## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Numerical simulation of flow reversal at high Rayleigh number in a vertical square duct - an application of the spectral method

**ABSTRACT**

In this paper we numerically study the mixed convection in hydrodynamically as well as thermally developed incompressible laminar flow of nanofluids in a vertical square duct subject to the thermal boundary condition of constant heat flux per unit axial length with constant peripheral temperature at any cross section, using the spectral method and the finite difference method. We have considered three different water-based nanofluids containing Alumina, Titanium Oxide or Silver nanoparticles. We observe that the Rayleigh number remarkably reduces the fluid velocity and even the flow reversal may occur while developing an equi-temperature region for a small region in the centre of the duct. It has also been noted that, for Siler-water nanofluid, the nanoparticle volume fraction increases the Nusselt number more rapidly while slowly decreasing the fRe.

**KEYWORDS**

PAPER SUBMITTED: 2016-01-02

PAPER REVISED: 2017-05-31

PAPER ACCEPTED: 2017-06-12

PUBLISHED ONLINE: 2017-07-08

- Lanczos, C., Trigonometric interpolation of empirical and analytical functions, J. Math. Phys., (1938), pp. 17
- Lanczos, C., Applied Analysis, Prentice-Hall, 1956
- Fox, L., et al., Chebyshev Polynomials in Numerical Analysis, Oxford U. Press, 1968
- Gottlieb, D., Orszag, S. A., Numerical Analysis of Spectral Methods: Theory and Applications, SIAM, 1977
- Fornberg, B., A Practical Guide to Pseudospectral Methods, Cambridge University Press, 1996
- Karniadakis, G. E., Sherwin, S. J., Spectral/hp Element Methods for CFD, Oxford University Press, 1999
- Calakli, F., Taubin, G., Smooth Signed Distance Surface Reconstruction, Pacific Graphics, 2011
- Choi, S., Enhancing thermal conductivity of fluids with nanoparticles, ASME Publications, 66 (1995), pp. 99-105
- Daungthongsuk, W., Wongwises, S., A critical review of convective heat transfer nanofluids, Renew Syst Energy Rev, 11 (2007), pp. 797-817
- Trisaki, V., Wongwises, S., Critical review of heat transfer characteristics of nanofluids, Renew Sust Energy Rev., 11 (2007), pp. 512-523
- Wang, X., Mujumdar, A. S., Heat transfer characteristics of nanofluids: A review, Int J Therm Sci. 46 (2007), pp. 1-19
- Hartnett, J. P., Kostic, M., Heat transfer to Newtonian and non-Newtonian fluids in rectangular ducts, Adv. Heat Transfer, 19 (1989), pp. 247-356
- Cheng, C. H., et al., Buoyancy effect on the flow reversal of three-dimensional developing flow in a vertical rectangular duct--a parabolic model solution, ASME J. Heat Transfer, 117 (1995), pp. 236-241
- Cheng, C. H., et al., Buoyancy-assisted flow reversal and convective heat transfer in entrance region of a vertical rectangular duct, Int. J. Heat Fluid Flow, 21 (2000), pp. 403-411
- Lee, K. T., Laminar natural convection heat and mass transfer in vertical rectangular ducts, Int. J. Heat Mass Transfer, 42 (1999), pp. 4523-4534
- Hwang, G. J., et al., A computer-aided parametric analysis of mixed convection in ducts, Int. J. Heat Mass Transfer, 44 (2001), pp. 1857-1867
- Alami, N. A., Campo, A., Experimental investigation on flow and heat transfer for cooling flush-mounted ribbons in a channel: Application of an EHD active enhancement method, Therm Sc, 20(2016), No. 2, pp. 505-516
- StankoviÄ‡, B.D., et al., Specific aspects of turbulent flow in rectangular ducts, Therm Sci, (2017), Suppl. 1, pp. xxx-xxx.
- Ali,.K., et al., On combined effect of thermal radiation and viscous dissipation in hydromagnetic micropolar fluid flow between two stretchable disks, Thermal Science, 2015 OnLine-First (00): pp. 96-96
- Farahi, S.M., Hossein, N.A., Investigation of MHD flow and heat transfer in the presence of a confined square cylinder using SM82 equations, THERMAL SCIENCE, Year 2017, Vol. 21, No. 2, pp. 889-899
- Karthikeyan, S., et al., Experimental study of developing turbulent flow and heat transfer in ribbed convergent/divergent rectangular ducts, Therm Sci, 19(2015), No. 6, pp. 2219-2231.
- Turgut, O., Arslan, K., Periodically fully developed laminar flow and heat transfer in a two- dimensional horizontal channel with staggered fins, Thermal Science, 2015 OnLine-First (00):160-160.
- Kays, W. M., et al., Convective Heat and Mass Transfer (4th Edition), McGraw-Hill, New York, 2005
- Incropera, F. P., Dewitt, D. P., Fundamentals of Heat and Mass Transfer, John Wiley and Sons Ltd., 2011
- Dong, Z. F., Ebadian, M. A., Analysis of Combined Natural and Forced Convection in Vertical Semicircular Ducts with Radial Internal Fins, Numerical Heat Transfer Applications, 10 (1995), pp. 359-372