Abstract
Buoyancy-driven flows were investigated inside an enclosure with an inner cylinder embedded within it. The square enclosure contains the power law fluids. The effects are reported for the position of the cylinder along the horizontal and diagonal directions on the flow and thermal characteristics based on a rigorous unsteady numerical analysis. The cylinder was placed at several locations along the diagonal near the top-left corner, the center, and near the bottom right corner. The cylinder was also placed along the horizontal centerline near the right wall. This paper reports the effects of shear thickening and thinning fluids on the heat transfer mechanism in the enclosure. The thermal characteristics were more pronounced when the cylinder was near the bottom right corner than when near the top left corner and at the center. Pseudoplastic and dilatant fluids can be used in applications requiring increased and decreased heat transfer rates, respectively.
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Abbreviations
- D :
-
Diameter of internal circular cylinder, m
- G :
-
Grid
- g :
-
Gravitational acceleration, m/s2
- H :
-
Apparent viscosity
- k :
-
Thermal conductivity, W/mK
- L :
-
Length of the enclosure, m
- m :
-
Consistency index, Ns2/m2
- N :
-
Total number of grid elements
- N c :
-
Number of circumferential grid points along the cylinder
- Nu :
-
Instantaneous local Nusselt number
- \(\overline {Nu}\) :
-
Instantaneous surface-averaged Nusselt number
- 〈Nu〉:
-
Time-averaged local Nusselt number
- \(\left\langle {\overline {Nu}} \right\rangle \) :
-
Time and surface-averaged Nusselt number
- n :
-
Power law index
- p :
-
Pressure, Pa
- P :
-
Dimensionless pressure, \(P = {{{L^2}p} \over {\rho {\alpha ^2}}}\)
- Pr :
-
Prandtl number
- Ra :
-
Rayleigh number
- R :
-
Radius of internal circular cylinder, m
- R 2 :
-
Coefficient of multiple determination
- T :
-
Temperature, K
- T 0 :
-
Reference temperature, K
- T m :
-
Mean temperature, K
- ΔT :
-
Temperature difference between the hot and cold surfaces (Th-Tc), K
- t :
-
Time, s
- u, v :
-
Velocities in x and y directions, m/s
- U, V :
-
Dimensionless velocities in x and y directions
- x, y :
-
Cartesian coordinates in x and y directions, m
- X, Y :
-
Dimensionless coordinates in x and y directions
- 2D :
-
Two dimensional
- α :
-
Thermal diffusivity, m2/s
- β :
-
Thermal expansion coefficient, 1/K
- δ :
-
Distance of the center of circular cylinder from the center of the enclosure measured horizontally
- η :
-
Effective viscosity, Ns/m2
- ρ :
-
Density, Kg/m3
- ϕ :
-
Angle of internal cylinder
- θ :
-
Dimensionless temperature
- τ :
-
Dimensionless time, \(T = {{t\alpha} \over {{L^2}}}\)
- ξ :
-
Distance between the center of circular cylinder and center of enclosure measured diagonally
- c :
-
Cold/cooled
- h :
-
Hot/heated
- m :
-
Mean
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Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1A5A808320111).
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Recommended by Editor Yong Tae Kang
Sudhanshu Pandey received his M.S. degree from Indian Institute of Technology Madras, India in 2016, and pursuing Ph.D. at Pusan National University, Korea. His research interests are focused on natural convection, non-Newtonian fluids and computational fluid dynamics.
Yong Gap Park received his B.S. degree from Pusan National University, Korea, in 2008, and Ph.D. degree from Pusan National University, Korea in 2014. Dr. Park is currently a Professor at the School of Mechanical Engineering, Changwon National University in Changwon. His research interests are focused on natural convection, heat exchanger and computational fluid dynamics.
Man Yeong Ha received his B.S. degree from Pusan National University, Korea, in 1981, M.S. degree, in 1983, from Korea Advanced Institute of Science and Technology, Korea, and Ph.D. degree from Pennsylvania State University, USA in 1990. Dr. Ha is currently a Professor at the School of Mechanical Engineering at Pusan National University in Busan, Korea. He served as an Editor of the Journal of Mechanical Science and Technology. He is the member of Honorary Editorial Advisory Board of the International Journal of Heat and Mass Transfer. His research interests are focused on thermal management, computational fluid dynamics, and micro/nano fluidics.
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Pandey, S., Park, Y.G. & Ha, M.Y. Flow and heat transfer characteristics of non-Newtonian fluid in a square enclosure containing an internal cylinder. J Mech Sci Technol 34, 3079–3094 (2020). https://doi.org/10.1007/s12206-020-0639-9
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DOI: https://doi.org/10.1007/s12206-020-0639-9