Effects of Slip Boundaries on Mixed Convection of Al2O3-water Nanofluid in Microcavity


Department of Mechanical Engineering, University of Kashan, Iran


Due to the importance of the slip effect on modeling of microchannel and microcavity, numerical investigations have been introduced in this work for studying the mixed convection of Al2O3-water nanofluid in a square microcavity. Governing equations are discretized and solved using the Finite Volume Method and SIMPLER algorithm. The Knudsen number is selected between 0.001 and 0.1 to consider slip velocity and the temperature jump boundary conditions in slip flow regime. In this study we investigate the influence of the Knudsen number on the average Nusselt number and heat transfer rate of Al2O3-water nanofluid. Results shows that the average Nusselt number is the function of Richardson number, Knudsen number and volume fraction of nanoparticles. Increasing the Richardson number, makes the forced convection less effective and leads in reduction of the Nusselt number. Hence, increasing the Knudsen number, leads to the temperature gradient reduction and reducing the average Nusselt number. As a result, the average Nusselt number could be enhanced up to 10.93% by using nanoparticles in the base fluid.


[1]      Beskok, A., Karniadakis, “Microflows Fundamentals and Simulation”, Springer, USA, 2001.

[2]      Muneer, A. Ismael, Ioan, Pop, and Ali, J., Chamkha, “Mixed convection in a lid-driven square cavity with partial slip”, International Journal of Thermal Sciences, Vol. 82, 2014, pp. 47-61.

[3]      Trisaksri, V., Wongwises, S., “Critical review of heat transfercharacteristics of nanofluids”, Renewable and Sustainable Energy Reviews, Vol. 11, No. 3, 2007, pp. 512-523.

[4]       Ozerinc, S., Kakac, S. and YazIcIoglu, A.G., “Enhanced thermal conductivity of nanofluid: a state-of-the-art review”, Microfluidics and Nanofluidics, Vol. 8, No. 2, 2010, pp. 145-170.

[5]      Wang, X. Q, Mujumdar, A. S, “Heat transfer characteristics of nanofluids: a review”, International Journal of Thermal Sciences, Vol. 46, No. 1, 2007, pp. 1–19.

[6]      Wang, X. Q., Mujumdar, A. S., “A review on nanofluids— part I: theoretical and numerical investigations”, Brazilian Journal of Chemical Engineering, Vol. 25, No. 4, 2008, pp. 613- 630.

[7]       Li Y, Zhou J, Tung S, Schneider E, Xi S, “A review on development of nanofluid preparation and characterization”, Powder Technology, Vol. 196, No. 2, 2009, pp. 89-101.

[8]       Kakac, S.¸ Pramuanjaroenkij, A., “Review of convective heat transfer enhancement with nanofluids”, International Journal of Heat and Mass Transfer, Vol. 52, No. 13-14, 2009,  pp. 3187-3196.

[9]      Talebi, F., Mahmoudi, A. H., and Shahi, M., “Numerical study of mixed convection flows in a square lid-driven cavity utilizing nanofluid”, International Communications in Heat and Mass Transfer, Vol. 37, 2010, pp. 79-90.

[10]   Kandlikar, Satish G., “Heat transfer and fluid flow in minichannels and microchannels”, Elsevier, 2006.

[11]   Kuddusi, L., Cetegen, E., “Predication of temperature distribution and Nuseelt number in rectangular microchannelsat wall slip condition for all version of constant heat flux”, International Journal of Heat and Fluid Flow, Vol. 28, pp. 777-786.

[12]    Renksizbulut, M., Niazmand, H., and Tercan, G., “Slip-flow and heat transfer in rectangular microchannel with constant wall temperature”, International Journal of Thermal Sciences, Vol. 45, 2006, pp. 870-881.

[13]   Mizzi, S., Emerson, D. R., Stefanov, S., Barbery, R.W., and Reese, J. M., “Micro-scale cavities in the slip and Transition flow regimes”, European Conference on Computational Fluid Dynamics, Netherlands, 2006.

