## THERMAL SCIENCE

International Scientific Journal

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

**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.

**KEYWORDS**

PAPER SUBMITTED: 2015-07-22

PAPER REVISED: 2016-06-26

PAPER ACCEPTED: 2016-06-28

PUBLISHED ONLINE: 2016-08-07

**THERMAL SCIENCE** YEAR

**2018**, VOLUME

**22**, ISSUE

**1**, PAGES [391 - 399]

- Nield, D.A., Bejan, A., Convection in Porous Media (4th edition), Springer, New York, 2013.
- Ingham, D.B., Pop, I., Transport Phenomena in Porous Media, Vol. III, Elsevier, Oxford, 2005.
- Vafai, K., Porous Media: Applications in Biological Systems and Biotechnology, CRC Press, Tokyo 2010.
- Pop, I., Ingham, D.B., Convective Heat Transfer: Mathematical and Computational Modeling of Viscous Fluids and Porous Media, Pergamon, Oxford, 2001.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Modest, M.F., Radiative heat transfer, Academic Press, New York, 2003.
- 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.
- Bejan, A., Convection Heat Transfer (4th edition), Wiley, Hoboken, 2013.
- 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.
- 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.
- 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.