Abstract
Magnetohydrodynamic free convection in a horizontal annulus formed by two isothermal surfaces and partially partitioned with a conductive ring was numerically studied by using finite element method. The numerical investigation was performed for various values of Rayleigh numbers (between 10^{4} and 10^{6}), Hartmann number (between 0 and 40), magnetic inclination angle (between 0° and 90°), thermal conductivity ratio (between 0.01 and 100) and various locations of the conductive partition. Average Nusselt number enhances as the value of Rayleigh number, magnetic inclination angle and thermal conductivity ratio increases and as the value of Hartmann number decreases. The location of the partial conductive partition on the average Nusselt number becomes more effective for higher values of Rayleigh number and lower values of Hartmann number. Heat transfer process is effective when the partition is located on the bottom part of the hot wall. Heat transfer enhancement with location of the partition depends on the inclination angle of the magnetic field. Second law analysis of the system with entropy generation was also performed. It was observed that for higher values of magnetic field strength and lower values of magnetic inclination angle the entropy generation rate reduces, while the conductivity ratio increases the entropy generation rate.
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Abbreviations
 \({B}_{0}\) :

Magnetic field strength
 Gr:

Grashof number, \(\frac{g \beta _{\text{f}}(T_{\mathrm{h}}T_{\mathrm{c}}H^3}{\nu _{\mathrm{f}}^2}\)
 h :

Local heat transfer coefficient (W m^{−2} K^{−1})
 Ha:

Hartmann number, \(B_{0} H \sqrt{\frac{\sigma _{\mathrm{nf}}}{\rho _{\mathrm{nf}} \nu _\mathrm{f}}}\)
 k :

Thermal conductivity (W m^{−1} K^{−1})
 D :

Diameter (m)
 n :

Unit normal vector
 Nu:

Local Nusselt number
 p :

Pressure (Pa)
 Pr:

Prandtl number \(\frac{\nu _\mathrm{f}}{\alpha _{\mathrm{f}}}\)
 r :

Radius (m)
 S :

Entropy generation rate per unit volume (W m^{−3} K^{−1})
 S* :

Normalized entropy generation rate
 T :

Temperature (K)
 t :

Thickness (m)
 u, v :

x–y velocity components (m s^{−1})
 x, y :

Cartesian coordinates (m)
 \(\alpha\) :

Thermal diffusivity (m^{2} s^{−1})
 \(\alpha\) :

Location of the partition
 \(\beta\) :

Expansion coefficient (K^{−1})
 \(\gamma\) :

Magnetic inclination angle
 \(\theta\) :

Nondimensional temperature,
 \(\mu\) :

Dynamic viscosity (kg ms^{−1})
 \(\nu\) :

Kinematic viscosity (m^{2} s^{−1})
 \(\rho\) :

Density of the fluid (kg m^{−3})
 \(\sigma\) :

Electrical conductivity (S m^{−1})
 c:

Cold wall
 m:

Average
 h:

Hot wall
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Selimefendigil, F., Oztop, H.F. & Mahian, O. Effects of a partially conductive partition in MHD conjugate convection and entropy generation for a horizontal annulus. J Therm Anal Calorim 139, 1537–1551 (2020). https://doi.org/10.1007/s1097301908532x
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Keywords
 Natural convection
 Partially partitioned annulus
 Magnetohydrodynamics
 Finite element method