## THERMAL SCIENCE

International Scientific Journal

### NUMERICAL INVESTIGATION OF NATURAL CONVECTION HEAT TRANSFER IN A SYMMETRICALLY COOLED SQUARE CAVITY WITH A THIN FIN ON ITS BOTTOM WALL

**ABSTRACT**

In the present paper, natural convection fluid flow and heat transfer in a square cavity heated from below and cooled from sides and the ceiling with a thin fin attached to its hot bottom wall is investigated numerically. The right and the left walls of the cavity, as well as its horizontal top wall are maintained at a constant temperature Tc, while the bottom wall is kept at a constant temperature Th ,with Th > Tc. The governing equations are solved numerically using the finite volume method and the couple between the velocity and pressure fields is done using the SIMPLER algorithm. A parametric study is performed and the effects of the Rayleigh number and the length of the fin on the flow pattern and heat transfer inside the cavity are investigated. Two competing mechanisms that are responsible for the flow and thermal modifications are observed. One is the resistance effect of the fin due to the friction losses which directly depends on the length of the fin, whereas the other is due to the extra heating of the fluid that is offered by the fin. It is shown that for high Rayleigh numbers, placing a hot fin at the middle of the bottom wall has more remarkable effect on the flow field and heat transfer inside the cavity.

**KEYWORDS**

PAPER SUBMITTED: 2011-06-12

PAPER REVISED: 2012-06-21

PAPER ACCEPTED: 2012-07-17

**THERMAL SCIENCE** YEAR

**2014**, VOLUME

**18**, ISSUE

**Issue 4**, PAGES [1119 - 1132]

- Ostrach, S., Natural Convection in Enclosures, ASME J. Heat Trans., 110 (1988), pp. 1175-1190.
- Zimmerman, E. and Acharya, S., Natural Convection in an Enclosure with a Vertical Baffle, Commun. Appl. Numer. Meth., 4 (1988), pp. 314-338.
- Frederick, R.L., Natural Convection in an Inclined Square Enclosure with a Partition Attached to its Cold Wall, Int. J. Heat and Mass Trans., 32 (1989), pp. 87-94.
- Frederick, R.L., Valencia, A., Heat Transfer in a Square Cavity with a Conducting Partition on its Hot Wall, Int. Commun. Heat and Mass Trans., 16 (1989), pp. 347-354.
- Nag, A., Sarkar, A., Sastri, V.M.K., Natural Convection in a Differentially Heated Square Cavity with a Horizontal Partition Plate on the Hot Wall, Comput. Methods Appl. Mech. Eng., 110 (1993), pp. 143-156.
- Lakhal, E.K., Hasnaousi, M., Bilgen, E., Vasseur, P., Natural Convection in Inclined Rectangular Enclosures with Perfectly Conducting Fins Attached on the Heated Wall, Heat Mass Transfer, 32 (1997), pp. 365-373.
- Bilgen, E., Natural Convection in Enclosures with Partial Partitions, Renewable Energy, 26 (2002), pp. 257-270.
- Shi, X., Khodadadi, J.M., Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall, ASME J. Heat Trans., 125 (2003), pp. 624-634.
- Rahnama, M., Farhadi, M., Effect of Radial Fins on Two-dimensional Turbulent Natural Convection in a Horizontal Annulus, Int. J. Therm. Sci., 43 (2004), pp. 255-264.
- Kim, M., and Ha, J., Numerical Simulation of Natural Convection in Annuli with Internal Fins, KSME Int. J., 18 (2004) pp. 718-730.
- Ben-Nakhi, A., Chamkha, A.J., Effect of Length and Inclination of a Thin Fin on Natural Convection in a Square Enclosure, Numer. Heat Trans.-Part A, 50 (2006), pp. 381-399.
- Terekhov, V.I., Terekhov, V.V., Heat Transfer in a High Vertical Enclosure with Fins Attached to One of the Side Walls, High Temp., 44 (2006), pp. 436-44.
- Ben-Nakhi, A., Chamkha, A.J., Conjugate natural convection around a finned pipe in a square enclosure with internal heat generation, Int. J. Heat and Mass Trans., 50 (2007), pp. 2260-2271.
- Kasayapanand, N., A computational Fluid Dynamics Modeling of Natural Convection in Finned Enclosure Under Electric Field, Appl. Therm. Eng., 29 (2009), pp. 131-141.
- Xu, F., Patterson, J.C., Lei, C., Transition to a Periodic Flow Induced by a Thin Fin on the Sidewall of a Differentially Heated Cavity, Int. J. Heat Mass Trans., 52 (2009), pp. 620-628.
- Sharifi, N., Bergman, T.L., Faghri, A., Enhancement of PCM melting in enclosures with horizontally-finned internal surfaces, Int. J. Heat Mass Trans., 54 (2011) pp. 4182-4192.
- Jani, S., Amini, M., Mahmoodi, M., Numerical Study of Free Convection Heat Transfer in a Square Cavity with a Fin Attached to Its Cold Wall, Heat Transfer Research, 42 (2011) pp. 251-266.
- Varol, Y., Oztop, H.F., Ozgen, F., Koca, A., Experimental and numerical study on laminar natural convection in a cavity heated from bottom due to an inclined fin, Heat Mass Transfer, 48 (2012) pp. 61-70.
- Bejan, A., Convection heat transfer, New Jersey: John Wiley & Sons Inc., 2004.
- Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Taylor and Francis Group, New York, 1980.
- Davis G.V., Natural convection of air in a square cavity, a benchmark numerical solution, Int. J. Numer. Methods fluids, 3 (1983) pp. 249-264.
- Markatos N.C., Pericleous K.A., Laminar and turbulent natural convection an enclosed cavity, Int. J. Heat Mass Tran., 27 (1984) pp. 772-775.
- Fusegi T., Hyun J.M., Kawahara K., Farouk B., A Numerical study of Tree-dimensional natural convection in a differentially heated cubical enclosure, Int. J. Heat Mass Tran., 34 (1991) pp. 1543-1557.