Mixed Convection Heat Transfer for Nanofluids in a Lid-Driven Shallow Rectangular Cavity Uniformly Heated and Cooled from the Vertical Sides: The Opposing Case

Affiliation(s)

Physics Department, Faculty of Sciences and Technologies, Sultan Moulay Slimane University, Laboratory of Flows and Transfers Modelling (LAMET), Beni-Mellal, Morocco.

Polydisciplinary Faculty, Sultan Moulay Slimane University, Interdisciplinary Laboratory of Research in Sciences and Technologies (LIRST), Beni-Mellal, Morocco.

Physics Department, Faculty of Sciences Semlalia, Cadi Ayyad University, Laboratory of Fluid Mechanics and Energetics (LMFE), Marrakech, Morocco.

Physics Department, Faculty of Sciences and Technologies, Sultan Moulay Slimane University, Laboratory of Flows and Transfers Modelling (LAMET), Beni-Mellal, Morocco.

Polydisciplinary Faculty, Sultan Moulay Slimane University, Interdisciplinary Laboratory of Research in Sciences and Technologies (LIRST), Beni-Mellal, Morocco.

Physics Department, Faculty of Sciences Semlalia, Cadi Ayyad University, Laboratory of Fluid Mechanics and Energetics (LMFE), Marrakech, Morocco.

ABSTRACT

An investigation on flow and heat transfer due to mixed convection,
in a lid-driven rectangular cavity filled with *Cu*- water nanofluids and submitted to uniform heat flux along with its
vertical short sides, has been conducted numerically by solving the full
governing equations with the finite volume method and the SIMPLER algorithm. In
the case of a slender enclosure, these equations are considerably reduced by
using the parallel flow concept. Solutions, for the flow and temperature
fields, and the heat transfer rate, have been obtained depending on the
governing parameters, which are the Reynolds, the *Cu*-nanoparticles, into the pure water,
has been seen enhancing and degrading heat transfer by lid and buoyancy-driven
effects, respectively.

Cite this paper

Harfi, H. , Naïmi, M. , Lamsaadi, M. , Raji, A. and Hasnaoui, M. (2013) Mixed Convection Heat Transfer for Nanofluids in a Lid-Driven Shallow Rectangular Cavity Uniformly Heated and Cooled from the Vertical Sides: The Opposing Case.*Journal of Electronics Cooling and Thermal Control*, **3**, 111-130. doi: 10.4236/jectc.2013.33013.

Harfi, H. , Naïmi, M. , Lamsaadi, M. , Raji, A. and Hasnaoui, M. (2013) Mixed Convection Heat Transfer for Nanofluids in a Lid-Driven Shallow Rectangular Cavity Uniformly Heated and Cooled from the Vertical Sides: The Opposing Case.

References

[1] S. U. S. Choi, “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” In: D. A. Siginer and H. P. Wang, Eds., Developments and Applications of Non-Newtonian Flows, American Society of Mechanical Engineers, New York, 1995, pp. 99-105.

[2] W. Yu, D. M. France, S. U. S. Choi and J. L. Routbort, “Review and Assessment of Nanofluid Technology for Transportation and Other Applications,” Technical Report ANL/ESD/07-9, Argonne National Laboratory, Energy Systems Division, Argonne, 2007. http://www.osti.gov/bridge

[3] M. Corcione, “Heat Transfer Features of Buoyancy- Driven Nanofluids inside Rectangular Enclosures Differentially Heated at the Sidewalls,” International Journal of Thermal Sciences, Vol. 49, No. 9, 2010, pp. 1536-1546. doi:10.1016/j.ijthermalsci.2010.05.005

[4] L. A. B. Pilkington, “Review Lecture. The Float Glass Process,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 314, No. 1516, 1969, pp. 1-25. doi:10.1098/rspa.1969.0212

