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The Numerical Simulation of Double-Diffusive Mixed Convection Flow in a Lid-Driven Porous Cavity with Magnetohydrodynamic Effect

  • Research Article - Mechanical Engineering
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Abstract

In this paper, the numerical investigation of double-diffusive mixed convection with magnetohydrodynamic flow in an enclosed cavity is presented. The uniform temperature and concentration are imposed along the vertical walls and the horizontal walls which are considered as insulated. The flow behaviour is analysed for two different conditions. In first case, the top wall moves towards left at a constant velocity (U o), while the other walls remain stationary. In the second case, the top wall moves towards right with constant velocity (U o), while the other walls remain stationary. The convective flux in the transport equations is discretized using finite volume technique with third-order deferred quadratic upwind interpolation for convection kinematics scheme at the inner nodes and the second-order central difference scheme at the outer nodes. The pressure and velocity terms are coupled by SIMPLE algorithm. The present numerical simulation is compared with the reported literature and is found to be in good agreement. The Hartmann number (1 ≤ Ha ≤ 25), Lewis number (1 ≤ Le ≤ 50) and aspect ratio (1 ≤ A ≤ 2) are varied over a wide range to analyse the non-dimensional horizontal (U) and vertical velocities (V), stream line contours, temperature and concentration gradients. The present analysis is carried out at constant Buoyancy ratio (N = 1) and Prandtl (Pr = 0.7), Richardson (Ri = 1.0), Darcy (Da = 1.0) and Reynolds (Re = 100) numbers. The effect of Ha, Le and A on the average Nusselt (Nu) and Sherwood (Sh) numbers is also presented.

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Abbreviations

A :

Aspect ratio

B o :

Magnetic induction (tesla)

C :

Concentration

D :

Mass diffusivity (m2s−1)

Da :

Darcy number (K / L 2)

F c :

Geometric function

g :

Gravitational acceleration (ms−2)

Gr C :

Grashof number ( = gβ C ΔCL 3 / ν 2)

Gr T :

Grashof number ( = gβ T ΔTL 3 / ν 2)

h s :

Mass transfer coefficient (ms−1)

H :

Enclosure height (m)

Ha :

Hartmann number

k :

Thermal conductivity (Wm−1K−1)

K :

Permeability (m2)

L :

Enclosure length (m)

Le :

Lewis number ( = Sc / Pr)

N :

Buoyancy ratio (= Gr T / Gr C )

Nu :

Nusselt number (= hL / k)

P :

Dimensionless pressure (= pH2 / ρν 2)

Pr :

Prandtl number ( = ν / α)

Re :

Reynolds number (= V o L / ν)

Ri :

Richardson number (Gr T / Re 2)

Sc :

Schmidt number (= ν / D)

Sh :

Sherwood number (= hsL/D)

T :

Dimensional temperature (K)

U, V :

Dimensionless velocity components along x and y axes (= u / V o)

X, Y :

Dimensionless Cartesian coordinates (= x / H)

α :

Thermal diffusivity (m2 s−1)

β :

Fluid thermal expansion coefficient (K−1)

θ :

Dimensionless temperature (T−T C / T H −T C )

μ :

Effective dynamic viscocity (Pa-s)

ν :

Effective kinematic viscocity (m2s−1)

ρ :

Local fluid density (kgm−3)

ρ o :

Fluid density at bottom surface (kgm−3)

ɛ :

Porosity

σ :

Fluid electrical conductivity (Wm−1K−1)

avg:

Average

C :

Cold, concentration

f :

Fluid

H :

Hot

T :

Temperature

L :

Low

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Authors and Affiliations

  1. School of Mechanical and Building Sciences, VIT University, Vellore, Tamil Nadu, 632014, India

    C. G. Mohan & A. Satheesh

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  1. C. G. Mohan
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  2. A. Satheesh
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Mohan, C.G., Satheesh, A. The Numerical Simulation of Double-Diffusive Mixed Convection Flow in a Lid-Driven Porous Cavity with Magnetohydrodynamic Effect. Arab J Sci Eng 41, 1867–1882 (2016). https://doi.org/10.1007/s13369-015-1998-x

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  • DOI: https://doi.org/10.1007/s13369-015-1998-x

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