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Flow and heat transfer characteristics of non-Newtonian fluid in a square enclosure containing an internal cylinder

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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

References

  1. S. Ostrach, Natural convection in enclosures, Advances in Heat Transfer, 8 (1972) 161–227.

    Article  Google Scholar 

  2. G. De Vahl Davis, Natural convection of air in a square cavity: A bench mark numerical solution, International Journal for Numerical Methods in Fluids, 3 (1983) 249–264.

    Article  Google Scholar 

  3. A. K. De and A. Dalal, A numerical study of natural convection around a square, horizontal, heated cylinder placed in an enclosure, International Journal of Heat and Mass Transfer, 49 (2006) 4608–4623.

    Article  Google Scholar 

  4. B. S. Kim, D. S. Lee, M. Y. Ha and H. S. Yoon, A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations, International Journal of Heat and Mass Transfer, 51 (2008) 1888–1906.

    Article  Google Scholar 

  5. S. H. Hussain and A. K. Hussein, Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations, International Communications in Heat and Mass Transfer, 37 (2010) 1115–1126.

    Article  Google Scholar 

  6. H. S. Yoon, M. Y. Ha, B. S. Kim and D. H. Yu, Effect of the position of a circular cylinder in a square enclosure on natural convection at Rayleigh number of 107, Physics of Fluids, 21 (2009) 047101.

    Article  Google Scholar 

  7. J. M. Lee, M. Y. Ha and H. S. Yoon, Natural convection in a square enclosure with a circular cylinder at different horizontal and diagonal locations, International Journal of Heat and Mass Transfer, 53 (2010) 5905–5919.

    Article  Google Scholar 

  8. D. H. Kang, M. Y. Ha, H. S. Yoon and C. Choi, Bifurcation to unsteady natural convection in square enclosure with a circular cylinder at Rayleigh number of 107, International Journal of Heat and Mass Transfer, 64 (2013) 926–944.

    Article  Google Scholar 

  9. H. S. Yoon, J. H. Jung and Y. G. Park, Natural convection in a square enclosure with two horizontal cylinders, Numerical Heat Transfer, Part A: Applications, 62 (2012) 701–721.

    Article  Google Scholar 

  10. Y. G. Park, M. Y. Ha, C. Choi and J. Park, Natural convection in a square enclosure with two inner circular cylinders positioned at different vertical locations, International Journal of Heat and Mass Transfer, 77 (2014) 501–518.

    Article  Google Scholar 

  11. Y. G. Park, H. S. Yoon and M. Y. Ha, Natural convection in square enclosure with hot and cold cylinders at different vertical locations, International Journal of Heat and Mass Transfer, 55 (2012) 7911–7925.

    Article  Google Scholar 

  12. Y. G. Park, M. Y. Ha and H. S. Yoon, Study on natural convection in a cold square enclosure with a pair of hot horizontal cylinders positioned at different vertical locations, International Journal of Heat and Mass Transfer, 65 (2013) 696–712.

    Article  Google Scholar 

  13. Y. G. Park, M. Y. Ha and J. Park, Natural convection in a square enclosure with four circular cylinders positioned at different rectangular locations, International Journal of Heat and Mass Transfer, 81 (2015) 490–511.

    Article  Google Scholar 

  14. Y. M. Seo, Y. G. Park, M. Kim, H. S. Yoon and M. Y. Ha, Two-dimensional flow instability induced by natural convection in a square enclosure with four inner cylinders. Part I: Effect of horizontal position of inner cylinders, International Journal of Heat and Mass Transfer, 113 (2017) 1306–1318.

    Article  Google Scholar 

  15. Y. M. Seo, G. S. Mun, Y. G. Park and M. Y. Ha, Two-dimensional flow instability induced by natural convection in a square enclosure with four inner cylinders. Part II: Effect of various positions of inner cylinders, International Journal of Heat and Mass Transfer, 113 (2017) 1319–1331.

    Article  Google Scholar 

  16. S. Pandey, Y. G. Park and M. Y. Ha, An exhaustive review of studies on natural convection in enclosures with and without internal bodies of various shapes, International Journal of Heat and Mass Transfer, 138 (2019) 762–795.