[5] F. J. K Ideriah, “Prediction of Turbulent Cavity Flow Driven by Buoyancy and Shear,” Journal of Mechanical Engineering Sciences, Vol. 22, No. 6, 1980, pp. 287-295. doi:10.1243/JMES_JOUR_1980_022_054_02

[6] J. Imberger and P. F. Hamblin, “Dynamics of Lakes, Reservoirs, and Cooling Ponds,” Annual Review of Fluid Mechanics, Vol. 14, 1982, pp. 153-187. doi:10.1146/annurev.fl.14.010182.001101

[7] C. K. Cha and Y. Jaluria, “Recirculating Mixed Convection Flow for Energy Extraction,” International Journal of Heat Mass Transfer, Vol. 27, No. 10, 1984, pp. 1801-1810. doi:10.1016/0017-9310(84)90162-5

[8] R. K. Tiwari and M. K. Das, “Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 50, No. 9-10, 2007, pp. 2002-2018. doi:10.1016/j.ijheatmasstransfer.2006.09.034

[9] E. Abu-Nada and A. J. Chamkha, “Mixed Convection Flow in a Lid-Driven Square Enclosure Filled with a Nanofluid,” European Journal of Mechanic B/Fluids, Vol. 29, No. 6, 2010, pp. 472-482. doi:10.1016/j.euromechflu.2010.06.008

[10] M. Mahmoodi, “Mixed Convection inside Nanofluid Filled Rectangular Enclosures with Moving Bottom Wall,” International Journal of Thermal Sciences, Vol. 15, No. 3, 2011, pp. 889-903. doi:10.2298/TSCI101129030M

[11] M. A. Mansour, R. A. Mohamed, M. M. Abd-Elaziz and S. E. Ahmed, “Numerical Simulation of Mixed Convection Flows in a Square Lid-Driven Cavity Partially Heated from below Using Nanofluid,” International Communication in Heat and Mass Transfer, Vol. 37, No. 10, 2010, pp. 1504-1512. doi:10.1016/j.icheatmasstransfer.2010.09.004

[12] M. Muthtamilselvan, P. Kandaswamy and J. Lee, “Heat Transfer Enhancement of Copper-Water Nanofluids in a Lid-Driven Enclosure,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 6, 2010, pp. 1501-1510. doi:10.1016/j.cnsns.2009.06.015

[13] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi and A. A. R. Darzi, “Lattice Boltzmann Simulation of Nanofluid in Lid-Driven Cavity,” International Communication in Heat and Mass Transfer, Vol. 37, No. 10, 2010, pp. 1528- 1534. doi:10.1016/j.icheatmasstransfer.2010.08.004

[14] F. Talebi, A. H. Mahmoudi and M. Shahi, “Numerical Study of Mixed Convection Flows in a Square Lid- Driven Cavity Utilizing Nanofluid,” International Communication in Heat and Mass Transfer, Vol. 37, No. 1, 2010, pp. 79-90. doi:10.1016/j.icheatmasstransfer.2009.08.013

[15] G. A. Sheikhzadeh, N. Hajialigol, M. E. Qomi and A. Fattahi, “Laminar Mixed Convection of Cu-Water Nano- fluid in Two Sided Lid-Driven Enclosures,” Journal of Nanostructures, Vol. 1, No. 1, 2012, pp. 44-53.

[16] M. A. Karimipour and M. M. Bazofti, “Periodic Mixed Convection of a Nanofluid in a Cavity with Top Lid Sinusoidal Motion,” International Journal of Mechanical and Materials Engineering, Vol. 1, No. 1, 2010, pp. 34- 39.

