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Suspensions of nanoscale particles and fluids have been recently subject of intense research, since it was proved that they considerably improve heat transfer capabilities of the fluid which can be crucial in several technological processes. Several applications can be found in the field of porous media flow, such as oil recovery systems, thermal and geothermal energy, nuclear reactors cooling. Since nanofluids are a mixture of a solid and fluid phase, in general, the two phase mathematical model would be the most appropriate to use. However, due to very small size of nanoparticles (1–100 nm) can be assumed, that they behave as a water molecule and a single phase model along with empirical correlations for nanofluid properties can be used. In the present study a convective flow through porous cavity fully saturated with nanofluid is analyzed in detail using the single phase mathematical model based on the Navier-Stokes equations taking into account the non-Darcy parameters. The mathematical model is written at a macroscopic level enabling the simulation of the porous media flow. The solutions are obtained with the in house numerical code based on the Boundary Element Method, which was already proved to have some unique advantages when considering fluid flow problems in different configurations. The effects of the presence of different types of nanoparticles as well as the porous matrix were investigated in detail for different values of governing parameters in order to examine the improved heat transfer characteristics of added nanoparticles.
boundary element method, Darcy-Brinkman-Forchheimer formulation, nanofluids, porous medium flow
[1] Choi, S.U.S. & Eastman, J.A., Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress Exposition, San Francisco, CA, 1995.
[2] Kakac, S. & Pramuanjaroenkij, A., Review of convective heat transfer enhancement with nanofluids. International Journal of Heat and Mass Transfer, 52, pp. 3187–3196, 2009. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2009.02.006
[3] Haddad, Z., Oztop, H.F., Abu-Nada, E. & Mataoui, A., A review on natural convective heat transfer of nanofluids. Renewable and Sustainable Energy Reviews, 16(7), pp. 5363–5378, 2012. http://dx.doi.org/10.1016/j.rser.2012.04.003
[4] Tiwari, R.K. & Das, M.K., Heat transfer augmentation in a two-sided lid driven differentially heated square cavity utilizing nanofluids. International Journal of Heat and Mass Transfer, 50(9–10), pp. 2002–2018, 2007. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.09.034
[5] Sheremet, M.A., Grosan, T. & Pop, O., Free convection in a square cavity filled with a porous medium saturated by nanofluid using Tiwari and Das’ nanofluid model. Transport in Porous Media, 106, pp. 595–610, 2015. http://dx.doi.org/10.1007/s11242-014-0415-3
[6] Nguyen, M.T., Aly, A.M. & Lee, S.W., Natural convection in a non-darcy porous cavity
filled with Cu-water nanofluid using the characteristic-based split procedure in finiteelement method. Numerical Heat Transfer, A: Applications, 67, pp. 224–247, 2015. http://dx.doi.org/10.1080/10407782.2014.923225
[7] Buongiorno, J., Convective transport in nanofluids. Journal of Heat Transfer, 128, pp. 240–250, 2006. http://dx.doi.org/10.1115/1.2150834
[8] Sheremet, M.A. & Pop, I., Conjugate natural convection in a square porous cavity filled by a nanofluid using Buongiorno’s mathematical model. International Journal of Heat and Mass Transfer, 79, pp. 137–145, 2014. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.07.092
[9] Gro§an, T., Revnic, C., Pop, I. & Ingham, D.B., Free convection heat transfer in a square cavity filled with a porous medium saturated by a nanofluid. International Journal of Heat and Mass Transfer, 87, pp. 36–41, 2015. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.03.078
[10] Ramsak, M., Skerget, L., Hribersek, M. & Zunic, Z., A multidomain boundary element
method for unsteady laminar flow using stream function vorticity equations. Engineering Analysis with Bound Elements, 29, pp. 1–14, 2005. http://dx.doi.org/10.1016/j.enganabound.2004.09.002
[11] Ravnik, J., Skerget, L. & Hribersek, M., Analysis of three-dimensional natural convection of nanofluids by BEM. Engineering Analysis with Boundary Elements, 34, pp. 1018–1030, 2010. http://dx.doi.org/10.1016/j.enganabound.2010.06.019
[12] Ravnik, J., Skerget, L. & Zunic, Z., Velocity-vorticity formulation for 3D natural convection in an inclined enclosure by BEM. International Journal of Heat and Mass Transfer, 51, pp. 4517–4527, 2008. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2008.01.018
[13] Ravnik, J., Skerget, L. & Zunic, Z., Combined single domain and subdomain BEM for 3D laminar viscous flow. Engineering Analysis with Boundary Elements, 33, pp. 420–424, 2009. http://dx.doi.org/10.1016/j.enganabound.2008.06.006
[14] Kramer, J., Ravnik, J., Jecl, R. & Skerget, L., Simulation of 3D flow in porous media by boundary element method. Engineering Analysis with Boundary Elements, 35, pp. 1256–1264, 2011. http://dx.doi.org/10.1016/j.enganabound.2011.06.002
[15] Kramer, J., Ravnik, J., Jecl, R. & Skerget, L., Three-dimensional double-diffusive natural convection with opposing buoyancy effects in porous enclosure by boundary element method. International Journal of Computational Methods and Experimental Measurements, 1, pp. 103–115, 2013. http://dx.doi.org/10.2495/CMEM-V1-N2-103-115
[16] Oztop, H.F. & Abu-Nada, E., Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow, 29, pp. 1326–1336, 2008.
http://dx.doi.org/10.1016/j.ijheatfluidflow.2008.04.009
[17] Brinkman, H.C., The viscosity of concentrated suspensions and solutions. The Journal of Chemical Physics, 20, pp. 571–581, 1952. http://dx.doi.org/10.1063/1.1700493
[18] Wasp, F.J., Solid-Liquid Slurry Pipeline Transportation, Trans. Tech. Berlin, 1977.
[19] Bear, J., Dynamics of Fluids in Porous Media, Dover Publications, Inc., New York, 1972.
[20] Bourantas, G.C., Skouras, E.D., Loukopoulos, V.C. & Burganos, V.N., Heat transfer and natural convection of nanofluids in porous media. European Journal of Mechanics B/Fluid, 43, pp. 45–56, 2014.
[21] Nield, D.A. & Bejan, A., Convection in Porous Media, 4th edn., Springer, 2013. http://dx.doi.org/10.1007/978-1-4614-5541-7