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Chebyshev Approximation for Nanofluid flow of Non-Isothermal Channel Flow under Constant Heat Flux

Year 2016, Volume: 19 Issue: 1, 11 - 20, 10.05.2016

Coşkun Özalp , Betül Teymur Bülent Yanıktepe , Muharrem İmal

https://doi.org/10.17780/ksujes.14532

Abstract

This paper investigates the Nano-fluid for a non-isothermal channel flow under the effect of a constant pressure gradient acting along the channel axis. Two-dimensional, non-isothermal, steady flow of an incompressible fluid in a channel is taken into consideration. Upper and lower walls of the channel are kept at the same constant heat flux. To consider the effect of conductivity and viscosity, Maxwell and Brinkman’s models are used respectively. The effects of volume fraction, pressure gradient and Reynolds numbers on velocity and temperature profiles are discussed for the Nano-fluid Alumina. Water is used as a base fluid. The comparisons of the flow characteristics, including the distributions of velocity, temperature and volumetric flow rate of aluminum oxide are also given in the paper. Shear stress distribution along the channel axis and pressure gradient for different volume fraction are presented as well.  Discretization is performed using a Pseudospectral technique based on Chebyshev polynomial expansions. The resulting nonlinear, coupled boundary value problem is solved iteratively using Chebyshev pseudospectral method.

