Soret and Dufour Effects on Double Diffusive Natural Convection in a Chamber Using Nanofluid

Page:

111-120

DOI:

https://doi.org/10.18280/ijht.300116

OPEN ACCESS

Abstract:

A study has been carried out to analyze the combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) coefficients and Schmidt number on natural convection in a partially heated square chamber. The working fluid is water based Al2O3 nanofluid. Energy and concentration equations take into account of Dufour and Soret effects respectively. The governing differential equations are transformed into a set of non-linear coupled ordinary differential equations and solved using similarity analysis with numerical technique using appropriate boundary conditions for various parameters. The numerical solution for the governing nonlinear boundary value problem is based on Penalty Finite Element Method using Galerkin’s weighted residual scheme over the entire range of relevant parameters. The variation of the dimensionless velocity, temperature and concentration profiles are depicted graphically and analyzed in detail. Favorable comparison with previously published work of the problem is obtained. Numerical results for average Nusselt and Sherwood numbers, average temperature and concentration and horizontal and vertical velocities at the middle of the chamber are presented as functions of the governing parameters mentioned above.

Keywords:

*soret and dufour coefficients, double-diffusive natural convection, finite element method, water-Al _{2}O_{3}, nanofluid.*

1. Introduction

2. Formulation of Problem

3. Numerical Procedure

4. Results and Discussion

5. Conclusion

References

[1] A. Bahloul, N. Boutana, P. Vasseur, Doublediffusive and Soret-induced convection in a shallow horizontal porous layer, J. Fluid Mech., vol. 491, pp. 325–352, 2003.

[2] N. Nithyadevi, R.J. Yang, Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects. Int. J. Heat and Fluid Flow, vol. 30, pp. 902–910, 2009.

[3] I. Sezai, A.A. Mohamad, Double diffusive convection in a cubic enclosure with opposing temperature and concentration gradients, Phys. Fluids, vol. 12, pp. 2210–2223, 2000.

[4] S. Sivasankaran, P. Kandaswamy, Double diffusive convection of water in a rectangular partitioned enclosure with temperature dependent species diffusivity, Int. J. Fluid Mech. Res., vol. 33, pp. 345–361, 2006.

[5] S. Sivasankaran, P. Kandaswamy, Double diffusive convection of water in a rectangular partitioned enclosure with concentration dependent species diffusivity, J. Korean Soc. Industrial Appl. Math., vol. 11, pp. 71–83, 2007.

[6] A. Mansour, A. Amahmid, M. Hasnaoui, M. Bourich, Multiplicity of solutions induced by thermosolutal convection in a square porous cavity heated from below and submitted to horizontal

concentration gradient in the presence of Soret effect, Num. Heat Trans., vol. 49, pp. 69–94, 2006.

[7] F. Joly, P. Vasseur, G. Labrosse, Soret-driven thermosolutal convection in a vertical enclosure, Int. Commun. Heat Mass Trans., vol. 27, pp. 755–764, 2000.

[8] J.K. Platten, The Soret effect: a review of recent experimental results, J. Appl. Mech., vol. 73, pp. 5–15, 2006.

[9] M.K. Patha, P.V.S.N. Murthy, G.P.R. Sekhar, Soret and Dufour effects in a non-darcy porous medium, J. Heat Trans., vol. 128, pp. 605–610, 2006.

[10] H.F. Oztop, Natural convection in partially cooled and inclined porous rectangular enclosures, Int. J. Thermal Sci., vol. 46, pp. 149–156, 2007.

[11] R.L. Frederick, F. Quiroz, On the transition from conduction to convection regime in a cubical enclosure with a partially heated wall, Int. J. Heat Mass Trans., vol. 44, pp. 1699–1709, 2001.

[12] B. Erbay, Z. Altac, B. Sulus, Entropy generation in a square enclosure with partial heating from a vertical lateral wall, Heat Mass Trans., vol. 40, pp. 909–918, 2004.

