Document Type : Full Lenght Research Article

**Authors**

Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

**Abstract**

Effects of different volumetric fractions and Reynolds number on forced convection heat transfer through water/aluminum oxide nanofluid in a horizontal tube are investigated. The flow regime is laminar and the method of simulation is the axisymmetric lattice Boltzmann method (ALBM). The profiles of velocity and temperature were uniform at the input section, on the tube walls the uniform heat flux was considered; moreover, hydrodynamic, and thermal development conditions at the output section were applied. It was observed that an increase in the volumetric concentration of the nanoparticles added to the forced convection heat transfer coefficient and Nusselt number of the nanofluid, as compared to the base fluid. For a volumetric fraction of 5% and Reynolds number of 100 at the input section of the tube (0.1≤X/D≤7) the forced convection heat transfer coefficient increased by 24.165%, while an average increase of 21.361% was observed along the entire length of the tube (0≤x/D≤30). A comparison between the improvements in heat transfer at the two input temperatures, it was found that the forced convection heat transfer coefficient and Nusselt number will increase further at the lower input temperature; Moreover, with increasing the Reynolds number, the percent improvements in forced convention heat transfer coefficient and Nusselt number increased.

**Keywords**

**Main Subjects**

[2] Wang, X.Q. and Mujumdar, A.S., 2008. A review on nanofluids-part I: theoretical and numerical investigations. Brazilian Journal of Chemical Engineering, 25(4), pp.613-630.

[3] Eastman, J.A., Choi, U.S., Li, S., Thompson, L.J. and Lee, S., 1996. Enhanced thermal conductivity through the development of nanofluids (No. ANL/MSD/CP-90462; CONF-961202-94). Argonne National Lab., IL (United States).

[4] Lee, S., Choi, S.S., Li, S.A. and Eastman, J.A., 1999. Measuring thermal conductivity of fluids containing oxide nanoparticles.

[5] Xuan, Y. and Roetzel, W., 2000. Conceptions for heat transfer correlation of nanofluids. International Journal of heat and Mass transfer, 43(19), pp.3701-3707.

[6] Wen, D. and Ding, Y., 2004. Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions. International journal of heat and mass transfer, 47(24), pp.5181-5188.

[7] Shah, R.K., 1975, December. Thermal entry length solutions for the circular tube and parallel plates. In Proceedings of 3rd national heat and mass transfer conference, 1, pp.11. Indian Institute of Technology Bombay.

[8] Noghrehabadi, A. and Pourrajab, R., 2016. Experimental investigation of forced convective heat transfer enhancement of γ-Al 2 O 3/water nanofluid in a tube. Journal of

84 R.Bahoosh / JHMTR 8 (2021) 71- 85

Mechanical Science and Technology, 30(2), pp.943-952.

[9] Hassanzadeh, R., Ozbek, A. and Bilgili, M., 2016. Analysis of alumina/water nanofluid in thermally developing region of a circular tube. Thermal Engineering, 63(12), pp.876-886.

[10] Nourgaliev, R.R., Dinh, T.N., Theofanous, T.G. and Joseph, D., 2003. The lattice Boltzmann equation method: theoretical interpretation, numerics and implications. International Journal of Multiphase Flow, 29(1), pp.117-169.

[11] Xuan, Y. and Yao, Z., 2005. Lattice Boltzmann model for nanofluids. Heat and mass transfer, 41(3), pp.199-205.

[12] Kefayati, G.R., Hosseinizadeh, S.F., Gorji, M. and Sajjadi, H., 2011. Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid. International Communications in Heat and Mass Transfer, 38(6), pp.798-805.

[13] Javaherdeh, K. and Ashorynejad, H.R., 2014. Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using Lattice Boltzmann Method. Advanced Powder Technology, 25(2), pp.666-675.

[14] Sidik, N.A.C. and Mamat, R., 2015. Recent progress on lattice Boltzmann simulation of nanofluids: A review. International Communications in Heat and Mass Transfer, 66, pp.11-22.

[15] Cheng, P., Gui, N., Yang, X., JiyuanTu and Jiang, S., 2018. Application of lattice Boltzmann methods for the multiphase fluid pipe flow on graphical processing unit. The Journal of Computational Multiphase Flows, 10(3), pp.109-118.

