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Numerical study of magnetic field effect on natural convection heat and mass transfers in a square enclosure containing non-Newtonian fluid and submitted to horizontal temperature and concentration gradients

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Abstract

We study numerically natural convection driven heat and mass transfers in a square enclosure filled with electrically conducting non-Newtonian binary mixture in the presence of tilted external magnetic field. Dirichlet boundary conditions for the temperature and the concentration are applied to the vertical walls of the enclosure, while the two horizontal ones are assumed impermeable and insulated. A uniform magnetic field inclined with an angle θ relative to the horizontal axis is externally applied. Relevant parameters of the present problem are the Prandtl number, Pr, thermal Rayleigh number, RaT, Hartmann number, Ha, Lewis number, Le, buoyancy ratio, N, and behavior index, n. The numerical simulations are based on the complete governing equations for two-dimensional flows. The combined effect of behavior index and certain governing parameters on the flow structure and the heat and mass transfers is studied.

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Abbreviations

\(\overrightarrow {{B_{0}^{\prime } }}\) :

Applied magnetic field

D:

Mass diffusivity

g :

Gravitational acceleration

\(H^{\prime}\) :

Height of the enclosure

Ha :

Hartmann number

k :

Consistency index for a power-law fluid

Le :

Lewis number

N :

Buoyancy ratio

n :

Behavior index of power-law fluid

Nu :

Nusselt number

Nu r :

Ratio of Nusselt number

Pr :

Prandtl number

\(Ra_{T}\) :

Thermal Rayleigh number

S:

Dimensionless concentration

Sh :

Sherwood number

Sh r :

Ratio of Sherwood number

T :

Dimensionless temperature

\(\Delta T\) :

Characteristic difference of temperature

\(\Delta S\) :

Characteristic difference of concentration

\((u,v)\) :

Dimensionless axial and transverse velocities

\((x,y)\) :

Dimensionless axial and transverse co-ordinates

α :

Thermal diffusivity of fluid

\(\beta_{S}\) :

Solutal expansion coefficient of fluid

\(\beta_{T}\) :

Thermal expansion coefficient of fluid

θ :

Inclination angle of the applied magnetic field

λ :

Thermal conductivity of fluid

\(\mu_{a}\) :

Dimensionless apparent viscosity of fluid

ρ :

Density of fluid

\(\sigma\) :

Electrical conductivity of fluid

\(\psi\) :

Stream function

\(\nabla\) :

Nabla operator

':

Dimensional variable

C:

Cold wall

H:

Hot wall

max:

Maximum value

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Authors and Affiliations

  1. Faculty of Sciences and Technologies, Laboratory of Flows and Transfers Modelling, Sultan Moulay Slimane University, B.P. 523, Béni-Mellal, Morocco

    T. Makayssi & M. Lamsaadi

  2. Faculty of Sciences and Technologies, Industrial Engineering Laboratory, Sultan Moulay Slimane University, B.P. 523, Béni-Mellal, Morocco

    M. Kaddiri

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Makayssi, T., Lamsaadi, M. & Kaddiri, M. Numerical study of magnetic field effect on natural convection heat and mass transfers in a square enclosure containing non-Newtonian fluid and submitted to horizontal temperature and concentration gradients. Eur. Phys. J. Plus 136, 996 (2021). https://doi.org/10.1140/epjp/s13360-021-01986-9

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