Keywords

Nano-Fluid Non isothermal channel flow Pseudospectral technique

References

  • 1]. Maxwell, J.C. (1904). A Treatise on Electricity and Magnetism, second ed. Oxford University Press, Cambridge, pp. 435–441.
  • [2]. Jeffrey, D.J. (1973). “Conduction through a random suspension of spheres”, Proc. R. Soc. Lond., Series A 335, pp. 355–367.
  • [3]. Batchelor, G.K. (1977). “The effect of Brownian motion on the bulk stress in a suspension of spherical particles”, J. Fluid Mech., 83 (Pt.1), pp. 97–117.
  • [4]. Gupte, S.K., Advani, S.G., Huq, P. (1995). “Role of micro-convection due to non-affine motion of particles in a mono-disperse suspension”, Int. J. Heat Mass Transfer, 38 (16), pp. 2945–2958.
  • [5]. Boothroyd, R.G., Haque, H. (1970). “Fully developed heat transfer to a gaseous suspension of particles flowing turbulently in duct of different size”, J. Mech. Eng. Sci., 12 (3), pp. 191–200.
  • [6]. Sohn, C.W., Chen, M.M., (1981). “Microconvective thermal conductivity in disperse two-phase mixtures as observed in a low velocity Couette flow experiment”, J. Heat Transfer, 103, pp. 45–51.
  • [7]. Kurosaki, Y., Murasaki, T. (1986). “Study on heat transfer mechanism of a gas–solid suspension impinging jet (effect of particle size and thermal properties)”, Proceedings of the 8th International Heat Transfer Conference, vol. 5, pp. 2587–2592.
  • [8]. Ahuja, A.S. (1982). “Thermal design of a heat exchanger employing laminar flow of particle suspensions”, Int. J. Heat Mass Transfer, 25 (5), pp. 725–728.
  • [9]. Masuda, H., Ebata, A., Teramae, K., Hishinuma, N. (1993). “Alteration of thermal conductivity and viscosity of liquid by dispersing ultrafine particles (dispersion of c
  • Al2O3, SiO2 and TiO2 ultra-fine particles)”, Netsu Bussei, 4 (4), pp. 227–233. [10]. Choi, S.U.-S. (1995). “Enhancing thermal conductivity of fluids with nanoparticles.” ASME Publications FED-vol. 231/MD-vol. 66, pp. 99–105.
  • [11]. Lee, S., Choi, S.U.-S., Li, S., Eastman, J.A. (1999). “Measuring thermal conductivity of fluids containing oxide nanoparticles”. J. Heat Transfer, 121, pp. 280–289.
  • [12]. Yu, W., France, D.M., Choi, S.U.S., Routbort, J.L. (2007). “Review and Assessment of Nanofluid Technology for Transportation and Other Applications.” ANL/ESD/07–9,
  • Argonne National Laboratory, Argonne, IL. [13]. Wang, X., Xu, X., Choi, S.U.S., (1999). “Thermal conductivity of nanoparticle-fluid mixture”, J. Thermophys. Heat Transfer, 13, pp. 474–480.
  • [14]. Xie, H., Wang, J., Xi, T., Liu, Y. (2002a). “Thermal conductivity of suspensions containing nanosized SiC particles”, Int. J. Thermophys., 23, pp. 571–580.
  • [15]. Xie, H., Wang, J., Xi, T., Ai, F. (2002b). “Thermal conductivity enhancement of suspensions containing nanosized alumina particles”, J. Appl. Phys., 91, pp. 4568–4572.
  • [16]. Xie, H., Wang, J., Xi, T., Liu, Y., Ai, F. (2002). “Dependence of the thermal conductivity of nanoparticles-fluid mixture on the base fluid”, J. Mater. Sci. Lett., 21, pp. 1469–1471.
  • [17]. Das, S.K., Putra, N., Thiesen, P., Roetzel, W. (2003). “Temperature dependence of thermal conductivity enhancement of nanofluids”, Trans. ASME, J. Heat Transfer, 125, pp. 567– 574.
  • [18]. Das, S.K., Putra, N., Roetzel, W. (2003). “Pool boiling of nano-fluids on horizontal narrow tubes”, Int. J. Multiphase Flow, 29, pp. 1237–1247.
  • [19]. Maiga, S.E.B., Palm, S.J., Nguyen, C.T., Roy, G., Galanis, N. (2005). “Heat transfer enhancement by using nanofluids in forced convection flows”, Int. J. Heat and Fluid Flow, 26, pp. 530–546.
  • [20]. Utomo A.T., Poth, H., Robbins, P. T., Pacek, A.W. (2012). “Experimental and theoretical studies of thermal conductivity, viscosity and heat transfer coefficient of titania and alumina nanofluids”, International Journal of Heat and Mass Transfer, 55, pp. 7772–7781.
  • [21]. Shojaeian, M., Kosar, A. (2014). “Convective heat transfer and entropy generation analysis on Newtonian and non-Newtonian fluid flows between parallel-plates under slip boundary conditions”, International Journal of Heat and Mass Transfer, 70, pp. 664–673.
  • [22]. Mohammeda, H.A., Al-aswadi, A.A., Shuaib, N.H., Saidur, R. (2011). “Convective heat transfer and fluid flow study over a step using nanofluids: A review”, Renewable and Sustainable Energy Reviews, 15, pp. 2921– 2939.
  • [23]. “Hatami, M., Ganji, D.D., (2013). Heat transfer and flow analysis for SA-TiO2 non - Newtonian nanofluid passing through the porous media between two coaxial cylinders”, Journal of Molecular Liquids, 188, pp. 155– 161.
  • [24]. Bianco,V., Manca,, O., Nardini, S. (2011). “Numerical investigation on nanofluids turbulent convection heat transfer inside a circular tube”, International Journal of Thermal Sciences, 50, pp. 341-349.
  • [25]. Tso, C.P., Sheela-Francisca, J., Mun Hung, Y. (2010). “Viscous dissipation effects of powerlaw fluid flow within parallel plates with constant heat fluxes”, J. Non-Newtonian Fluid Mech., 165, pp. 625–630.
  • [26]. Lotfi, R., Saboohi, Y., Rashidi, A.M. (2010). “Numerical study of forced convective heat transfer of Nanofluids: Comparison of different approaches”, International Communications in Heat and Mass Transfer, 37, pp. 74–78.
  • [27]. Duangthongsuk, W., Wongwises, S., (2009). “Measurement of temperature-dependent thermal conductivity and viscosity of TiO2- water nanofluids”, Experimental Thermal and Fluid Science, 33, pp. 706–714.
  • [28]. Heidary,H., Kermani, M.J., (2010).“Effect of nano-particles on forced convection in sinusoidal-wall channel”, International Communications in Heat and Mass Transfer, 37, pp. 1520–1527.
  • [29]. Mohammed , H.A., Bhaskaran , G., Shuaib , N.H., Abu-Mulaweh, H.I. (2011). “Influence of nanofluids on parallel flow square microchannel heat exchanger performance”, ,International Communications in Heat and Mass Transfer, 38, pp. 1–9.
  • [30]. Mahbubul, I.M., Saidur, R., Amalina, M.A. (2012). “Latest developments on the viscosity of nanofluids”, International Journal of Heat and Mass Transfer, 55, pp., 874–885.
  • [31]. Sun, W., Kakac, S., Yazicioglu, A.G. (2007). “A numerical study of single-phase convective heat transfer in microtubes for slip flow”, International Journal of Thermal Sciences, 46, pp. 1084–1094.
  • [32]. Heyhat, M.M., Kowsary, F., Rashidi , A.M., Momenpour, M.H., Amrollahi, A. (2013). “Experimental investigation of laminar convective heat transfer and pressure drop of water-based Al2O3 nanofluids in fully developed flow regime”, Experimental Thermal and Fluid Science, 44, pp. 483–489. KSU Mühendislik Bilimleri Dergisi,
  • [33]. Pelevi, N., Van der Meer, Th.H., (2012). “Numerical investigation of the effective thermal conductivity of nano-fluids using the lattice Boltzmann model”, International Journal of Thermal Sciences, 62, pp. 154-159.
  • [34]. Manca, O., Nardini, S., Ricci, D. (2012). “A numerical study of nanofluid forced convection in ribbed channels”, Appl Therm Eng, 37, pp. 280–292.

