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Thermal magneto-hydrodynamics in a ventilated porous enclosure

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Abstract

The present study examines mixed convection in a ventilated cavity saturated with porous substance and heated at the right-bottom and top-left corners under the influence of uniform magnetic field applied externally. The analysis is carried out numerically using in-house CFD code. Five different heating configurations are analyzed. The effects of pertinent parameters such as Reynolds number (Re = 1–1000), Richardson number (Ri = 0.1–100), Darcy number (Da = 10−7–10−3), Hartmann number (Ha = 1–100), angle of magnetic field (\( \gamma \) = 0–180°) and porosity (ε = 0.1–1.0), on the flow and temperature fields are examined for the search of the appropriate configuration yielding optimum heat transfer rate. Furthermore, heat transfer characterization at different heating configurations and parametric combinations is assessed.

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Abbreviations

B :

magnetic field, Wb/m2

Da:

Darcy number

F C :

Forchheimer coefficient

g :

acceleration due to gravity, m/s2

Gr:

Grashof number

H :

height of the cavity/length scale, m

Ha:

Hartmann number

K :

permeability of porous medium, m2

L :

length of the cavity, m

Nu:

average Nusselt number

p :

pressure, Pa

P :

dimensionless pressure

Pr:

Prandtl number

Re:

Reynolds number

Ri:

Richardson number, Gr/Re2

T :

temperature, K

u,v :

velocity components, m/s

U,V :

dimensionless velocity components

x,y :

Cartesian coordinates, m

X,Y :

dimensionless coordinates

α :

thermal diffusivity, m2/s

β :

volumetric thermal expansion coefficient of fluid, K−1

Ψ :

dimensionless stream function

θ :

dimensionless temperature

η :

heat transfer parameter

ε :

porosity

ν :

kinematic viscosity, m2/s

ρ :

density, kg/m3

κ :

electrical conductivity, μS/cm

γ :

angle of the magnetic field

b,t :

bottom, top

c,h :

cooling, heating

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Acknowledgement

This is the extended version of a conference paper INCOM 2018 held at Jadavpur University during January 4–6, 2018 (INCOM18-195).

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Authors and Affiliations

  1. Department of Mechanical Engineering, Jadavpur University, Kolkata, 700032, India

    CHANDRACHUR HAZRA & NIRMAL K. MANNA

  2. Department of Power Engineering, Jadavpur University, Salt Lake, Kolkata, 700106, India

    NIRMALENDU BISWAS

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  1. CHANDRACHUR HAZRA
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Correspondence to NIRMAL K. MANNA.

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HAZRA, C., BISWAS, N. & MANNA, N.K. Thermal magneto-hydrodynamics in a ventilated porous enclosure. Sādhanā 45, 224 (2020). https://doi.org/10.1007/s12046-020-01459-2

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