Numerical study of natural convection heat transfer of Al2 O3/Water nanofluid in a Γ-shaped microchannel

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Bu-Ali Sina University, Hamedan, Iran

2 Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran

Abstract

Finite-volume procedure is presented for solving the natural convection of the laminar  nanofluid flow in a Γ shaped microchannel in this article. Modified Navier-Stokes equations for nanofluids are the basic equations for this problem. Slip flow region, including the effects of velocity slip and temperature jump at the wall, are the main characteristics of flow in the slip flow region. Steady state equations were solved by using time marching method. In provided FORTRAN code, the finite volume method and an explicit fourth-order Runge–Kutta integration algorithm were applied to find the steady state solutions. Also an artificial compressibility technique was used to couple the continuity to the momentum equations as it is simpler and converges faster. The Grashof numbers from  to  were considered. The results showed that Nusselt number increases with the Grashof number and the parameter R (the ratio of minimum diameter of nanoparticles and maximum one).. As the parameter R increases, the distortion of the isotherm lines increases to some extent.

Keywords


[1] Dagtekin I., Oztop H. F., Natural Convection Heat Transfer by Heated Partitions within Enclouser, Heat Mass Transfer (2001) 28(6): 823-834.

[2] Masuda H., Ebata A.  , Teramae K., Hishinuma N.  , Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles (Dispersions of -Al2O3, SiO2, and TiO2 Ultra-Fine Particles) Netsu Bussei (Japanese) (1993) 4: 227–233.

[3] Eastman J. A.  , Choi S. U. S.  , Li S., Yu W., Thompson L.J., Anomalously Increased Effective Thermal Conductivities of Ethylene Glycol Based Nanofluids Containing Copper Nanoparticles, Applied Physics Letters (2001) 78: 718–720.

[4] Xie H., Wang J., Xi T.  , Liu Y., Ai F., Dependence of the Thermal Conductivity of Nanoparticle–Fluid Mixture on the Base Fluid, Journal of Materials Science Letters (2002) 21: 1469–1471.

[5] Xie H., Wang J., Xi T.  , Liu Y., Ai F., Thermal Conductivity Enhancement of Suspensions Containing Nanosized Alumina Particles, Journal of Applied Physics (2002) 91: 4568–4572.

[6] Wang B. X., Li H., Peng X.F.  , Research on the Heat-Conduction Enhancement for Liquid with Nanoparticle Suspensions, Journal of Thermal Science(2002)11 (3): 214–219.

[7] Das S. K., Putra N., Thiesen P., Roetzel W., Temperature Dependence of Thermal Conductivity Enhancement for Nanofluids, Journal of Heat Transfer (2003) 125: 567–574.

[8] Zhang H., Shao S., Xu H., Tian C., Heat Transfer and Flow Features of Al2O3-Water Nanofluids Flowing Through a Circular Microchannel – Experimental Results and Correlations, Applied Thermal Engineering (2013) 61: 86-92.

[9] Arie M., Shooshtari A., Dessiatoun S., Al-Hajri E., Ohadi M., Numerical Modeling and Thermal Optimization of a Single-Phase Flow Manifold-Microchannel Plate Heat Exchanger, International Journal of Heat and Mass Transfer(2015) 81: 478-89.

[10] Ebrahimi A., Roohi E., Kheradmand S., Numerical Study of Liquid Flow and Heat Transfer in Rectangular Microchannel with Longitudinal Vortex Generators, Applied Thermal Engineering (2014)78: 576-83.

[11] Yue Y.  , Mohammadian S. K., Zhang Y., Analysis of Performances of a Manifold Microchannel Heat Sink with Nanofluids, International Journal of Thermal Sciences(2015) 89: 305- 13.

[12] Hedayati F., Domairry G., Effects of Nanoparticle Migration and Asymmetric Heating on Mixed Convection of TiO 2–H 2 O Nanofluid Inside a Vertical Microchannel, Powder Technology (2015) 272: 250-59.

[13] Zhu X. W., Fu Y. H., Zhao J. Q., Zhu L., Three-Dimensional Numerical Study of the Laminar Flow and Heat Transfer in a Wavy-Finned Heat Sink Filled with Al2O3/ethylene Glycol-Water Nanofluid, Numerical Heat TransferPart A: Applications (2015)1-14.

[14] Yang Y. T., Wang Y. H., Tseng P. K., Numerical Optimization of Heat Transfer Enhance- 531 Ment in a Wavy Channel Using Nanofluids, International Communications in Heat and Mass Transfer (2014) 51 (532):  9-17

[15] Esfahanian V., Akbarzadeh P., The Jameson's Numerical Method for Solving the Incompressible Viscous and Inviscid Flows by Means of Artificial Compressibility and Preconditioning Method, Applied Mathematics and Computation (2008) 206:651-661.

[16] Chorin A. J., A Numerical Method for Solving Incompressible Viscous Flow Problems, Journal of Computational physics(1997) 112: 118-125.

[17] Bassi F., Crivellini A., Pietro D. A., Rebay S., An Artificial Compressibility Flux for the Discontinuous Galerkin Solution of the Incompressible Navier-Stokes Equations, Journal of Computational Physics(2006) 218:794-815.

[18] Jang S. P., Lee J. H., Hwang K. S., Choi S. U. S., Particle Concentration and Tube Size Dependence of Viscosities of Al2O3-Water Nanofluids Flowing Through Micro- and Mini Tubes, Applied Physics Letters (2007)91: 243112.

[19] Hamilton R. L., Crosser O. K., Thermal Conductivity of Heterogeneous Two Component Systems, Journal of Industrial & Engineering Chemistry Fundamentals (1962) 1: 187–191.

[20] Xu J.  , Yu B., Zou M.  , Xu P.,  A New Model for Heat Conduction of Nanofluids Based on Fractal Distributions of Nanoparticles, The Journal of Physics D (2006) 39:4486–4490.

[21] Chorin A. J., A Numerical Method for Solving Incompressible Navier-Stokes Equations, The Journal of Computational Physics (1967) 2: 12-26.

[22] Ohwada T., Asinari P., Artificial Compressibility Method Revisited: Asymptotic Numerical Method for Incompressible Navier-Stokes Equations, Journal of Computational Physics (2010) 229: 1698-1723.

[23] Beskok A., Karniadakis G. E., Simulation of Heat and Momentum Transfer in Complex Micro –Geometries, Journal of  Thermophysics and Heat Transfer  (1994) 8:355 –370.

[24] Zhang T., Jia L., Yang L., Jaluria Y., Effect of Viscous Heating on Heat Transfer Performance in Microchannel Slip Fow Region, International Journal of Heat and Mass Transfer (2010) 53: 4927 –4934.

[25] Shojaeian M., Dibaji R., Three-Dimensional Numerical Simulation of the Slip Flow Through Triangular Microchannels, International Communications in Heat and Mass Transfer (2010) 37: 324-329.

[26] Harley J., Huang Y., Bau H., Zemel J. N., Gas Flows in Micro-Rohsenow W. M., and Choi  H. Y., 1961, Heat, Mass, and Momentum Transfer, Prentice-Hall, Englewood Cliffs, Chapter 11(1995).

[27] Dehnavi R., Rezvani A., Numerical Investigation of Natural Convection Heat Transfer of Nanofluids in a Γ Shaped Cavity, Superlattices and Microstructures (2012) 52:312–325