Sabit Isı Akısı Altında İzotermal Olmayan Kanal Akışında Nanoakışlar İçin Chebyshev Yaklaşımı

Year 2016, Volume: 19 Issue: 1, 11 - 20, 10.05.2016

Coşkun Özalp , Betül Teymur Bülent Yanıktepe , Muharrem İmal

https://doi.org/10.17780/ksujes.14532

Abstract

Bu çalışmada sabit basınç gradyanının etkisi altındaki nanoakışkanın izotermal olmayan kanaldaki akışı sayısal olarak incelenmiştir. Kanal akışının çözümünde akışın iki boyutlu, izotermal olmayan, sıkıştırılamaz, hidrodinamik ve ısıl olarak tam gelişmiş ve sürekli olduğu kabul edilmiştir. Kanal alt ve üst cidarlarına sabit ısı akısı sınır şartı uygulanmış olup alümina-su nanoakışkanın tek fazlı ve homojen olduğu varsayılmıştır. Momentum ve enerji denklemlerinde yer alan ısıl iletkenlik ve viskozite değerleri için hacimsel konsantrasyona bağlı olarak sırasıyla Maxwell ve Brinkman modelleri kullanılmıştır. Kanal içindeki alümina-su nanoakışkanın hacimsel konsantrasyon, basınç gradyanı ve Reynolds sayısının sıcaklık ve hız profiline etkisi incelenmiştir. Su temel akışkan olarak ele alınmıştır. Ayrıca kanal merkezi boyunca kayma gerilmesi dağılımı ve farklı hacimsel debilerdeki basınç gradyanı değişimi de incelenmiştir. Denklemlerin ayrıklaştırılması Chebyshev polinom açılımlarına dayanan Pseudospectral yöntemi kullanılarak yapılmış ve doğrusal olmayan sınır değer problemleri Chebyshev Pseudospectral yöntemi ile sayısal olarak çözülmüştür

