Numerical Study of Natural Convection Heat Transfer of Nanofluid in a Square Shaped Porous Media using Lattice Boltzmann Method
Authors
Abstract
In this study, for the first time natural convection heat transfer of Al2O3-water nanofluid with constant and variable
properties is investigated within square shape porous media using the lattice Boltzmann method. The horizontal walls of the
cavity are insulated, and left and right vertical walls are hot and cold, respectively. The Study have been carried out for Rayleigh
numbers of 103, 104, 105, 106, Darcy numbers of 10-2, 10-4, porosity coefficients of 0.4, 0.6, 0.9 and solid volume fraction of 0, 0.01,
0.02 and 0.03. In order to consider the effect of porous media, Darcy-Forchheimer model is used. The results show that the presence of the porous media decreases the velocity of nanofluid and consequently decreases the strength of the flow. With decreasing Darcy number and porosity coefficient, natural convection heat transfer weakens and the mechanism of natural convection of nano-fluids tends to that of thermal conduction. With increasing Rayleigh number, the strength of flow in cavity and average Nusselt number increases. In all cases studied, increase in volume fraction improves heat transfer. In constant properties model, by increasing solid volume fraction, average Nusselt number increases more than that of variable properties model. The results show that Lattice Boltzmann method has the ability to simulate flow in porous media.
properties is investigated within square shape porous media using the lattice Boltzmann method. The horizontal walls of the
cavity are insulated, and left and right vertical walls are hot and cold, respectively. The Study have been carried out for Rayleigh
numbers of 103, 104, 105, 106, Darcy numbers of 10-2, 10-4, porosity coefficients of 0.4, 0.6, 0.9 and solid volume fraction of 0, 0.01,
0.02 and 0.03. In order to consider the effect of porous media, Darcy-Forchheimer model is used. The results show that the presence of the porous media decreases the velocity of nanofluid and consequently decreases the strength of the flow. With decreasing Darcy number and porosity coefficient, natural convection heat transfer weakens and the mechanism of natural convection of nano-fluids tends to that of thermal conduction. With increasing Rayleigh number, the strength of flow in cavity and average Nusselt number increases. In all cases studied, increase in volume fraction improves heat transfer. In constant properties model, by increasing solid volume fraction, average Nusselt number increases more than that of variable properties model. The results show that Lattice Boltzmann method has the ability to simulate flow in porous media.
1. De Vahl Davis, G., “Natural Convection of Air in a
Square Cavity a Bench Mark Numerical Solution”,
International Journal for Numerical Methods in
Fluids, Vol. 3, pp. 249-264, 1983.
2. Nithiarasu, P., Seetharamu, K., and Sundararajan, T.,
“Natural Convective Heat Transfer in a Fluid
Saturated Variable Porosity Medium”, International
Journal Heat and Mass Transfer, Vol. 40, pp. 3955-
3967, 1997.
3. Guo, Z., and Zhao, T., “Lattice Boltzmann Model for
Incompressible Flows through Porous Media”,
Physical Rewiew, Vol. 66, pp. 036304, 2002.
4. Seta, T., Takegoshi, E., and Okui, K., “Lattice
Boltzmann Simulation of Natural Convection in
Porous Media”, Mathematics and Computers in
Simulation, Vol. 72, pp. 195-200, 2006.
5. Shokouhmand, H., Jam, F., and Salimpour, M.,
“Simulation of Laminar flow and Convective Heat
Transfer in Conduits Filled with Porous Media Using
Lattice Boltzmann Method”, International
Communication in Heat and Mass Transfer, Vol. 36,
pp. 378-384, 2009.
6. Haghshenas, A., Rafatinasr, M., and Rahimian, M.,
“Numerical Simulation of Natural Convection in an
Open-ended Square Cavity Filled with Porous
Medium by Lattice Boltzamann Method”,
Intrernational Communications in Heat and Mass
Transfer, Vol. 37, pp. 1513-1519, 2010.
7. Lai, F., and Yang, Y., “Lattice Boltzmann Simulation
of Natural Convection Heat Transfer of Al2O3/Water
Nanofluids in a Squre Enclosure”, International
Journal of Thermal Sciences, Vol. 50, pp. 1930-
1941, 2011.
8. Liu, Q., He, Y., Li, Q., and Tao, W., “A Multiple-
Relaxation-Time Lattice Boltzmann Model for
Convection Heat Transfer in Porous Media”,
International Journal of Heat and Mass Transfer,
Vol. 73, pp. 761-775, 2014.
