# FREE CONVECTION IN WAVY POROUS ENCLOSURES WITH NON-UNIFORM TEMPERATURE BOUNDARY CONDITIONS FILLED WITH A NANOFLUID: BUONGIORNO’S MATHEMATICAL MODEL

## Main Article Content

## Abstract

In the present work, the influence of the amplitude ratio, phase deviation and undulation number on natural convection in a wavy-walled enclosures differentially heated and filled with a water based nanofluid is studied. The upper and bottom walls are wavy with several undulations. The sinusoidal distribution of temperature is imposed at the vertical walls. The flow, heat and mass transfer are calculated by solving governing equations for embody the conservation of total mass, momentum, thermal energy, and nanoparticles, taking into account the Darcy–Boussinesq–Buongiorno approximation with second order finite difference method in «stream function–temperature–concentration» formulation. Results are presented in the form of streamlines, isotherm and isoconcentration contours, and distributions of the average Nusselt number for the different values of the amplitude ratio of the sinusoidal temperature on the right side wall to that on the left side wall (g = 0–1), phase deviation (j = 0–p) and undulation number (k = 1–4). It has been found that variations of the undulation number allow to control the heat and mass transfer rates. Moreover an increase in the undulation number leads to an extension of the non- homogeneous zones.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2086>. Date accessed: 19 aug. 2017. doi: https://doi.org/10.2298/TSCI140814089S.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.

The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.

Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

Accepted 2017-03-13

Published 2017-03-13

## References

[2] Khanafer, K., Al-Azmi, B., Marafie, A., Pop, I., Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure, Int. J. Heat Mass Transfer, 52 (2009), 7-8, pp. 1887-1896.

[3] Choi, S.U.S., Enhancing thermal conductivity of fluids with nanoparticles, Proceedings (D.A.Siginer, H.P.Wang), Development and Applications of Non-Newtonian Flows, ASME FED, 1995, Vol.231/MD, Vol. 66, pp. 99-105.

[4] Masuda, H., Ebata, A., Teramae, K., Hishinuma, N., Alteration of thermal conductivity and viscosity of liquid by dispersing ultra fine particles, Netsu Bussei, 7 (1993), pp. 227-233.

[5] Buongiorno, J., Convective transport in nanofluids, ASME J. Heat Transfer, 128 (2006), pp. 240-250.

[6] Nield, D.A., Bejan, A., Convection in Porous Media (4th edition), Springer, New York, 2013.

[7] Ingham, D.B., Pop, I., Transport Phenomena in Porous Media, Vol. III, Elsevier, Oxford, 2005.

[8] Vafai K., Porous Media: Applications in Biological Systems and Biotechnology, CRC Press, Tokyo 2010.

[9] Pop, I., Ingham, D.B., Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, Oxford, 2001.

[10] Akbar, N.S., Nadeem, S., Haq, R.U., Khan, Z.H., Radiation effects on MHD stagnation point flow of nano fluid towards a stretching surface with convective boundary condition, Chinese Journal of Aeronautics, 26 (2013), 6, pp. 1389-1397.

[11] Akbar, N.S., Nadeem, S., Haq, R.U., Khan, Z.H., Numerical solutions of magnetohydrodynamic boundary layer flow of tangent hyperbolic fluid towards a stretching sheet, Indian Journal of Physics, 87 (2013), 11, pp. 1121-1124.

[12] Akbar, N.S., Khan, Z.H., Nadeem, S., The combined effects of slip and convective boundary conditions on stagnation-point flow of CNT suspended nanofluid over a stretching sheet, Journal of Molecular Liquids, 196 (2014), pp. 21-25.

[13] Akbar, N.S., Double-diffusive natural convective peristaltic flow of a Jeffrey nanofluid in a porous channel, Heat Transfer Research, 45 (2014), 4, pp. 293-307.

[14] Akbar, N.S., Peristaltic Sisko nano fluid in an asymmetric channel, Applied Nanoscience, 4 (2014), 6, pp. 663-673.

[15] Vadasz, P., Heat conduction in nanofluid suspensions, ASME J. Heat Transfer, 128 (2006), pp. 465-477.

[16] Sheremet, M.A., Pop, I., Natural convection in a square porous cavity with sinusoidal temperature distributions on both side walls filled with a nanofluid: Buongiorno’s mathematical model, Transport in Porous Media, 105 (2014), pp. 411-429.

[17] Sheremet, M.A., Pop, I., Natural convection in a wavy porous cavity with sinusoidal temperature distributions on both side walls filled with a nanofluid: Buongiorno's mathematical model, ASME J. Heat Transfer, 137 (2015), 072601.

[18] Nield, D.A., Kuznetsov, A.V., Thermal instability in a porous medium layer saturated by a nanofluid: A revised model, Int. J. Heat Mass Transfer, 68 (2014), pp. 211-214.

[19] Deng, Q.-H., Chang, J.-J., Natural convection in a rectagular enclosure with sinusoidal temperature distributions on both side walls, Numer. Heat Transfer, Part A, 54 (2008), 5, pp. 507-524.

[20] Oztop, H.F., Abu-Nada, E., Varol, Y., Chamkha, A., Natural convection in wavy enclosures with volumetric heat sources, Int. J. Thermal Sciences, 50 (2011), 4, pp. 502-514.

[21] Sheremet, M.A., Grosan, T., Pop, I., Free convection in shallow and slender porous cavities filled by a nanofluid using Buongiorno’s model, ASME J. Heat Transfer, 136 (2014), 082501.

[22] Sheremet, M.A., Pop, I., Conjugate natural convection in a square porous cavity filled by a nanofluid using Buongiorno’s mathematical model, Int. J. Heat Mass Transfer, 79 (2014), pp. 137-145.