Impact of Magnetic Field on Thermal Convection in a Linearly Heated Porous Cavity

  • Aakash Gupta
  • Sayanta Midya
  • Nirmalendu Biswas
  • Nirmal K. Manna
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)


Combined effect of magnetic field and buoyancy on the thermo-fluid flow in a porous cavity is examined in this work considering top cold, bottom insulated and sidewalls linearly heated. The study is conducted extensively using an indigenous code. Fundamentals of thermo-fluid flow in the cavity are explored to appreciate heat transfer characteristics under the parametric variations of Rayleigh number (Ra), Hartmann number (Ha) and Darcy number (Da). The ranges of these parameters are Ra = 103 − 105, Ha = 10–100, Da = 10−7–10−3. Moreover, the variations in magnetic field inclination angle (\(\gamma\) = 0 − 180°, with respect to the cavity base) and porosity (\(\varepsilon\) = 0 − 1) are included. The temperature and flow fields are analyzed using isotherms and streamlines, whereas the visualization of convective heat flow is presented using heatlines. The exceptions in the general trends of the obtained average Nusselt number for clear domain as well as porous domain with the magnetic fields are noted along with the heat transfer characterization.


Natural convection Porous cavity Magnetic fields Heatlines Heat transfer 



Uniform magnetic field (tesla)


Darcy number


Cavity height/length scale, m


Hartmann number


Porous medium permeability, m2


Cavity length, m


Average Nusselt number


Pressure, Pa


Prandtl number


Rayleigh number


Temperature, K

u, v

Velocity components, m/s

U, V

Dimensionless velocity components

x, y

Cartesian coordinates, m

X, Y

Non-dimensional coordinates

Greek symbols


Thermal diffusivity, m2/s


Volumetric expansion coefficient, K−1


Inclination angle of the magnetic field


Non-dimensional temperature




Kinematic viscosity, m2/s


Non-dimensional heatfunction


Density, kg/m3


Electrical conductivity (μS cm−1)


Non-dimensional stream function









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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Aakash Gupta
    • 1
  • Sayanta Midya
    • 1
  • Nirmalendu Biswas
    • 1
  • Nirmal K. Manna
    • 1
  1. 1.Department of Mechanical EngineeringJadavpur UniversityKolkataIndia

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