[17] Y. Xuan and W. Roetzel, “Conceptions for Heat Transfer Correlation of Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 43, No. 19, 2000, pp. 3701-3707. doi:10.1016/S0017-9310(99)00369-5

[18] E. B. Ogut, “Natural Convection of Water-Based Nano- fluids in an Inclined Enclosure with a Heat Source,” International Journal of Thermal Sciences, Vol. 48, No. 11, 2009, pp. 2063-2073. doi:10.1016/j.ijthermalsci.2009.03.014

[19] M. Lamsaadi, M. Naimi and M. Hasnaoui, “Natural Convection Heat Transfer in Shallow Horizontal Rectangular Enclosures Uniformly Heated from the Side and Filled with Non-Newtonian Power Law Fluids,” Energy Conversion and Management, Vol. 47, No. 15-16, 2006, pp. 2535-2551. doi:10.1016/j.enconman.2005.10.028

[20] S. Patankar, “Numerical Heat Transfer and Fluid Flow,” Hemisphere, Washington DC, 1980.

[21] A. Bejan, “The Boundary Layer Regime in a Porous Layer with Uniform Heat Flux from Side,” International Journal of Heat Mass Transfer, Vol. 26, No. 9, 1983, pp. 1339-1346. doi:10.1016/S0017-9310(83)80065-9

[22] E. Abu-Nada, Z. Masoud and A. Hijazi, “Natural Convection Heat Transfer Enhancement in Horizontal Concentric Annuli Using Nano?uids,” International Communication in Heat and Mass Transfer, Vol. 35, No. 5, 2008, pp. 657-665. doi:10.1016/j.icheatmasstransfer.2007.11.004

[1] S. U. S. Choi, “Enhancing Thermal Conductivity of Fluids with Nanoparticles,” In: D. A. Siginer and H. P. Wang, Eds., Developments and Applications of Non-Newtonian Flows, American Society of Mechanical Engineers, New York, 1995, pp. 99-105.

[2] W. Yu, D. M. France, S. U. S. Choi and J. L. Routbort, “Review and Assessment of Nanofluid Technology for Transportation and Other Applications,” Technical Report ANL/ESD/07-9, Argonne National Laboratory, Energy Systems Division, Argonne, 2007. http://www.osti.gov/bridge

[3] M. Corcione, “Heat Transfer Features of Buoyancy- Driven Nanofluids inside Rectangular Enclosures Differentially Heated at the Sidewalls,” International Journal of Thermal Sciences, Vol. 49, No. 9, 2010, pp. 1536-1546. doi:10.1016/j.ijthermalsci.2010.05.005

[4] L. A. B. Pilkington, “Review Lecture. The Float Glass Process,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 314, No. 1516, 1969, pp. 1-25. doi:10.1098/rspa.1969.0212

[5] F. J. K Ideriah, “Prediction of Turbulent Cavity Flow Driven by Buoyancy and Shear,” Journal of Mechanical Engineering Sciences, Vol. 22, No. 6, 1980, pp. 287-295. doi:10.1243/JMES_JOUR_1980_022_054_02

[6] J. Imberger and P. F. Hamblin, “Dynamics of Lakes, Reservoirs, and Cooling Ponds,” Annual Review of Fluid Mechanics, Vol. 14, 1982, pp. 153-187. doi:10.1146/annurev.fl.14.010182.001101

[7] C. K. Cha and Y. Jaluria, “Recirculating Mixed Convection Flow for Energy Extraction,” International Journal of Heat Mass Transfer, Vol. 27, No. 10, 1984, pp. 1801-1810. doi:10.1016/0017-9310(84)90162-5

[8] R. K. Tiwari and M. K. Das, “Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 50, No. 9-10, 2007, pp. 2002-2018. doi:10.1016/j.ijheatmasstransfer.2006.09.034

[9] E. Abu-Nada and A. J. Chamkha, “Mixed Convection Flow in a Lid-Driven Square Enclosure Filled with a Nanofluid,” European Journal of Mechanic B/Fluids, Vol. 29, No. 6, 2010, pp. 472-482. doi:10.1016/j.euromechflu.2010.06.008

[10] M. Mahmoodi, “Mixed Convection inside Nanofluid Filled Rectangular Enclosures with Moving Bottom Wall,” International Journal of Thermal Sciences, Vol. 15, No. 3, 2011, pp. 889-903. doi:10.2298/TSCI101129030M