9. Neild, D., and Bejan, A., Convection in Porous
Media, 3rd Edition, Springer, 2006.
10. Irwan, M., and Azwadi, C., “Simplified Mesoscale
Lattice Boltzmann Numerical Model for Predication
of Natural Convection in a Square Enclosure Filled
with Homogeneous Porous Media”, Wseas
Transactions on Fluid Mechanics, Vol. 5, pp. 186-
195, 2010.
11. Maxwell, J., A Treatise on Electricity and Magnetism
Unabridged, Dover, 1954.
12. Sheikhzadeh, G., and Nazari, S., “Numerical Study
of Natural Convection in a Square Cavity Filled with
a Porous Medium Saturated with Nanofluid”,
Transport Phenomena in Nano and Micro Scale,
Vol. 1, pp. 138-146, 2013.
13. Incropera, F., Dewitt, D., Bergman, T., and Lavine,
A., Fundamentals of Heat and Mass Transfer, John
Wiley, 2011.
14. Brinkman, H., “The Viscosity of Concentrated
Suspensions and Solutions”, Journal of Chemical
Physics, Vol. 20, pp. 571-581, 1952.
15. Lai, F., and Yang, Y., “Lattice Boltzmann Simulation
of Natural Convection Heat Transfer of Al2O3/water
Nanofluids in a Squre Enclosure”, International
Journal of Thermal Sciences, Vol. 50, pp. 1930-
1941, 2011.
16.Guiet, J., Reggio, M., and Vasseur, P., “Natural
Convection of Nanofluids in Heated Enclosures
using the Lattice Boltzmann Method”,
Computational Thermal Sciences, Vol.3, 2011.
17. Mohamad, A., Lattice Boltzmann Method, Springer,
2011.
18. Rong, F., Guo, Z., Chai, Z., and Shi, B., “A Lattice
Boltzmann Model for Axisymmetric Thermal Flows
through Porous Media”, International Journal of
Heat and Mass Transfer, Vol. 53, pp. 5519-5527,
2010.
19.Hasanpour, A., Sedighi, K., and Farhadi, M., “Effect
of Porous Screen on Flow Stabilization and Heat
Transfer in a Channel using Variable Porosity Model
by the Lattice Boltzmann Method”, Turkish Journal
of Engineering and Environmental Sciences, Vol. 36,
pp. 45-58, 2012.
20. Bejan, A., Convection Heat Transfer, 3rd Edition,
John Wiley and Sons, 2004.
21. Sukop, M., and Thorne, D., Lattice Boltzmann
Modeling, Springer, 2005.
22. Lomaazzi, A., Lattice Boltzmann Method for three
Dimentional Fluid Flow Simulation, Anno
Accadmico, 2011.
23. Wolf-Gladrow, D., Lattice Gas Cellular Automata
and Lattice Boltzmann Models, Springer, 2000.
24. T. Bach, A Python Environment for Cellular and
Lattice Gas Automata, Boston University, 2005.
25. Irwan, M., Fudhail, A., Nor Azwadi, C., and Masoud,
G., “Numerical Investigation of Incompressible Fluid
Flow through Porous Media in a Lid Driven Square
Cavity”, American Journal of Applied Sciences,
Vol. 7, pp. 1341-1344, 2010.
26. Vafai, K., Hand Book of Porous Media, Taylor &
Francis, 2005.
Square Cavity a Bench Mark Numerical Solution”,
International Journal for Numerical Methods in
Fluids, Vol. 3, pp. 249-264, 1983.
2. Nithiarasu, P., Seetharamu, K., and Sundararajan, T.,
“Natural Convective Heat Transfer in a Fluid
Saturated Variable Porosity Medium”, International
Journal Heat and Mass Transfer, Vol. 40, pp. 3955-
3967, 1997.
3. Guo, Z., and Zhao, T., “Lattice Boltzmann Model for
Incompressible Flows through Porous Media”,
Physical Rewiew, Vol. 66, pp. 036304, 2002.
4. Seta, T., Takegoshi, E., and Okui, K., “Lattice
Boltzmann Simulation of Natural Convection in
Porous Media”, Mathematics and Computers in
Simulation, Vol. 72, pp. 195-200, 2006.
