The effects of inclination $180deg\u2265\phi \u22650deg$ on steady-state laminar natural convection of yield-stress fluids, modeled assuming a Bingham approach, have been numerically analyzed for nominal values of Rayleigh number Ra ranging from 10^{3} to 10^{5} in a square enclosure of infinite span lying horizontally at $\phi =0deg$, then rotated about its axis for $\phi >0deg$ cases. It has been found that the mean Nusselt number $Nu\xaf$ increases with increasing values of Rayleigh number but $Nu\xaf$ values for yield-stress fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to the weakening of convective transport. For large values of Bingham number Bn (i.e., nondimensional yield stress), the mean Nusselt number $Nu\xaf$ value settles to unity ($Nu\xaf=1.0$) as heat transfer takes place principally due to thermal conduction. The mean Nusselt number $Nu\xaf$ for both Newtonian and Bingham fluids decreases with increasing $\phi $ until reaching a local minimum at an angle $\phi *$ before rising with increasing $\phi $ until $\phi =90deg$. For $\phi >90deg$ the mean Nusselt number $Nu\xaf$ decreases with increasing $\phi $ before assuming $Nu\xaf=1.0$ at $\phi =180deg$ for all values of $Ra$. The Bingham number above which $Nu\xaf$ becomes unity (denoted $Bnmax$) has been found to decrease with increasing $\phi $ until a local minimum is obtained at an angle $\phi *$ before rising with increasing $\phi $ until $\phi =90deg$. However, $Bnmax$ decreases monotonically with increasing $\phi $ for $90deg<\phi <180deg$. A correlation has been proposed in terms of $\phi $, Ra, and Bn, which has been shown to satisfactorily capture $Nu\xaf$ obtained from simulation data for the range of Ra and $\phi $ considered here.

Article navigation

Research-Article

# Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures

Şahin Yİğİt

,
Şahin Yİğİt

School of Mechanical and Systems Engineering,

Newcastle University

,Newcastle-Upon-Tyne NE1 7RU

, UK

Department of Mechanical Engineering,

e-mail: syigit@ktu.edu.tr

Karadeniz Technical University

,Trabzon 61080

, Turkey

e-mail: syigit@ktu.edu.tr

Search for other works by this author on:

Robert J. Poole

,
Robert J. Poole

School of Engineering,

e-mail: robpoole@liv.ac.uk

University of Liverpool

,Brownlow Hill

,Liverpool L69 3GH

, UK

e-mail: robpoole@liv.ac.uk

Search for other works by this author on:

Nilanjan Chakraborty

Nilanjan Chakraborty

School of Mechanical and Systems Engineering,

e-mail: nilanjan.chakraborty@ncl.ac.uk

Newcastle University

,Newcastle-Upon-Tyne NE1 7RU

, UK

e-mail: nilanjan.chakraborty@ncl.ac.uk

1

1

Corresponding author.
Search for other works by this author on:

Şahin Yİğİt

School of Mechanical and Systems Engineering,

Newcastle University

,Newcastle-Upon-Tyne NE1 7RU

, UK

Department of Mechanical Engineering,

e-mail: syigit@ktu.edu.tr

Karadeniz Technical University

,Trabzon 61080

, Turkey

e-mail: syigit@ktu.edu.tr

Robert J. Poole

University of Liverpool

,Brownlow Hill

,Liverpool L69 3GH

, UK

e-mail: robpoole@liv.ac.uk

Nilanjan Chakraborty
1

Newcastle University

,Newcastle-Upon-Tyne NE1 7RU

, UK

e-mail: nilanjan.chakraborty@ncl.ac.uk

1

Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received February 7, 2014; final manuscript received January 19, 2015; published online March 3, 2015. Assoc. Editor: Oronzio Manca.

*J. Heat Transfer*. May 2015, 137(5): 052504 (12 pages)

**Published Online:**May 1, 2015

Article history

Received:

February 7, 2014

Revision Received:

January 19, 2015

Online:

March 3, 2015

Citation

Yİğİt, Ş., Poole, R. J., and Chakraborty, N. (May 1, 2015). "Laminar Natural Convection of Bingham Fluids in Inclined Differentially Heated Square Enclosures Subjected to Uniform Wall Temperatures." ASME. *J. Heat Transfer*. May 2015; 137(5): 052504. https://doi.org/10.1115/1.4029763

Download citation file:

- Ris (Zotero)
- Reference Manager
- EasyBib
- Bookends
- Mendeley
- Papers
- EndNote
- RefWorks
- BibTex
- ProCite
- Medlars

Close

#### Sign In

### Get Email Alerts

### Cited By

Effect of Operational Parameters on the Thermal Performance of Flat Plate Oscillating Heat Pipe

J. Heat Transfer (December 2019)

Heat Transfer and Flow Structurein a Latticework Duct WithDifferent Sidewalls

J. Heat Transfer (December 2019)

Thermoelastic Interactions in a Slim Strip Due to a Moving Heat Source Under Dual-Phase-Lag Heat Transfer

J. Heat Transfer (December 2019)

### Related Articles

The Effect of Spatially Nonuniform Internal Heating on the Onset of Convection in a Horizontal Fluid Layer

J. Heat Transfer (June, 2016)

Effect of Phase Thermal Modulation Without Stationary Temperature Gradient on the Threshold of Convection

J. Heat Transfer (October, 2016)

Natural Convection of Viscoplastic Fluids in a Square Enclosure

J. Heat Transfer (December, 2013)

A Dimensionless Model for Transient Turbulent Natural Convection in Isochoric Vertical Thermal Energy Storage Tubes

J. Thermal Sci. Eng. Appl (June, 2018)

### Related Chapters

Heating a Room by Natural Convection

Case Studies in Fluid Mechanics with Sensitivities to Governing Variables

Optimum Geometric Arrangment of Vertical Rectangular Fin Arrays in Natural Convection

Inaugural US-EU-China Thermophysics Conference-Renewable Energy 2009 (UECTC 2009 Proceedings)

Numerical Analysis of a Latent Heat Storage Heat Exchanger Considering the Effect of Natural Convection

Inaugural US-EU-China Thermophysics Conference-Renewable Energy 2009 (UECTC 2009 Proceedings)