J. Kramer | J. Ravnik | R. Jecl | L. Škerget
OPEN ACCESS
A three-dimensional double-diffusive natural convection with opposing buoyancy effects in a cubic enclosure filled with fluid saturated porous media is studied numerically using the boundary element method (BEM). The mathematical model is based on the space-averaged Navier–Stokes equations, which are coupled with the energy and species equations. The simulation of coupled laminar viscous flow, heat and solute transfer is performed using a combination of single-domain BEM and subdomain BEM, which solves the velocity-vorticity formulation of governing equations. The numerical simulations for a case of negative values of buoyancy coefficient are presented, focusing on the situations where the flow field becomes three-dimensional. The results are analyzed in terms of the average heat and mass transfer at the walls of the enclosure. When possible, the results are compared with previous existing numerical data published in literature.
boundary element method, Brinkman-extended Darcy formulation, porous media, velocity-vorticity formulation, three-dimensional double-diffusive natural convection
[1] Nield, D.A., & Bejan, A., Convection in Porous Media, (3rd edn., Springer, 2006.
[2] Vafai, K., Handbook of Porous Media. Taylor & Francis, 2005. doi: http://dx.doi.org/10.1201/9780415876384
[3] Bejan, A. & Khair, K.R., Heat and mass transfer by natural convection in a porousmedium. International Journal of Heat and Mass Transfer, 28, pp. 909–918, 1985. doi:http://dx.doi.org/10.1016/0017-9310(85)90272-8
[4] Trevisan, O.V. & Bejan, A., Natural convection with combined heat and mass transferbuoyancy effects in a porous medium. International Journal of Heat and Mass Transfer,28, pp. 1597–1611, 1985. doi: http://dx.doi.org/10.1016/0017-9310(85)90261-3
[5] Trevisan, O.V. & Bejan, A., Mass and heat transfer by natural convection in a verticalslot fi lled with porous medium. International Journal of Heat and Mass Transfer, 29,pp. 403–415, 1986. doi: http://dx.doi.org/10.1016/0017-9310(86)90210-3
[6] Trevisan, O.V. & Bejan, A., Combined heat and mass transfer by natural convection ina porous medium. Advances in Heat Transfer, 20, pp. 315–348, 1990. doi: http://dx.doi.org/10.1016/S0065-2717(08)70029-7
[7] Alavyoon, F., On natural convection in vertical porous enclosures due to prescribedfl uxes of heat and mass at the vertical boundaries. International Journal of Heatand Mass Transfer, 36, pp. 2479–2498, 1993. doi: http://dx.doi.org/10.1016/S0017-9310(05)80188-7
[8] Mamou, M., Vasseur, P. & Bilgen, E., Multiple solutions for double diffusive convectionin a vertical porous enclosure. International Journal of Heat and Mass Transfer, 38,pp. 1787–1798, 1995. doi: http://dx.doi.org/10.1016/0017-9310(94)00301-B
[9] Goyeau, B., Songbe, J.-P. & Gobin, D., Numerical study of double-diffusive naturalconvection in a porous cavity using the darcy-brinkman formulation. InternationalJournal of Heat and Mass Transfer, 39, pp. 1363–1378, 1996. doi: http://dx.doi.org/10.1016/0017-9310(95)00225-1
[10] Nithiarasu, P., Seetharamu, K. N. & Sundararajan, T., Double-diffusive naturalconvection in an enclosure fi lled with fl uid-saturated porous medium: a generalizednon-darcy approach. Numerical Heat Transfer, 30, pp. 413–426, 1996. doi: http://dx.doi.org/10.1080/10407789608913848
[11] Alavyoon, F., Masuda, Y. & Kimura, S., On natural convection in vertical porousenclosures due to opposing fl uxes of heat and mass prescribed at the vertical walls.International Journal of Heat and Mass Transfer 37, pp. 195–206, 1994. doi: http://dx.doi.org/10.1016/0017-9310(94)90092-2
[12] Angirasa, D., Peterson, G.P. & Pop, I., Combined heat and mass transfer by naturalconvection with opposing buoyancy effects in a fl uid saturated porous medium.International Journal of Heat and Mass Transfer, 40, pp. 2755–2773, 1997. doi: http://dx.doi.org/10.1016/S0017-9310(96)00354-7
[13] Sezai, I. & Mohamad, A.A., Double diffusive convection in a cubic enclosure withopposing temperature and concentration gradient. Physics of Fluids, 12, pp. 2210–2223,2000. doi: http://dx.doi.org/10.1063/1.1286422
[14] Mohamad, A.A., Bennacer, R. & Azaiez, J., Double diffusion natural convection ina rectangular enclosure fi lled with binary fl uid saturated porous media the effect oflateral aspect ratio. Physics of Fluids, 16, pp. 184–199, 2004. doi: http://dx.doi.org/10.1063/1.1630798
[15] Ravnik, J., Škerget, L. & Žuni , Z., Velocity-vorticity formulation for 3D naturalconvection in an inclined enclosure by BEM. International Journal of Heat and MassTransfer, 51, pp. 4517–4527, 2008. doi: http://dx.doi.org/10.1016/j.ijheatmasstransfer.2008.01.018
[16] Ravnik, J., Škerget, L. & Hriberšek, M., Analysis of three-dimensional naturalconvection of nanofl uids by BEM. Engineering Analysis With Boundary Elements, 34,pp. 1018–1030, 2010. doi: http://dx.doi.org/10.1016/j.enganabound.2010.06.019
[17] Bear, J., Dynamics of Fluids in Porous Media. Dover Publications, Inc.: New York,1972.
[18] Škerget, L., Hriberšek, M. & Kuhn, G., Computational fl uid dynamics by boundarydomainintegral method. International Journal for Numerical Methods in Engineering,46, pp. 1291–1311, 1999. doi: http://dx.doi.org/10.1002/(SICI)1097-0207(19991120)46:8<1291::AID-NME755>3.0.CO;2-O
[19] Kramer, J., Jecl, R. & Škerget, L., Boundary domain integral method for the studyof double diffusive natural convection in porous media. Engineering Analysiswith Boundary Elements, 31, pp. 897–905, 2007. doi: http://dx.doi.org/10.1016/j.enganabound.2007.04.001
[20] Kramer, J., Jecl, R., Ravnik, J. & Škerget, L., Simulation of 3d fl ow in porous mediaby boundary element method. Engineering Analysis with Boundary Elements, 35,pp. 1256–1264, 2011. doi: http://dx.doi.org/10.1016/j.enganabound.2011.06.002
[21] Wrobel, L. C., The Boundary Element Method. John Willey & Sons, LTD, 2002.
[22] Jecl, R., Škerget, L. & Petrešin, E., Boundary domain integral method for transportphenomena in porous media. International Journal for Numerical Methods in Fluids,35, pp. 39–54, 2001. doi: http://dx.doi.org/10.1002/1097-0363(20010115)35:1<39::AIDFLD81>3.0.CO;2-3