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

  • Fetta Danane
  • Ahlem Boudiaf
  • Abdelkader Boutra
  • Nabila Labsi
  • Seif-Eddine Ouyahia
  • Youb Khaled Benkahla
Technical Paper


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.


Mixed convection Bingham plastic fluid Viscous dissipation Unyielded plugs 

List of symbols


Width of ducts (m)


Height of ducts (m)


Bingham number


Brinkman number


Equivalent hydraulic diameter (m)


Friction factor


Gravitational acceleration (m s−2)


Thermal conductivity (W m−1 K−1)


Grashof number


Greatz number


Stress growth exponent (s)


Nusselt number


Cross-sectional mean pressure (Pa)


Dimensionless cross mean pressure


Prandtl number


Rayleigh number


Reynolds number


Temperature (K)


Inlet fluid temperature (K)


Longitudinal coordinate velocity (m s−1)


Dimensionless longitudinal velocity


Transverse coordinate velocity (m s−1)


Dimensionless transverse velocity


Transverse coordinate velocity (m s−1)


Dimensionless transverse velocity


Longitudinal coordinate (m)


Dimensionless longitudinal coordinate


Transverse coordinate (m)


Dimensionless transverse coordinate


Transverse coordinate (m)


Dimensionless transverse coordinate

Greek characters


Thermal diffusivity (m2 s−1)


Coefficient of thermal expansion (K−1)


Dimensionless temperature


Density (kg m−3)


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Laboratory of Transport Phenomena, Faculty of Mechanical and Process EngineeringUSTHBAlgiersAlgeria
  2. 2.Centre de Développement DES Energies Renouvelables, CDERAlgiersAlgeria

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