[13] N. Nithyadevi, P. Kandaswamy, S. Sivasankaran, Natural convection in a square cavity with partially active vertical walls: time periodic boundary condition, Math. Prob. Eng., pp.1–16, 2006.

[14] N. Nithyadevi, P. Kandaswamy, J. Lee, Natural convection in a rectangular cavity with partially active side walls, Int. J. Heat Mass Trans., vol. 50, pp. 4688– 4697, 2007.

[15] P. Kandaswamy, S. Sivasankaran, N. Nithyadevi, Buoyancy-driven convection of water near its density maximum with partially active vertical walls, Int. J. Heat Mass Trans., vol. 50, pp. 942–

948, 2007.

[16] H.F. Oztop, E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. of Heat and Fluid Flow, vol. 29, pp. 1326–1336, 2008.

[17] A. Rouboa, A. Silva, A.J. Freire, A. Borges, J. Ribeiro, P. Silva, J.L. Alexandre, Numerical analysis of convective heat transfer in nanofluid, AIP Conference Proceedings, 1048, pp. 819–822, 2008.

[18] J.A. Esfahani and V. Bordbar, Double Diffusive Natural Convection Heat Transfer Enhancement in a Square Enclosure Using Nanofluids, J. of Nanotechnology in Engg. and Medicine, vol. 2, no. 2, 021002, 2011, doi:10.1115/1.4003794.

[19] R.S.R. Gorla, A.J. Chamkha, A.M. Rashad, Mixed convective boundary layer flow over a vertical wedge embedded in a porous medium saturated with a nanofluid: Natural Convection Dominated Regime, Nanoscale Research Letters, vol. 6, pp. 207, 2011, doi:10.1186/1556-276X-6-207.

[20] A.V. Kuznetsov, D.A. Nield, Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. of Thermal Sciences, vol. 50, no. 5, pp. 712-717, 2011.

[21] D.A. Nield, A.V. Kuznetsov, The onset of doublediffusive convection in a nanofluid layer, Int. J. of Heat and Fluid Flow, vol. 32, no. 4, pp. 771-776, 2011.

[22] D A Nield, A V Kuznetsov, The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid, Int. J. of Heat and Mass Transfer 54, pp. 374–378, 2011.

[23] D. Pal, H. Mondal, Effects of SoretDufour, chemical reaction and thermal radiation on MHD non-Darcy unsteady mixed convective heat and mass transfer over a stretching sheet, Commu. in Nonlinear Science and Num. Simulation, vol. 16, no. 4, pp. 1942–1958, 2011.

[24] K.C. Lin, A. Violi, Natural convection heat transfer of nanofluids in a vertical cavity: Effects of nonuniform particle diameter and temperature on thermal conductivity, Int. J. of Heat and Fluid Flow, vol. 31, pp. 236–245, 2010.

[25] H. Saleh, R. Roslan, I. Hashim, Natural convection heat transfer in a nanofluid-filled trapezoidal enclosure, Int. J. of Heat and Mass Transfer, vol. 54, pp. 194–201, 2011.

[26] H.C. Brinkman, The viscosity of concentrated suspensions and solution, J. Chem. Phys., vol. 20, pp. 571–581, 1954.

[27] J.C. Maxwell-Garnett, Colours in metal glasses and in metallic films, Philos. Trans. Roy. Soc. A, vol. 203, pp. 385–420, 1904.

[28] C. Taylor, P. Hood, A numerical solution of the Navier-Stokes equations using finite element technique, Computer and Fluids, vol. 1, pp. 73–89, 1973.

[29] P. Dechaumphai, Finite Element Method in Engineering, 2nd ed., Chulalongkorn University Press, Bangkok, 1999.

[30] T. Basak, S. Roy, I. Pop, Heat flow analysis for natural convection within trapezoidal enclosures based on heatline concept, Int. J. Heat Mass Transfer, vol. 52, pp. 2471–2483, 2009.