## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Laminar natural convection of non-Newtonian power-law fluid in an eccentric annulus

**ABSTRACT**

This work is about studying the natural convection of two-dimensional steady state non-Newtonian power law fluid numerically. The inner cylinder was put eccentrically into the outer one. The cylinders are held at constant temperatures with the inner one heated isothermally at temperature Th and the outer one cooled isothermally at temperature Tc (Th>Tc). The simulations have been taken for the parameters 103≤Ra≤105, 10≤Pr≤103, 0.6≤n≤1.4, 0≤ɛ≤0.9 and an inclination angle ϕ from 0° up to 90°. The average Nusselt numbers for the previous parameters are obtained and discussed numerically. The results revealed that the average Nusselt number has the highest values when n=0.6, Ra=105 at ϕ=0 which is a signal for the large transfer herein and has the lowest values for n=1.4, Ra=103 at ϕ=90° which is a signal that the transfer is by conduction more than convection. Furthermore, the increasing of eccentricity causes an increase in the Nusselt number for all the cases. Finally, the best case where we can get the best heat transfer is at ϕ = 0, ɛ=0.9 among them all. The results have compared with some precedent works and showed good agreement.

**KEYWORDS**

PAPER SUBMITTED: 2019-08-05

PAPER REVISED: 2019-09-24

PAPER ACCEPTED: 2019-10-30

PUBLISHED ONLINE: 2019-11-17

- Mack, L.R., Bishop, E.H., Natural Convection between Horizontal Concentric Cylinders for Low Rayleigh Numbers, Quart. J. Mech Appl Math 21 (1968), pp. 223-241.
- Kuehn, T.H., Goldstein R.J., An Experimental and Theoretical Study of Natural Convection in the Annulus between Horizontal Concentric Cylinders, J. Fluid Mechanics 74 (1976), pp. 695-719.
- Char, M.I., Lee, G.C., Maximum Density Effects on Natural Convection of Micropolar Fluids between Horizontal Eccentric Cylinders, Int. J. Eng. Sci. 36 (1998), pp. 157-169.
- Kim, G.B., et al., Transient Buoyant Convection of a Power-Law Non-Newtonian Fluid in an Enclosure, Int. J. Heat Mass Transfer 46 (2003), pp. 3605-3617.
- Naïmi, M., et al., Natural Convection of Non-Newtonian Power Law Fluids in a Shallow Horizontal Rectangular Cavity Uniformly Heated from Below,Springer, Heat Mass Transfer 41 (2005), pp. 239-249.
- Sakr, R.Y., et al., Experimental and Numerical Investigation of Natural Convection Heat Transfer in Horizontal Elliptic Annuli, Int .J. Che Reactor Eng 6 (2008), pp. 1-29.
- Kumar, R., Study of Natural Convection in Horizontal Annuli. Int. J. Heat Mass Transfer 31 (1988), pp. 1137-1148.
- Yigit, S., et al., Numerical Investigation of Laminar Rayleigh-Bénard Convection of Power-Law Fluids in Square Cross-Sectional Cylindrical Annular Enclosures, Int Commun in Heat Mass Transfer 78 (2016), pp. 112-120.
- Abu-Nada, E., et al., Natural Convection Heat Transfer Enhancement in Horizontal Concentric Annuli Using Nanofluids, Int Commun in Heat Mass Transfer 35 (2008), pp. 657-665.
- Chamkha, A.J., Ben-Nakhi, A., Natural Convection in Inclined Partitioned Enclosures, Heat Mass Transfer 42 (2006), pp. 311-321.
- Ben-Nakhi, A., Chamkha, A.J., Conjugate Natural Convection in a Square Enclosure with Inclined Thin Fin of Arbitrary Length, Int. J. Thermal Sci 46 (2007), pp. 467-478.
- Khezzar, L., et al., Natural Convection of Power Law Fluids in Inclined Cavities, Int. J. Thermal Sci 53 (2012), pp. 8-17.
- Parvin, S., et al., Thermal Conductivity Variation on Natural Convection Flow of Water-Alumina Nanofluid in an Annulus, Int. J. Heat Mass Transfer 55 (2012), pp. 5268-5274.
- Chhabra, R.P., et al., Free Convection from a Heated Circular Cylinder in Bingham Plastic Fluids, Int. J. Therm. Sci. 83 (2014), pp. 33-44.