[14]   Hettiarachchi, M., Golubovic, M., Worek, W. M., and Minkowycz, W. J., “Three dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature”, International Journal of Heat and Mass Transfer, Vol. 51, 2008, pp. 5088-5096.

[15]   Perumal, D. A., Krishna, V., Sarvesh, G., and Dass, A. K., “Numerical simulation of gaseous microflows by lattice boltzmann method”, International Journal of Recent Trends in Engineering, Vol. 1, No. 5,  2009.

[16]   Kuo, L. S., Chou, W. P., and Chen, P. H., “Effects of slip boundaries on thermal convection in 2D box using lattice Boltzmann method”, International Journal of Heat and Mass Transfer, Vol. 54, 2011, pp. 1340-1343.

[17]    Liu, X., Guoa, Zh., “Lattice Boltzmann study of gas flows in a long micro-channel”, Computers and Mathematics with Applications, Vol. 65, 2013, pp. 186-193.

[18]   Babaie, A., Saidi, M. H., and Sadeghi, A., “Heat transfer characteristics of mixed electroosmotic and pressure driven flow of power-law fluids in a slit microchannel”, International Journal of Thermal Sciences, Vol. 53, 2012, pp. 71-79.

[19]   Shojaeian, M., Dibaji, S. A. R., “Three-dimensional numerical simulation of the slip flow through triangular microchannels”, International Communications in Heat and Mass Transfer, Vol. 37, 2010, pp. 324-329.

[20]   Shojaeian, M., Kosar, A., “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, Vol. 70, 2014, 664-673.

[21]   Shetab Bushehri, M. R., Ramin, H., and Salimpour, M. R., “A new coupling method for slip-flow and conjugate heat transfer in a parallel plate micro heat sink”, International Journal of Thermal Sciences, Vol. 89, 2015, pp. 174- 184.

[22]   Alloui, Z., Vasseur, P., and Reggio, M., “Natural convection of nanofluids in a shallow cavity heated from below”, International Journal of Thermal Sciences, Vol. 50, 2010, pp. 1-9.

[23]   Pak, B. C., Cho, Y. I., “Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particle”, Exp. Heat Transfer, Vol. 11, 1999, pp. 151-170.

[24]   Hwang, K. S., Lee, J. H., and Jang, S. P., “Buoyancy-driven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity”, International Journal of Heat and Mass Transfer, Vol. 50, 2007, pp. 4003-4010.

[25]   Maxwell, J., “A Treatise on Electricity and Magnetism”, Second ed, Oxford University Press, Cambridge, UK, 1904.

[26]   Brinkman, H. C., “The viscosity of concentrated suspensions and solutions”. Journal of Chemical Physics, Vol. 20, 1952, pp. 571-581.

[27]    Karniadakis, G., Beskok, A., Aluru, N., “Microflows and Nanoflows, Fundamentals and Simulation”, Springer, USA, 2005.

[28]   Abu-Nada, E., Chamkha, A. J., “Mixed convection flow in a lid driven square enclosure filled with a nanofluid”, European Journal of Mechanics B/Fluids, Vol. 29, 2010, pp. 472-482.

[29]   Liu, Zh. Q., Jiang, S. R., Tamar, A., Yinnon, Mu, X. M., Kong, and Li, Y. J., “Effects of interfaces on dynamics in micro-fluidic devices slip-boundaries’ impact on rotation characteristics of polar liquid film motors”, ar Xiv: 1404.5136v1 [cond-mat.soft].

[30]   Aparajita, A., Satapathy, A. K., “Numeical analysis heat transfer characteristic of combined electroosmotic and pressure-driven fully developed flow of power law nanofluid in microchannels”, Proceedings of the 3rd European Conference on Microfluidics - Microfluidics 2012.

[31]   Aly, E. H., Ebaid, A., and Abd Elazem, N. Y., “Analytical and Numerical Investigations for the Flow and Heat Transfer of Nanofluids over a Stretching Sheet with Partial Slip Boundary Condition”, Applied Mathematics and Information Sciences, Vol. 8, No. 4, 2014, pp. 1639-1645.