Advertisement

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)

Abstract

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.

Keywords

Natural convection Porous cavity Magnetic fields Heatlines Heat transfer 

Nomenclature

B

Uniform magnetic field (tesla)

Da

Darcy number

H

Cavity height/length scale, m

Ha

Hartmann number

K

Porous medium permeability, m2

L

Cavity length, m

Nu

Average Nusselt number

p

Pressure, Pa

Pr

Prandtl number

Ra

Rayleigh number

T

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

\(\alpha\)

Thermal diffusivity, m2/s

\(\beta\)

Volumetric expansion coefficient, K−1

\(\gamma\)

Inclination angle of the magnetic field

\(\theta\)

Non-dimensional temperature

\(\varepsilon\)

Porosity

\(\upsilon\)

Kinematic viscosity, m2/s

\(\varPi\)

Non-dimensional heatfunction

\(\rho\)

Density, kg/m3

\(\kappa\)

Electrical conductivity (μS cm−1)

\(\psi\)

Non-dimensional stream function

Subscripts

a

Ambient

c

Cooling

h

Heating

References

  1. 1.
    Rashidi, S., Esfahani, J.A., Maskaniyan, M.: Applications of magneto-hydrodynamics in biological systems-a review on the numerical studies. J. Magn. Magn. Mater. 439, 358–372 (2017)CrossRefGoogle Scholar
  2. 2.
    Sivaraja, C., Sheremet, M.A.: MHD natural convection in an inclined square porous cavity with a heat conducting solid block. J. Magn. Magn. Mater. 426, 351–360 (2017)CrossRefGoogle Scholar
  3. 3.
    Nayak, A.K., Malik, S., Venkateshwarlu, K., Jena, P.K.: Magneto-convection and its effect on partially active thermal zones in a porous square domain. Int. J. Heat Mass Transf. 95, 913–926 (2016)CrossRefGoogle Scholar
  4. 4.
    Sivasankaran, S., Ho, C.J.: Effect of temperature dependent properties on MHD convection of water near its density maximum in a square cavity. Int. J. Thermal Sci. 47, 1184–1194 (2008)CrossRefGoogle Scholar
  5. 5.
    Yu, P.X., Qiu, J.X., Qin, Q., Tian, Z.F.: Numerical investigation of natural convection in a rectangular cavity under different directions of uniform magnetic field. Int. J. Heat Mass Transfer 67, 1131–1144 (2013)CrossRefGoogle Scholar
  6. 6.
    Sathiyamoorthy, M., Chamkha, A.: Effect of magnetic field on natural convection flow in a liquid gallium filled square cavity for linearly heated side wall(s). Int. J. Thermal Sci. 49(9), 1856–1865 (2010)CrossRefGoogle Scholar
  7. 7.
    Ghasemi, B., Aminossadati, S.M., Raisi, A.: Magnetic field effect on natural convection in a nanofluid-filled square enclosure. Int. J. Thermal Sci. 50(9), 1748–1756 (2011)CrossRefGoogle Scholar
  8. 8.
    Mliki, B., Abbassi, M.A., Omri, A., Zeghmati, B.: Augmentation of natural convective heat transfer in linearly heated cavity by utilizing Nanofluid in the presence of magnetic field and uniform heat generation/absorption. Powder Tech. 284, 312–325 (2015)CrossRefGoogle Scholar
  9. 9.
    Mahmoudi, A.H., Pop, I., Shahi, M., Talebi, F.: MHD natural convection and entropy generation in a trapezoidal enclosure using Cu–water nanofluid, Computer. Fluids 72, 46–62 (2013)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Mansour, M.A., Bakier, M.A.Y.: Influence of thermal boundary conditions on MHD natural convection in square enclosure using Cu–water nanofluid. Energy Reports 1, 134–144 (2015)CrossRefGoogle Scholar
  11. 11.
    Kefayati, G.H.R.: FDLBM simulation of magnetic field effect on natural convection of non-Newtonian power-law fluids in a linearly heated cavity. Powder Tech. 256, 87–99 (2014)CrossRefGoogle Scholar
  12. 12.
    Kefayati, G.H.R.: Natural convection of ferrofluid in a linearly heated cavity utilizing LBM. J. Mol. Liq. 191, 1–9 (2014)CrossRefGoogle Scholar
  13. 13.
    Sathiyamoorthy, M., Basak, T., Roy, S., Pop, I.: Steady natural convection flows in a square cavity with linearly heated side wall(s). Int. J. Heat Mass Transf. 50, 766–775 (2007)CrossRefGoogle Scholar
  14. 14.
    Rashad, A.M., Armaghani, T., Chamkha, A.J., Mansoure, M.A.: Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: effects of a heat sink and source size and location, Chinese. J. Phys. 56, 193–211 (2018)Google Scholar
  15. 15.
    Emami, R.Y., Siavashi, M., Moghaddam, G.S.: The effect of inclination angle and hot wall configuration on Cu-water nanofluid natural convection inside a porous square cavity. Adv. Powder Technol. 29, 519–536 (2018)CrossRefGoogle Scholar
  16. 16.
    Biswas, N., Manna, N.K., Mahapatra, P.S.: Merit of non-uniform over uniform heating in a porous cavity. Int. Commun. Heat Mass Transf. 78, 135–144 (2016)CrossRefGoogle Scholar
  17. 17.
    Nemati, H., Farhadi, M., Sedighi, K., Ashorynejad, H.R., Fattahi, E.: Magnetic field effects on natural convection flow of nanofluid in a rectangular cavity using the Lattice Boltzmann model. Sci. Iranica B 19, 303–310 (2012)CrossRefGoogle Scholar
  18. 18.
    Ghasemi, K., Siavashi, M.: Lattice Boltzmann numerical simulation and entropy generation analysis of natural convection of nanofluid in a porous cavity with different linear temperature distributions on side walls. J. Mol. Liq. 233, 415–430 (2017)CrossRefGoogle Scholar
  19. 19.
    Patankar, S.V.: Numerical Heat Transfer and Fluid Flow. Hemisphere, New York (1980)Google Scholar

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

Personalised recommendations