# EFFECT OF THERMAL RADIATION ON NATURAL CONVECTION IN A SQUARE POROUS CAVITY FILLED WITH A FLUID OF TEMPERATURE-DEPENDENT VISCOSITY

## Main Article Content

## Abstract

A numerical study of the natural convection combined with thermal radiation inside a square porous cavity filled with a fluid of temperature- dependent viscosity is carried out. The side horizontal walls are assumed to be adiabatic while both the left and right vertical walls are kept at constant but different temperatures. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The governing equations formulated in dimensionless stream function, vorticity and temperature variables are solved using finite difference method. A parametric analysis illustrating the effects of the radiation parameter (0 ≤ Rd ≤ 10), Darcy number (10^{–5} ≤ Da ≤ 10^{–2}) and viscosity variation parameter (0 ≤ C ≤ 6) on fluid flow and heat transfer is implemented. The results show an essential intensification of convective flow with an increase in the radiation parameter.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2190>. Date accessed: 24 june 2017. doi: https://doi.org/10.2298/TSCI150722164A.

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

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

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

[5] Badruddin, I.A., Zainal, Z.A., Narayana, P.A.A., Seetharamu, K.N., Numerical analysis of convection conduction and radiation using a non-equilibrium model in a square porous cavity, Int. J. Thermal Sciences, 46 (2007), pp. 20-29.

[6] Badruddin, I.A., Zainal, Z.A., Khan, Z.A., Mallick, Z., Effect of viscous dissipation and radiation on natural convection in a porous medium embedded within vertical annulus, Int. J. Thermal Sciences, 46 (2007), pp. 221-227.

[7] Ahmed, S.E., Hussein, A.K., Mohammed, H.A., Adegun, I.K., Zhang, X., Kolsi, L., Hasanpour, A., Sivasankaran, S., Viscous dissipation and radiation effects on MHD natural convection in a square enclosure filled with a porous medium, Nuclear Engineering and Design, 266 (2014), pp. 34-42.

[8] Ahmed, S.E., Oztop, H.F., Al-Salem, K., Natural convection coupled with radiation heat transfer in an inclined porous cavity with corner heater, Computers & Fluids, 102 (2014), 10, pp. 74-84.

[9] Mahapatra, T.R., Pal, D., Mondal, S., Combined effects of thermal radiation and heat generation on natural convection in a square cavity filled with Darcy-Forchheimer porous medium, Int. J. Applied Mathematics and Computation, 4 (2012), 4, pp. 359-368.

[10] Abdou, M.M.M., Effect of radiation with temperature dependent viscosity and thermal conductivity on unsteady a stretching sheet through porous media, Nonlinear Analysis: Modelling and Control, 15 (2010), 3, pp. 257-270.

[11] Makinde, O.D., Khan, W.A., Culham, J.R., MHD variable viscosity reacting flow over a convectively heated plate in a porous medium with thermophoresis and radiative heat transfer, Int. J. Heat Mass Transfer, 93 (2016), pp. 595-604.

[12] Astanina, M.S., Sheremet, M.A., Umavathi, J.C., Unsteady natural convection with temperature- dependent viscosity in a square cavity filled with a porous medium, Transp. Porous Med., 110 (2015), pp. 113-126.

[13] Hyun, J.M., Lee, J.W., Transient natural convection in a square cavity of a fluid with temperature-dependent viscosity, Int. J. Heat Fluid Flow, 9 (1988), 3, pp. 278-285.

[14] Umavathi, J.C., Ojjela, O., Effect of variable viscosity on free convection in a vertical rectangular duct, Int. J. Heat Mass Transfer, 84 (2015), pp. 1-15.

[15] Martyushev, S.G., Sheremet, M.A., Characteristics of Rosseland and P-1 approximations in modeling nonstationary conditions of convection-radiation heat transfer in an enclosure with a local energy source, J. Engineering Thermophysics, 21 (2012), 2, pp. 111-118.

[16] Modest, M.F., Radiative heat transfer, Academic Press, New York, 2003.

[17] Sheremet, M.A., Trifonova, T.A., Unsteady conjugate natural convection in a vertical cylinder containing a horizontal porous layer: Darcy model and Brinkman-extended Darcy model, Transport in Porous Media, 101 (2014), pp. 437-463.

[18] Bejan, A., Convection Heat Transfer (4th edition), Wiley, Hoboken, 2013.

[19] 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.

[20] Sheremet, M.A., Laminar natural convection in an inclined cylindrical enclosure having finite thickness walls, Int. J. Heat Mass Transfer, 55 (2012), 13-14, pp. 3582-3600.

[21] Sheremet, M.A., The influence of cross effects on the characteristics of heat and mass transfer in the conditions of conjugate natural convection, J. Engineering Thermophysics, 19 (2010), 3, pp. 119-127.