Abstract
This study examines the combined analytical and numerical investigations of fully developed mixed convective flow in vertical double-passage porous annuli formed by three vertical concentric cylinders. Also, the effects of viscous dissipation and magnetic field are considered. The governing fully developed equations are analytically solved in the absence of viscous dissipation, while an implicit finite difference technique has been applied to solve the governing equations when the viscous dissipation effects are taken into consideration. Detailed and systematic numerical simulations are carried out to explore the effects of porosity, magnetic field, viscous dissipation, modified Grashof number, baffle position and radius ratio on the flow pattern, temperature distribution and heat transfer rate and are discussed through the graphs. The numerical results reveal that the presence of viscous dissipation has profound influence of thermal distribution, whereas the velocity profiles are significantly altered by the Darcy and Hartmann numbers.
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Abbreviations
- B 0 :
-
Magnetic field strength
- Br :
-
Brinkmann number
- Da :
-
Darcy number
- g :
-
Acceleration due to gravity
- Gr :
-
Grashof number
- GR :
-
Modified Grashof number
- Ha :
-
Hartman number
- K :
-
Permeability of porous medium
- k :
-
Thermal conductivity
- N :
-
Baffle position
- Nu :
-
Nusselt number
- T :
-
Temperature
- Re :
-
Reynolds number
- u,v:
-
Velocity components
- V :
-
Dimensionless axial velocity
- \( \beta \) :
-
Volumetric coefficient of thermal expansion
- \( \gamma \) :
-
Pressure gradient
- \( \lambda \) :
-
Radius ratio
- \( \theta \) :
-
Dimensionless temperature
- \( \rho \) :
-
Density
- \( \Lambda \) :
-
Viscosity ratio
- 1:
-
Inner passage
- 2:
-
Outer passage
- c:
-
Cold wall
- h:
-
Hot wall
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Acknowledgements
The authors MS and GN are, respectively, grateful to the managements of Presidency University, Bengaluru and J S S Academy of Technical Education, Bengaluru, and to VTU, Belgaum, India for their support and encouragement. Also, M. Sankar was supported by the Vision Group of Science and Technology (VGST) K-FIST (L1) grant funded by the Government of Karnataka.
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Sankar, M., Girish, N., Siri, Z. (2018). Fully Developed Magnetoconvective Heat Transfer in Vertical Double-Passage Porous Annuli. In: Narayanan, N., Mohanadhas, B., Mangottiri, V. (eds) Flow and Transport in Subsurface Environment. Springer Transactions in Civil and Environmental Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-8773-8_7
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