 (2000)CrossRefMATH

52.

Sharma, A., Shandil, R.G.: Effect of magnetic field dependent viscosity on ferroconvection in the presence of dust particles. J. Appl. Math. Comput. 27, 7–22 (2008)MathSciNetCrossRefMATH

53.

Shivakumara, I.S., Kumar, S.B.N.: Linear and weakly nonlinear triple diffusive convection in a couple stress fluid layer. Int. J. Heat Mass Transf. 68, 542–553 (2014)CrossRef

54.

Siddheshwar, P.G., Kanchana, C.: Unicellular, unsteady Rayleigh–Bénard convection in Newtonian liqenclosure Newtonain nanloquids occupying enclosures. Int. J. Mech. Sci. (2017) (In press)

55.

Siddheshwar, P.G., Kanchana, C., Kakimoto, Y., Nakayama, A.: Steady finite-amplitude Rayleigh–Bénard convection in nanoliquids using a two-phase model: Theoretical answer to the phenomenon of enhanced heat transfer. ASME J. Heat Transf. 139, 012402 (2017)CrossRef

56.

Siddheshwar, P.G., Meenakshi, N.: Amplitude equation and heat transport of Rayleigh–Bénard convection in Newtonian liquids with nanoparticles. Int. J. Appl. Comput. Math. 2, 1–22 (2015)CrossRef

57.

Siddheshwar, P.G., Pranesh, S.: Effect of a non-uniform basic temperature gradient on Rayleigh–Bénard convection in a micropolar fluid. Int. J. Eng. Sci. 36, 1183–1196 (1998)CrossRef

58.

Siddheshwar, P.G., Pranesh, S.: Magnetoconvection in a micropolar fluid. Int. J. Eng. Sci. 36, 1173–1181 (1998)CrossRef

59.

Siddheshwar, P.G., Pranesh, S.: Suction-injection effects on the onset of Rayleigh–Bénard–Marangoni convection in a fluid with suspended particles. Acta Mech. 152, 241–252 (2001)CrossRefMATH

60.

Siddheshwar, P.G., Pranesh, S.: Magnetoconvection in fluids with suspended particles under 1g and \(\mu \)g. Aerosp. Sci. Tech. 6, 105–114 (2002)CrossRefMATH

61.

Siddheshwar, P.G., Pranesh, S.: An analytical study of linear and non-linear convection in Boussinesq–Stokes suspensions. Int. J. Nonlin. Mech. 39, 165–172 (2004)CrossRefMATH

62.

Siddheshwar, P.G., Sakshath, T.N.: Rayleigh–Bénard–Taylor convection of Newtonian nanoliquid. World Acad. Sci. Eng. Technol. Int. J. Mech. Aerosp. Ind. Mech. Manuf. Eng. 11, 1131–1135 (2017)

63.

Siddheshwar, P.G., Sekhar, G.N., Jayalatha, G.: Effect of time-periodic vertical oscillations of the Rayleigh–Bénard system on nonlinear convection in viscoelastic liquids. J. Non Newtonian Fluid Mech. 165, 1412–1418 (2010)CrossRefMATH

64.

Siddheshwar, P.G., Sekhar, G.N., Jayalatha, G.: Surface tension driven convection in viscoelastic liquids with thermorheological effect. Int. Commun. Heat Mass Transf. 38, 468–473 (2011)CrossRef

65.

Siddheshwar, P.G., Titus, S.P.: Nonlinear Rayleigh–Bénard convection with variable heat source. J. Heat Transf. 135, 1–12 (2013)CrossRef

66.

Siddheshwar, P.G., Veena, B.N.: Unsteady Rayleigh–Bénard convection of nanoliquids in enclosures. World Acad. Sci. Eng. Technol. Int. J. Mech. Aerosp. Ind. Mech. Manuf. Eng. 11(6), 1051–1060 (2017)

67.

Simo, C., Puigjaner, D., Herrero, J., Giralt, F.: Dynamics of particle trajectories in a Rayleigh–Bénard problem. Commun. Nonlin. Sci. Numer. Simul. 15, 24–39 (2010)CrossRefMATH

68.

Sofos, F., Karakasidis, T., Liakopoulos, A.: Transport properties of liquid argon in krypton nanochannels: anisotropy and non-homogeneity introduced by the solid walls. Int. J. Heat Mass Transf. 52(3), 735–743 (2009)CrossRefMATH

69.

Straughan, B.: The Energy Method, Stability, and Nonlinear Convection. Springer, Berlin (2013)MATH

70.

Thirlby, R.: Convection in an internally heated layer. J. Fluid Mech. 44, 673–693 (1970)CrossRefMATH

71.

Tiwari, R.K., Das, M.K.: Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Int. J. Heat Mass Transf. 50, 2002–2018 (2007)CrossRefMATH

72.

Tritton, D.J., Zarraga, M.N.: Convection in horizontal layers with internal heat generation. Exp. J. Fluid Mech. 30, 21–31 (1967)CrossRef

73.

Tveitereid, M., Palm, E.: Convection due to internal heat sources. J. Fluid Mech. 76, 481–499 (1976)CrossRefMATH

74.

Tzou, D.Y.: Instability of nanofluids in natural convection. J. Heat Transf. 130, 1–9 (2008)CrossRefMATH

75.

Tzou, D.Y.: Thermal instability of nanofluids in natural convection. Int. J. Heat Mass Transf. 51, 2967–2979 (2008)CrossRefMATH

76.

Wang, X.Q., Mujumdar, A.S.: Heat transfer characteristics of nanofluids: A review. Int. J. Therm. Sci. 46, 1–19 (2007)CrossRef

77.

Wen, D., Lin, G., Vafaei, S., Zhang, K.: Review of nanofluids for heat transfer applications. Particuology 7, 141–150 (2009)CrossRef

78.

Xuan, Y., Roetzel, W.: Conceptions for heat transfer correlation of nanofluids. Int. J. Heat Mass Transf. 43, 3701–3707 (2000)CrossRefMATH

79.

Yadav, D., Agrawal, G.S., Bhargava, R.: Rayleigh–Bénard convection in nanofluid. Int. J. Appl. Math. Mech. 7, 61–76 (2011)MATH

80.

Yadav, D., Agrawal, G.S., Bhargava, R.: Thermal instability of rotating nanofluid layer. Int. J. Eng. Sci. 49, 1171–1184 (2011)MathSciNetCrossRef

Title: A theoretical study of enhanced heat transfer in nanoliquids with volumetric heat source
Authors: N. Meenakshi
P. G. Siddheshwar
Publication date: 17-08-2017
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2018
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-017-1129-9

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Other articles of this Issue 1-2/2018

Resistance distances in the linear polyomino chain

A modified nonmonotone trust region line search method

An infeasible interior point method for the monotone SDLCP based on a transformation of the central path

Permanence and extinction of stochastic competitive Lotka–Volterra system with Lévy noise

New concepts in neutrosophic graphs with application

Existence results for nonlinear fractional differential equations in C[0, T)

Premium Partner