- Matin, M.H., Khan, W.A., Laminar Natural Convection of Non-Newtonian Power-Law Fluids between Concentric Circular Cylinders, Int Commun in Heat Mass Transfer 43 (2013), pp. 112-121.
- Turki, S., et al., Numerical Prediction of Flow and Heat Transfer of Power-Law Fluids in a Plane Channel with a Built-in Heated Square Cylinder, Int. J. Heat Mass Transfer 53 (2010), pp. 5420-5429.
- Chamkha, A.J., et al., Numerical Analysis of Unsteady Conjugate Natural Convection of Hybrid Water-Based Nanofluid in a Semi-Circular Cavity, J. Therm Sci & Eng apps 9 (2017), pp. 1116-1127.
- Chamkha, A.J., et al., Mixed Convection Heat Transfer of Air inside a Square Vented Cavity with a Heated Horizontal Square Cylinder, Num Heat Transfer, Part A: Applications 59 (2011), pp. 58-79.
- Khanafer, K., Chamkha, A.J., Mixed Convection within a Porous Heat Generating Horizontal Annulus, Int. J. Heat Mass Transfer 46 (2003), pp. 1725-1735.
- Matin, M.H., et al., Natural Convection of Power-Law Fluid between Two-Square Eccentric Duct Annuli, J. Non-Newtonian Fluid Mech 197 (2013), pp. 11-23.
- Alawi, O.A., et al., Natural Convection Heat Transfer in Horizontal Concentric Annulus between Outer Cylinder and Inner Flat Tube Using Nanofluid, Int Commun in Heat Mass Transfer 57 (2014), pp. 65-71.
- Parvin, S., Chamkha, A.J., An Analysis on Free Convection Flow Heat Transfer and Entropy Generation in an Odd-Shaped Cavity Filled with Nanofluid, Int Commun in Heat Mass Transfer 54 (2014), pp. 8-17.
- Chamkha, A.J., et al., Bouzerzour, A., Natural Convective Nanofluid Flow in an Annular Space between Confocal Elliptic Cylinders, J. Thermal Sci Eng Applications 9 (2017), pp. 1-9.
- Turan, O., et al., Laminar Natural Convection of Power-Law Fluids in a Square Enclosure with Differentially Heated Side Walls Subjected to Constant Temperatures, J. Non-Newtonian Fluid Mech 166 (2011), pp. 1049-1063.
- Chamkha, A.J., Ismael, M.A., Natural Convection in Differentially Heated Partially Porous Layered Cavities Filled with a Nanofluid, Num Heat Transfer, Part A: Applications 65 (2014), pp. 1089-1113.
- Ismael, M.A., Chamkha, A.J., Conjugate Natural Convection in a Differentially Heated Composite Enclosure Filled with a Nanofluid, J. Porous Media 18 (2015), pp. 699-716.
- Chhabra. R.P., et al., Effect of Aiding-Buoyancy on Mixed Convection from a Heated Cylinder in Bingham Plastic Fluids, J. Non-Newtonian Fluid Mech 220 (2015), pp. 3-21.
- Nasrin, R.,et al., Effect of Viscosity Variation on Natural Convection Flow of Water-Alumina Nanofluid in an Annulus with Internal Heat Generation, Heat Transfer-Asian Research 41 (2012), pp. 536-552.
- Tayebi, T., Chamkha, A.J., Free Convection Enhancement in an Annulus between Horizontal Confocal Elliptical Cylinders Using Hybrid Nanofluids, Num Heat Transfer, Part A: Applications 71 (2017), pp. 1159-1173.
- Chamkha, A.J., Ismael, M.A., Conjugate Heat Transfer in a Porous Cavity Heated by Triangular Thick Wall, Num Heat Transfer, Part A: Applications 63 (2012), pp. 144-158.
- Chamkha, A.J., Ismael, M.A., Conjugate Heat Transfer in a Porous Cavity Filled with Nanofluids and Heated by Triangular Thick Wall, Int. J. Thermal Sci 67 (2013), pp. 135-151.
- Selimefendigil, F., Chamkha, A.J., Natural Convection of a Hybrid Nanofluid-Filled Triangular Annulus with an Openning, Computational Thermal Sciences 8 (2016), pp. 555-566.
- Oztop, H.F., et al., Natural Convection in Wavy Enclosures with Volumetric Heat Sources, Int. J. Thermal Sci 50 (2011), pp. 502-514.
- Abu-Nada, E., Chamkha, A.J., Mixed Convection Flow of a Nanofluid in a Lid-Driven Cavity with a Wavy Wall, Int Commun in Heat Mass Transfer 57 (2014), pp. 36-47.
- Patankar, S.V, Numerical Heat Transfer and Fluid Flow, McGraw Hill, NY, USA, 1980.