Keywords

Nanoakışkan İzotermal Olmayan Kanal Akışı Pseudospectral yöntemi

References

  • 1]. Maxwell, J.C. (1904). A Treatise on Electricity and Magnetism, second ed. Oxford University Press, Cambridge, pp. 435–441.
  • [2]. Jeffrey, D.J. (1973). “Conduction through a random suspension of spheres”, Proc. R. Soc. Lond., Series A 335, pp. 355–367.
  • [3]. Batchelor, G.K. (1977). “The effect of Brownian motion on the bulk stress in a suspension of spherical particles”, J. Fluid Mech., 83 (Pt.1), pp. 97–117.
  • [4]. Gupte, S.K., Advani, S.G., Huq, P. (1995). “Role of micro-convection due to non-affine motion of particles in a mono-disperse suspension”, Int. J. Heat Mass Transfer, 38 (16), pp. 2945–2958.
  • [5]. Boothroyd, R.G., Haque, H. (1970). “Fully developed heat transfer to a gaseous suspension of particles flowing turbulently in duct of different size”, J. Mech. Eng. Sci., 12 (3), pp. 191–200.
  • [6]. Sohn, C.W., Chen, M.M., (1981). “Microconvective thermal conductivity in disperse two-phase mixtures as observed in a low velocity Couette flow experiment”, J. Heat Transfer, 103, pp. 45–51.
  • [7]. Kurosaki, Y., Murasaki, T. (1986). “Study on heat transfer mechanism of a gas–solid suspension impinging jet (effect of particle size and thermal properties)”, Proceedings of the 8th International Heat Transfer Conference, vol. 5, pp. 2587–2592.
  • [8]. Ahuja, A.S. (1982). “Thermal design of a heat exchanger employing laminar flow of particle suspensions”, Int. J. Heat Mass Transfer, 25 (5), pp. 725–728.
  • [9]. Masuda, H., Ebata, A., Teramae, K., Hishinuma, N. (1993). “Alteration of thermal conductivity and viscosity of liquid by dispersing ultrafine particles (dispersion of c
  • Al2O3, SiO2 and TiO2 ultra-fine particles)”, Netsu Bussei, 4 (4), pp. 227–233. [10]. Choi, S.U.-S. (1995). “Enhancing thermal conductivity of fluids with nanoparticles.” ASME Publications FED-vol. 231/MD-vol. 66, pp. 99–105.
  • [11]. Lee, S., Choi, S.U.-S., Li, S., Eastman, J.A. (1999). “Measuring thermal conductivity of fluids containing oxide nanoparticles”. J. Heat Transfer, 121, pp. 280–289.
  • [12]. Yu, W., France, D.M., Choi, S.U.S., Routbort, J.L. (2007). “Review and Assessment of Nanofluid Technology for Transportation and Other Applications.” ANL/ESD/07–9,
  • Argonne National Laboratory, Argonne, IL. [13]. Wang, X., Xu, X., Choi, S.U.S., (1999). “Thermal conductivity of nanoparticle-fluid mixture”, J. Thermophys. Heat Transfer, 13, pp. 474–480.
  • [14]. Xie, H., Wang, J., Xi, T., Liu, Y. (2002a). “Thermal conductivity of suspensions containing nanosized SiC particles”, Int. J. Thermophys., 23, pp. 571–580.
  • [15]. Xie, H., Wang, J., Xi, T., Ai, F. (2002b). “Thermal conductivity enhancement of suspensions containing nanosized alumina particles”, J. Appl. Phys., 91, pp. 4568–4572.
  • [16]. Xie, H., Wang, J., Xi, T., Liu, Y., Ai, F. (2002). “Dependence of the thermal conductivity of nanoparticles-fluid mixture on the base fluid”, J. Mater. Sci. Lett., 21, pp. 1469–1471.
  • [17]. Das, S.K., Putra, N., Thiesen, P., Roetzel, W. (2003). “Temperature dependence of thermal conductivity enhancement of nanofluids”, Trans. ASME, J. Heat Transfer, 125, pp. 567– 574.
  • [18]. Das, S.K., Putra, N., Roetzel, W. (2003). “Pool boiling of nano-fluids on horizontal narrow tubes”, Int. J. Multiphase Flow, 29, pp. 1237–1247.
  • [19]. Maiga, S.E.B., Palm, S.J., Nguyen, C.T., Roy, G., Galanis, N. (2005). “Heat transfer enhancement by using nanofluids in forced convection flows”, Int. J. Heat and Fluid Flow, 26, pp. 530–546.
  • [20]. Utomo A.T., Poth, H., Robbins, P. T., Pacek, A.W. (2012). “Experimental and theoretical studies of thermal conductivity, viscosity and heat transfer coefficient of titania and alumina nanofluids”, International Journal of Heat and Mass Transfer, 55, pp. 7772–7781.
