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.

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e-mail: robpoole@liv.ac.uk
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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

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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

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Nilanjan Chakraborty

Nilanjan Chakraborty
1

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

1Corresponding 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

Newcastle University

,Newcastle-Upon-Tyne NE1 7RU

, UK

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

1Corresponding 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

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