[16] Goodarzi, M., D’Orazio, A., Keshavarzi, A., Mousavi, S. and Karimipour, A., 2018. Develop the nano scale method of lattice Boltzmann to predict the fluid flow and heat transfer of air in the inclined lid driven cavity with a large heat source inside, Two case studies: Pure natural convection & mixed convection. Physica A: Statistical Mechanics and Its Applications, 509, pp.210-233.

[17] Nazari, M. and Kayhani, M.H., 2016. A Comparative Solution of Natural Convection in an Open Cavity using Different Boundary Conditions via Lattice Boltzmann Method. Journal of Heat and Mass Transfer Research, 3(2), pp.115-129.

[18] Bahoosh, R., Jafari, M. and Bahrainian, S.S., 2019. GDL construction effects on distribution of reactants and electrical current density in PEMFC. Journal of Heat and Mass Transfer Research, 6(2), pp.105-116. [19] Shomali, M. and Rahmati, A., 2020. Numerical analysis of gas flows in a microchannel using the Cascaded Lattice Boltzmann Method with varying Bosanquet parameter. Journal of Heat and Mass Transfer Research, 7(1), pp.25-38.

[20] Zhou, J.G., 2011. Axisymmetric lattice Boltzmann method revised. Physical review E, 84(3), p.036704.

[21] Zhou, J.G., 2008. Axisymmetric lattice Boltzmann method. Physical Review E, 78(3), p.036701.

[22] Guo, Z., Han, H., Shi, B. and Zheng, C., 2009. Theory of the lattice Boltzmann equation: lattice Boltzmann model for axisymmetric flows. Physical Review E, 79(4), p.046708.

[23] Li, Q., He, Y.L., Tang, G.H. and Tao, W.Q., 2010. Improved axisymmetric lattice Boltzmann scheme. Physical Review E, 81(5), p.056707.

[24] Li, Q., He, Y.L., Tang, G.H. and Tao, W.Q., 2009. Lattice Boltzmann model for axisymmetric thermal flows. Physical Review E, 80(3), p.037702.

[25] Chang, C., Liu, C.H. and Lin, C.A., 2009. Boundary conditions for lattice Boltzmann simulations with complex geometry flows. Computers & Mathematics with Applications, 58(5), pp.940-949.

[26] Ho, C.F., Chang, C., Lin, K.H. and Lin, C.A., 2009. Consistent boundary conditions for 2D and 3D lattice Boltzmann simulations. Computer Modeling in Engineering and Sciences (CMES), 44(2), p.137.

[27] Javaherdeh, K. and Ashorynejad, H.R., 2014. Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using Lattice Boltzmann Method. Advanced Powder Technology, 25(2), pp.666-675.

[28] Mohamad, A.A., 2011. Lattice Boltzmann Method, London, Springer.

[29] Pourrajab R., 2013, Experimental investigation of forced convective heat transfer through channel with nanofluids. Msc Thesis, Shahid Chamran University, Ahvaz, Iran.

[30] Pak, B.C. and Cho, Y.I., 1998. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles. Experimental Heat Transfer an International Journal, 11(2), pp.151-170.

[31] Huminic, G. and Huminic, A., 2012. Application of nanofluids in heat exchangers: A review. Renewable and Sustainable Energy Reviews, 16(8), pp.5625-5638.

R.Bahoosh / JHMTR 8 (2021) 71- 85 85

[32] Maiga, S.E.B., Palm, S.J., Nguyen, C.T., Roy, G. and Galanis, N., 2005. Heat transfer enhancement by using nanofluids in forced convection flows. International journal of heat and fluid flow, 26(4), pp.530-546.

[33] Maxwell, J.C., 1873. A treatise on electricity and magnetism, Oxford: Clarendon Press.

[34] Bejan, A., 2013. Convection heat transfer. John wiley & sons.

[35] Incropera, F.P., Lavine, A.S., Bergman, T.L. and DeWitt, D.P., 2007. Fundamentals of heat and mass transfer. Wiley.

[36] Hornbeck, R.W., 1966, January. AN ALL-NUMERICAL METHOD FOR HEAT TRANSFER IN INLET OF A TUBE. In MECHANICAL ENGINEERING, 88(1), pp. 76. 345 E 47TH ST, NEW YORK, NY 10017: ASME-AMER SOC MECHANICAL ENG.

Winter and Spring 2021

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**Receive Date:**02 November 2020**Revise Date:**21 April 2021**Accept Date:**26 April 2021