  • [21]. Shojaeian, M., Kosar, A. (2014). “Convective heat transfer and entropy generation analysis on Newtonian and non-Newtonian fluid flows between parallel-plates under slip boundary conditions”, International Journal of Heat and Mass Transfer, 70, pp. 664–673.
  • [22]. Mohammeda, H.A., Al-aswadi, A.A., Shuaib, N.H., Saidur, R. (2011). “Convective heat transfer and fluid flow study over a step using nanofluids: A review”, Renewable and Sustainable Energy Reviews, 15, pp. 2921– 2939.
  • [23]. “Hatami, M., Ganji, D.D., (2013). Heat transfer and flow analysis for SA-TiO2 non - Newtonian nanofluid passing through the porous media between two coaxial cylinders”, Journal of Molecular Liquids, 188, pp. 155– 161.
  • [24]. Bianco,V., Manca,, O., Nardini, S. (2011). “Numerical investigation on nanofluids turbulent convection heat transfer inside a circular tube”, International Journal of Thermal Sciences, 50, pp. 341-349.
  • [25]. Tso, C.P., Sheela-Francisca, J., Mun Hung, Y. (2010). “Viscous dissipation effects of powerlaw fluid flow within parallel plates with constant heat fluxes”, J. Non-Newtonian Fluid Mech., 165, pp. 625–630.
  • [26]. Lotfi, R., Saboohi, Y., Rashidi, A.M. (2010). “Numerical study of forced convective heat transfer of Nanofluids: Comparison of different approaches”, International Communications in Heat and Mass Transfer, 37, pp. 74–78.
  • [27]. Duangthongsuk, W., Wongwises, S., (2009). “Measurement of temperature-dependent thermal conductivity and viscosity of TiO2- water nanofluids”, Experimental Thermal and Fluid Science, 33, pp. 706–714.
  • [28]. Heidary,H., Kermani, M.J., (2010).“Effect of nano-particles on forced convection in sinusoidal-wall channel”, International Communications in Heat and Mass Transfer, 37, pp. 1520–1527.
  • [29]. Mohammed , H.A., Bhaskaran , G., Shuaib , N.H., Abu-Mulaweh, H.I. (2011). “Influence of nanofluids on parallel flow square microchannel heat exchanger performance”, ,International Communications in Heat and Mass Transfer, 38, pp. 1–9.
  • [30]. Mahbubul, I.M., Saidur, R., Amalina, M.A. (2012). “Latest developments on the viscosity of nanofluids”, International Journal of Heat and Mass Transfer, 55, pp., 874–885.
  • [31]. Sun, W., Kakac, S., Yazicioglu, A.G. (2007). “A numerical study of single-phase convective heat transfer in microtubes for slip flow”, International Journal of Thermal Sciences, 46, pp. 1084–1094.
  • [32]. Heyhat, M.M., Kowsary, F., Rashidi , A.M., Momenpour, M.H., Amrollahi, A. (2013). “Experimental investigation of laminar convective heat transfer and pressure drop of water-based Al2O3 nanofluids in fully developed flow regime”, Experimental Thermal and Fluid Science, 44, pp. 483–489. KSU Mühendislik Bilimleri Dergisi,
  • [33]. Pelevi, N., Van der Meer, Th.H., (2012). “Numerical investigation of the effective thermal conductivity of nano-fluids using the lattice Boltzmann model”, International Journal of Thermal Sciences, 62, pp. 154-159.
  • [34]. Manca, O., Nardini, S., Ricci, D. (2012). “A numerical study of nanofluid forced convection in ribbed channels”, Appl Therm Eng, 37, pp. 280–292.
There are 34 citations in total.

Details

Primary Language English
Subjects Material Production Technologies
Journal Section Research Articles
Authors

Coşkun Özalp

Betül Teymur

Bülent Yanıktepe

Muharrem İmal

Publication Date May 10, 2016
Submission Date March 1, 2016
Published in Issue Year 2016Volume: 19 Issue: 1

Cite

APA Özalp, C., Teymur, B., Yanıktepe, B., İmal, M. (2016). Chebyshev Approximation for Nanofluid flow of Non-Isothermal Channel Flow under Constant Heat Flux. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 19(1), 11-20. https://doi.org/10.17780/ksujes.14532