5. Shokouhmand, H., Jam, F., and Salimpour, M.,
“Simulation of Laminar flow and Convective Heat
Transfer in Conduits Filled with Porous Media Using
Lattice Boltzmann Method”, International
Communication in Heat and Mass Transfer, Vol. 36,
pp. 378-384, 2009.
6. Haghshenas, A., Rafatinasr, M., and Rahimian, M.,
“Numerical Simulation of Natural Convection in an
Open-ended Square Cavity Filled with Porous
Medium by Lattice Boltzamann Method”,
Intrernational Communications in Heat and Mass
Transfer, Vol. 37, pp. 1513-1519, 2010.
7. Lai, F., and Yang, Y., “Lattice Boltzmann Simulation
of Natural Convection Heat Transfer of Al2O3/Water
Nanofluids in a Squre Enclosure”, International
Journal of Thermal Sciences, Vol. 50, pp. 1930-
1941, 2011.
8. Liu, Q., He, Y., Li, Q., and Tao, W., “A Multiple-
Relaxation-Time Lattice Boltzmann Model for
Convection Heat Transfer in Porous Media”,
International Journal of Heat and Mass Transfer,
Vol. 73, pp. 761-775, 2014.
9. Neild, D., and Bejan, A., Convection in Porous
Media, 3rd Edition, Springer, 2006.
10. Irwan, M., and Azwadi, C., “Simplified Mesoscale
Lattice Boltzmann Numerical Model for Predication
of Natural Convection in a Square Enclosure Filled
with Homogeneous Porous Media”, Wseas
Transactions on Fluid Mechanics, Vol. 5, pp. 186-
195, 2010.
11. Maxwell, J., A Treatise on Electricity and Magnetism
Unabridged, Dover, 1954.
12. Sheikhzadeh, G., and Nazari, S., “Numerical Study
of Natural Convection in a Square Cavity Filled with
a Porous Medium Saturated with Nanofluid”,
Transport Phenomena in Nano and Micro Scale,
Vol. 1, pp. 138-146, 2013.
13. Incropera, F., Dewitt, D., Bergman, T., and Lavine,
A., Fundamentals of Heat and Mass Transfer, John
Wiley, 2011.
14. Brinkman, H., “The Viscosity of Concentrated
Suspensions and Solutions”, Journal of Chemical
Physics, Vol. 20, pp. 571-581, 1952.
15. Lai, F., and Yang, Y., “Lattice Boltzmann Simulation
of Natural Convection Heat Transfer of Al2O3/water
Nanofluids in a Squre Enclosure”, International
Journal of Thermal Sciences, Vol. 50, pp. 1930-
1941, 2011.
16.Guiet, J., Reggio, M., and Vasseur, P., “Natural
Convection of Nanofluids in Heated Enclosures
using the Lattice Boltzmann Method”,
Computational Thermal Sciences, Vol.3, 2011.
17. Mohamad, A., Lattice Boltzmann Method, Springer,
2011.
18. Rong, F., Guo, Z., Chai, Z., and Shi, B., “A Lattice
Boltzmann Model for Axisymmetric Thermal Flows
through Porous Media”, International Journal of
Heat and Mass Transfer, Vol. 53, pp. 5519-5527,
2010.
19.Hasanpour, A., Sedighi, K., and Farhadi, M., “Effect
of Porous Screen on Flow Stabilization and Heat
Transfer in a Channel using Variable Porosity Model
by the Lattice Boltzmann Method”, Turkish Journal
of Engineering and Environmental Sciences, Vol. 36,
pp. 45-58, 2012.
20. Bejan, A., Convection Heat Transfer, 3rd Edition,
John Wiley and Sons, 2004.
21. Sukop, M., and Thorne, D., Lattice Boltzmann
Modeling, Springer, 2005.
22. Lomaazzi, A., Lattice Boltzmann Method for three
Dimentional Fluid Flow Simulation, Anno
Accadmico, 2011.
23. Wolf-Gladrow, D., Lattice Gas Cellular Automata
and Lattice Boltzmann Models, Springer, 2000.
24. T. Bach, A Python Environment for Cellular and
Lattice Gas Automata, Boston University, 2005.
25. Irwan, M., Fudhail, A., Nor Azwadi, C., and Masoud,
G., “Numerical Investigation of Incompressible Fluid
Flow through Porous Media in a Lid Driven Square
Cavity”, American Journal of Applied Sciences,
Vol. 7, pp. 1341-1344, 2010.
26. Vafai, K., Hand Book of Porous Media, Taylor &
Francis, 2005.
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