## THERMAL SCIENCE

International Scientific Journal

### NUMERICAL STUDY OF DEVELOPING LAMINAR MIXED CONVECTION IN A HEATED ANNULAR DUCT WITH TEMPERATURE DEPENDENT PROPERTIES

**ABSTRACT**

This study presents a numerical simulation of the 3-D laminar mixed convection between two concentric horizontal cylinders with physical properties which depend on temperature. The outer cylinder is subjected to an internal energy generated by the Joule effect whereas the inner cylinder is adiabatic. The flow and thermal fields are modeled by the continuity, momentum, and energy equations with appropriate initial and boundary conditions using a cylindrical co-ordinate system. The model equations are numerically solved by a finite volume method with a second order accurate spatiotemporal discretization. For the considered geometric, dynamic and thermal controlling parameters, it is found that the transverse flow is always the cause of the circumferential variation of the temperature and the physical properties of the fluid. The phenomenon of the temperature stratification is highlighted and the vortices obtained lead to an improvement in the heat transfer quantified by the increase in the number of Nusselt. The obtained axial Nusselt number increases with the increased of Grashof number which is proportional to the heat flux imposed at the surface of the outer cylinder.

**KEYWORDS**

PAPER SUBMITTED: 2017-10-13

PAPER REVISED: 2018-01-09

PAPER ACCEPTED: 2018-01-31

PUBLISHED ONLINE: 2018-03-04

**THERMAL SCIENCE** YEAR

**2019**, VOLUME

**23**, ISSUE

**6**, PAGES [3411 - 3423]

- Rao,Y-F., et al., Flow patterns of natural convection in horizontal cylindrical annuli, International Journal of Heat and Mass Transfer, 28,(1985),3, pp. 705-714
- Ouazzani, M.T.,et al., Etude numérique et expérimentale de la convection mixte entre deux plans horizontaux à températures différentes, International Journal of Heat and Mass Transfer, 32, (1989), 2, pp. 261-269
- Chenier, E., et al., From natural to mixed convection in horizontal and differentially heated annular ducts: Linear stability analysis, International Journal of Heat and Mass Transfer, 54, (2011), pp. 5100-5108
- Hu, Y., et al., Study of multiple steady solutions for the 2D natural convection in a concentric horizontal annulus with a constant heat flux wall using immersed boundary-lattice Boltzmann method, International Journal of Heat and Mass Transfer,81, (2015), pp. 591-601
- Mojtabi , A., Caltagirone, J.P., Analyse du transfert de chaleur en convection mixte laminaire entre deux cylindres coaxiaux horizontaux, International Journal of Heat and Mass Transfer, 23 (1980), pp. 1369-137
- Mohammed, H. A., et al., Experimental study of forced and free convective heat transfer in the thermal entry region of horizontal concentric annuli, International Communications in Heat and Mass Transfer, 37, (2010), pp. 739-747
- Kotake, S., Hattori, N., Combined forced and free convection heat transfer for fully-developed laminar flow in horizontal annuli, International Journal of Heat and Mass Transfer, 28, (1985), pp. 2113-2120.
- Nazrul, I., et al., Mixed convection heat transfer in the entrance region of horizontal annuli, Int. Journal Heat Mass Transfer, 44, (2001), 11, pp. 2107-2120
- Touahri, S., Boufendi, T., Conjugate heat transfer with variable fluid properties in a heated horizontal annulus, Heat Transfer Research, 64, (2015), pp. 1019-1038
- Touahri, S., Boufendi, T., Numerical study of the conjugate heat transfer in a horizontal pipe heated by joulean effect, Thermal Sciences, 16, (2012), 1, pp. 53-67
- Jha, B. K., et al., Steady fully developed mixed convection flow in a vertical micro-concentric-annulus with heat generating/absorbing fluid: An exact solution, Ain Shams Engineering Journal, (2016) Article in press, dx.doi.org/10.1016/j.asej.2016.08.005
- Oni, M. O., Combined effect of heat source, porosity and thermal radiation on mixed convection flow in a vertical annulus: An exact solution, Engineering Science and Technology, an International Journal, 20, (2017), 1, pp. 518-527
- Quintino, A., et al., Buoyancy-induced convection of water-based nanofluids in differentially- heated horizontal semi- annuli, Thermal Sciences, 21, (2017), 6A, pp. 2643-2660
- Labsi, N., et al., Viscous dissipation effect on the flow of a thermodependent Hershel-Bulkley fluid, Thermal Sciences, 19, (2015), 5, pp. 1553-1564
- Baehr, H. D., Stephan, K., Heat and Mass Transfer, Berlin, Springer-Verlag, 1998
- Churchill, S. W., Chu, H. S., Correlating equation for laminar and turbulent free convection from a horizontal cylinder, International Journal Heat Mass Transfer, 18, (1975), pp. 1049-1053
- Patankar, S. V., Numerical Heat Transfer and Fluid Flow, New York: McGraw-Hill, 1980
- Carlo, N., Guidice, S. D., Finite element analysis of laminar mixed convection in the entrance region of horizontal annular ducts, Numerical Heat Transfer, Part A, 29, (1996), pp. 313-330