Abstract
The present study investigates the influence of magnetic field on the heat transfer phenomena of rotating cylinder kept in the center of the square cavity. The numerical code for mixed convective flow with Magnetohydrodynamics is developed on the open-source CFD platform OpenFOAM. The developed solver is capable of simulating steady and unsteady flows on any arbitrary geometry. The center of the cylinder is fixed at the center of the cavity with varying blockage ratio (L/d = 2 and 4). The surface of the cylinder is kept as hot, and the two opposite vertical sides are kept cold, while the top and bottom surface are maintained as thermally insulated. The cylinder is rotated clockwise (ω = 50) and anticlockwise (ω = −50) about its center. The fluid is assumed to be incompressible and electric conducting in nature and the all walls of the cavity is also maintained as electrically insulated. The intensity of magnetic field is varied in terms of Hartmann number (Ha) in the range of Ha = 0 and 100 for the fixed Rayleigh number of Ra = 105. The flow and thermal field are analyzed through streamlines, isotherm contours for various Ha and ω (angular rotation). Furthermore, pertinent transport quantities as the Nusselt number is also determined to analyze the influence of magnetic field and angular rotation of the cylinder on the heat transfer. It is observed that the heat transfer and fluid flow behavior is significantly affected by the magnetic field and rotation of the cylinder.
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Abbreviations
- U :
-
Velocity of fluid (m s−1)
- p :
-
Pressure (N m−2)
- T :
-
Temperature (K)
- T ref :
-
Ambient temperature (K)
- j :
-
Electric current density (A m−2)
- B :
-
Applied magnetic field (kg s−2 A−1)
- g :
-
Acceleration due to gravity (m s−2)
- ϕ :
-
Electric potential (m2 kg s−3 A−1)
- L :
-
Side length of cube (m)
- Gr :
-
Grashof number
- Ha :
-
Hartmann number
- Ra :
-
Rayleigh number
- F :
-
Lorentz force (j × B) (N m−3)
- Pr :
-
Prandtl number
- Nu :
-
Nusselt number
- d :
-
Diameter of cylinder (m)
- ω :
-
Angular velocity (rad/s)
- x, y :
-
Cartesian coordinates (m)
- α :
-
Thermal diffusivity (m2 s−1)
- β :
-
Coefficient of thermal expansion (K−1)
- ρ :
-
Fluid density (kg m−3)
- σ :
-
Fluid electrical conductivity (s3 A2 m−3 kg−1)
- µ :
-
Dynamic viscosity (kg m−1 s−1)
- ν :
-
Kinematic viscosity (m2 s−1)
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Acknowledgements
Authors are sincerely gratified to government of India for contributing the financial support through MHRD scholarship to conduct the present numerical investigation.
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Singh, R.J., Gohil, T.B. (2019). Mixed Convection Heat Transfer in a Cavity with Rotating Cylinder Under the Influence of Magnetic Field. In: Saha, P., Subbarao, P., Sikarwar, B. (eds) Advances in Fluid and Thermal Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-13-6416-7_6
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DOI: https://doi.org/10.1007/978-981-13-6416-7_6
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