[11] M. A. Mansour, R. A. Mohamed, M. M. Abd-Elaziz and S. E. Ahmed, “Numerical Simulation of Mixed Convection Flows in a Square Lid-Driven Cavity Partially Heated from below Using Nanofluid,” International Communication in Heat and Mass Transfer, Vol. 37, No. 10, 2010, pp. 1504-1512. doi:10.1016/j.icheatmasstransfer.2010.09.004

[12] M. Muthtamilselvan, P. Kandaswamy and J. Lee, “Heat Transfer Enhancement of Copper-Water Nanofluids in a Lid-Driven Enclosure,” Communications in Nonlinear Science and Numerical Simulation, Vol. 15, No. 6, 2010, pp. 1501-1510. doi:10.1016/j.cnsns.2009.06.015

[13] H. Nemati, M. Farhadi, K. Sedighi, E. Fattahi and A. A. R. Darzi, “Lattice Boltzmann Simulation of Nanofluid in Lid-Driven Cavity,” International Communication in Heat and Mass Transfer, Vol. 37, No. 10, 2010, pp. 1528- 1534. doi:10.1016/j.icheatmasstransfer.2010.08.004

[14] F. Talebi, A. H. Mahmoudi and M. Shahi, “Numerical Study of Mixed Convection Flows in a Square Lid- Driven Cavity Utilizing Nanofluid,” International Communication in Heat and Mass Transfer, Vol. 37, No. 1, 2010, pp. 79-90. doi:10.1016/j.icheatmasstransfer.2009.08.013

[15] G. A. Sheikhzadeh, N. Hajialigol, M. E. Qomi and A. Fattahi, “Laminar Mixed Convection of Cu-Water Nano- fluid in Two Sided Lid-Driven Enclosures,” Journal of Nanostructures, Vol. 1, No. 1, 2012, pp. 44-53.

[16] M. A. Karimipour and M. M. Bazofti, “Periodic Mixed Convection of a Nanofluid in a Cavity with Top Lid Sinusoidal Motion,” International Journal of Mechanical and Materials Engineering, Vol. 1, No. 1, 2010, pp. 34- 39.

[17] Y. Xuan and W. Roetzel, “Conceptions for Heat Transfer Correlation of Nanofluids,” International Journal of Heat and Mass Transfer, Vol. 43, No. 19, 2000, pp. 3701-3707. doi:10.1016/S0017-9310(99)00369-5

[18] E. B. Ogut, “Natural Convection of Water-Based Nano- fluids in an Inclined Enclosure with a Heat Source,” International Journal of Thermal Sciences, Vol. 48, No. 11, 2009, pp. 2063-2073. doi:10.1016/j.ijthermalsci.2009.03.014

[19] M. Lamsaadi, M. Naimi and M. Hasnaoui, “Natural Convection Heat Transfer in Shallow Horizontal Rectangular Enclosures Uniformly Heated from the Side and Filled with Non-Newtonian Power Law Fluids,” Energy Conversion and Management, Vol. 47, No. 15-16, 2006, pp. 2535-2551. doi:10.1016/j.enconman.2005.10.028

[20] S. Patankar, “Numerical Heat Transfer and Fluid Flow,” Hemisphere, Washington DC, 1980.

[21] A. Bejan, “The Boundary Layer Regime in a Porous Layer with Uniform Heat Flux from Side,” International Journal of Heat Mass Transfer, Vol. 26, No. 9, 1983, pp. 1339-1346. doi:10.1016/S0017-9310(83)80065-9

[22] E. Abu-Nada, Z. Masoud and A. Hijazi, “Natural Convection Heat Transfer Enhancement in Horizontal Concentric Annuli Using Nano?uids,” International Communication in Heat and Mass Transfer, Vol. 35, No. 5, 2008, pp. 657-665. doi:10.1016/j.icheatmasstransfer.2007.11.004