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3D analysis of the combined effects of thermal buoyancy and viscous dissipation on the mixed convection of Bingham plastic fluid in a rectangular channel

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Abstract

The present study investigates numerically the three-dimensional mixed convection flow behavior of a Bingham plastic fluid within a rectangular horizontal duct. The latter has a square cross section, which is symmetrically heated at uniform wall temperature. The effect of the viscous dissipation on the hydrodynamic and thermal fields is taking into account through the energy equation. The finite volume method is used to discretize the governing equations, and the resulting algebraic system is solved iteratively by TDMA algorithm. The simulations are conducted for different values of the Grashof number (104 ≼ | Gr | ≼ 5 × 105), the Brinkman number (0 ≼ | Br | ≼ 10), and the Bingham number (10 ≼ | Bn | ≼ 20), for Re = 100 and Pr = 50. The results are analyzed through the distribution of the Nusselt number, the temperature and velocity profiles as well as unyielded plugs. For Br = 0, the Grashof number variation affects greatly the heat transfer and the fluid flow, in particular at the duct intermediate region. However, for Br ≠ 0, the Grashof number variation effect is noticeable in both the central and the fully developed regions. Moreover, the combination of Grashof, Brinkman, and Bingham numbers constitutes pertinent parameters control of the unyielded plugs.

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Abbreviations

a :

Width of ducts (m)

b :

Height of ducts (m)

Bn :

Bingham number

Br :

Brinkman number

D h :

Equivalent hydraulic diameter (m)

fRe :

Friction factor

g :

Gravitational acceleration (m s−2)

k :

Thermal conductivity (W m−1 K−1)

Gr :

Grashof number

Gz :

Greatz number

m :

Stress growth exponent (s)

Nu :

Nusselt number

P :

Cross-sectional mean pressure (Pa)

P * :

Dimensionless cross mean pressure

Pr :

Prandtl number

Ra :

Rayleigh number

Re :

Reynolds number

T :

Temperature (K)

T 0 :

Inlet fluid temperature (K)

u :

Longitudinal coordinate velocity (m s−1)

U :

Dimensionless longitudinal velocity

v :

Transverse coordinate velocity (m s−1)

V :

Dimensionless transverse velocity

w :

Transverse coordinate velocity (m s−1)

W :

Dimensionless transverse velocity

x :

Longitudinal coordinate (m)

X :

Dimensionless longitudinal coordinate

y :

Transverse coordinate (m)

Y :

Dimensionless transverse coordinate

z :

Transverse coordinate (m)

Z :

Dimensionless transverse coordinate

α :

Thermal diffusivity (m2 s−1)

β :

Coefficient of thermal expansion (K−1)

ϕ :

Dimensionless temperature

ρ :

Density (kg m−3)

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Authors and Affiliations

  1. Laboratory of Transport Phenomena, Faculty of Mechanical and Process Engineering, USTHB, B.P. 32, El-Alia Bab-Ezzouar, 16111, Algiers, Algeria

    Fetta Danane, Ahlem Boudiaf, Abdelkader Boutra, Nabila Labsi, Seif-Eddine Ouyahia & Youb Khaled Benkahla

  2. Centre de Développement DES Energies Renouvelables, CDER, 16340, Algiers, Algeria

    Fetta Danane

Authors
  1. Fetta Danane
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  2. Ahlem Boudiaf
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  3. Abdelkader Boutra
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  4. Nabila Labsi
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  5. Seif-Eddine Ouyahia
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  6. Youb Khaled Benkahla
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Correspondence to Fetta Danane.

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Technical Editor: Francis H. R. Franca.

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Danane, F., Boudiaf, A., Boutra, A. et al. 3D analysis of the combined effects of thermal buoyancy and viscous dissipation on the mixed convection of Bingham plastic fluid in a rectangular channel. J Braz. Soc. Mech. Sci. Eng. 40, 126 (2018). https://doi.org/10.1007/s40430-018-1048-1

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  • DOI: https://doi.org/10.1007/s40430-018-1048-1

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