Numerical Study of Natural Convection in a Square Cavity Filled with a Porous Medium Saturated with Nanofluid

Document Type: Original Research Paper

Authors

Department of Mechanical Engineering, University of Kashan, Iran

Abstract

Steady state natural convection of Al2O3-water nanofluid inside a square cavity filled with a porous medium is investigated numerically. The temperatures of the two side walls of the cavity are maintained at TH and TC, where TC has been considered as the reference condition. The top and the bottom horizontal walls have been considered to be insulated i.e., non-conducting and impermeable to mass transfer. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The transport equations are solved numerically with finite volume approach using SIMPLER algorithm. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number, Ra, 104≤ Ra≤ 106, Darcy number, Da, 10-5≤ Da ≤ 10-3, and solid volume fraction, j, 0.0 ≤ j ≤ 0.1). Numerical results are presented in terms of streamlines, isotherms and average Nusselt number. It was found that heat transfer increases with increasing of both Rayleigh number and Darcy number. It is further observed that the heat transfer in the cavity is improved with the increasing of solid volume fraction parameter of nanofluids.

Keywords


[1] I.Pop, D. Ingham, Convective Heat Transfer:Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon 2001.

[2] A. Bejan, I. Dincer, S. Lorente, A.F. Miguel, A.H.Reis, Porous and Complex Flow Structures in Modern Technologies, Springer, New York 2004.

[3] K. Vafai, Handbook of Porous Media. Taylor & Francis, New York 2005.

[4] K. Vafai, Porous Media: Applications in BiologicalSystems and Biotechnology, CRC Press, New York 2010.

[5] P.Vadasz, Emerging Topics in Heat and MassTransfer in Porous Media, Springer, New York 2008.

[6] Y. Varol, H.F. Oztop, I. Pop, Natural convection inporous media-filled triangular enclosure with aconducting thin J. Mech, fin on the hot vertical wall, Eng. Sci, 222, (2008) 1735-1743.

[7] Y. Varol, H.F. Oztop, I. Pop, Numerical analysis ofnatural convection for a porous rectangular enclosurewith sinusoidally varying temperature profile on thebottom wall. International Communications in Heatand Mass Transfer, 35(2008) 56-64.

[8] T. Basak, S. Roy, D. Ramakrishna, I. Pop, Visualization of heat transport due to natural convection for hotmaterials confined within two entrapped poroustriangular cavities via heatline concept, Int. J. HeatMass Transf 53 (2010) 2100-2112.

[9] T. Basak, S. RoyRamakrishna, I. Pop,Visualization of heat transport during natural convection within poroustriangular cavities via heatline approach, Numerical Heat Transfer 57(2010) 431-452.

[10] T. Basak, S. Roy, T. Paul, I. Pop, Natural convection ina square cavity filled with a porous medium: Effects ofvarious thermal boundary conditions, Int. J. Heat Mass Transf 49(2006) 1430-1441.

[11] T. Basak, S. Roy, A.J. Chamkha, A Peclet numberbased analysis of mixed convection for lid-drivenporous square cavities with various heating of bottomwall, International Communications in Heat and MassTransfer, 39(2012) 657-664.

[12] S.U.S. Choi, Enhancing thermal conductivity of fluidswith nanoparticles, Int. Mech. Engng. Congress and Exposition San Franciscos, USA, 66(1995) 99-105.

[13] A. Akbarinia, Impacts of nanofluid flow on skinfriction factor and Nusselt number in curved tubes with constant mass flow, International Journal of Heat and Fluid Flow 29( 2008) 229-241.

[14] A. Akbarinia, A. Behzadmehr, Numerical study of laminar mixed convection of a nanofluid in horizontal curved tubes, Applied Thermal Engineering 27(2007)1327-1337.

[15] K. Khanafer, K.Vafai, M.Lightstone, Buoyancy-Drivenheat transfer enhancement in a two dimensional enclosure utilizing nanofluid, International Journal ofHeat and Mass Transfer 46 (2003) 3639-3653.

[16] A. Bejan, Convection heat transfer. John Wiley &Sons, Inc., Hoboken, New Jersey, USA 2004.

[17] H.C.Brinkman,The viscosity of concentratedsuspensions and solutions, Journal of Chemical Physics 20 (1952) 571–581.

[18] H.E. Patel, T. Sundarrajan, T. Pradeep, A. Dasgupta,N.Dasgupta, S.K.Das, A micro-convection model forthermal conductivity of nanofluid, Pramana journal ofphysics 65(2005) 863–869.

[19] Y. Xuan, Q. Li, Heat transfer enhancement ofnanofluids,International Journal of Heat and FluidFlow 21(2000) 58–64.

[20] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Taylor and Francis Group, New York 1980.