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

## 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* = 10^{3} − 10^{5}, *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, m

^{2}*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, m

^{2}/s- \(\beta\)
Volumetric expansion coefficient, K

^{−1}- \(\gamma\)
Inclination angle of the magnetic field

- \(\theta\)
Non-dimensional temperature

- \(\varepsilon\)
Porosity

- \(\upsilon\)
Kinematic viscosity, m

^{2}/s- \(\varPi\)
Non-dimensional heatfunction

- \(\rho\)
Density, kg/m

^{3}- \(\kappa\)
Electrical conductivity (μS cm

^{−1})- \(\psi\)
Non-dimensional stream function

## Subscripts

- a
Ambient

- c
Cooling

- h
Heating

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