    Article  Google Scholar 

  17. A. Acrivos, A theoretical analysis of laminar natural convection heat transfer to non-Newtonian fluids, AIChE Journal, 6 (1960) 584–590.

    Article  Google Scholar 

  18. H. Ozoe and S. W. Churchill, Hydrodynamic stability and natural convection in Ostwald-de Waele and Ellis fluids: The development of a numerical solution, AIChE Journal, 18 (1972) 1196–1207.

    Article  Google Scholar 

  19. M. L. Ng and J. P. Hartnett, Natural convection in power law fluids, International Communication in Heat and Mass Transfer, 13 (1986) 115–120.

    Article  Google Scholar 

  20. M. Ohta, M. Akiyoshi and E. Obata, A numerical study on natural convective heat transfer of Pseudoplastic fluids in a square cavity, Numerical Heat Transfer, Part A: Applications, 41 (2002) 357–372.

    Article  Google Scholar 

  21. G. B. Kim, J. M. Hyun and H. S. Kwak, Transient buoyant convection of a power-law non-Newtonian fluid in an enclosure, International Journal of Heat and Mass Transfer, 46 (2003) 3605–3617.

    Article  Google Scholar 

  22. M. Lamsaadi, M. Naimi and M. Hasnaoui, Natural convection of non-Newtonian power law fluids in a shallow horizontal rectangular cavity uniformly heated from below, Heat and Mass Transfer, 41 (2005) 239–249.

    Google Scholar 

  23. M. Lamsaadi, M. Naimi, M. Hasnaoui and M. Mamou, Natural convection in a vertical rectangular cavity filled with a non-Newtonian power law fluid and subjected to a horizontal temperature gradient, Numerical Heat Transfer, Part A: Applications, 49 (2006) 969–990.

    Article  Google Scholar 

  24. M. Lamsaadi, M. Naimi, M. Hasnaoui and M. Mamou, Natural convection heat transfer in shallow horizontal rectangular enclosures uniformly heated from the side and filled with non-Newtonian power law fluids, Energy Conversion and Management, 47 (2006) 2535–2551.

    Article  Google Scholar 

  25. O. Turan, A. Sachdeva, N. Chakraborty and R. J. Poole, Laminar natural convection of power-law fluids in a square enclosure with differentially heated side walls subjected to constant temperatures, Journal of Non-Newtonian Fluid Mechanics, 166 (2011) 1049–1063.

    Article  Google Scholar 

  26. O. Turan, A. Sachdeva, R. J. Poole and N. Chakraborty, Aspect ratio and boundary conditions effects on laminar natural convection of power-law fluids in a rectangular enclosure with differentially heated side walls, International Journal of Heat and Mass Transfer, 60 (2013) 722–738.

    Article  Google Scholar 

  27. O. Turan, J. Lai, R. J. Poole and N. Chakraborty, Laminar natural convection of power-law fluids in a square enclosure submitted from below to a uniform heat flux density, Journal of Non-Newtonian Fluid Mechanics, 199 (2013) 80–95.

    Article  Google Scholar 

  28. M. H. Matin and W. A. Khan, Laminar natural convection of non-Newtonian power-law fluids between concentric circular cylinders, International Communications in Heat and Mass Transfer, 43 (2013) 112–121.

    Article  Google Scholar 

  29. S. Pandey, Y. G. Park and M. Y. Ha, Unsteady analysis of natural convection in a square enclosure filled with non-Newtonian fluid containing an internal cylinder, Numerical Heat Transfer, Part B: Fundamentals, 77 (2020) 1–21.

    Article  Google Scholar 

  30. S. V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC (1980).

    MATH  Google Scholar 

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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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Authors and Affiliations

  1. School of Mechanical Engineering, Pusan National University, 2, Busandaehak-ro 63beon-gil, Geumjeong-gu, Busan, 46241, Korea

    Sudhanshu Pandey & Man Yeong Ha

  2. School of Mechanical Engineering, Changwon National University, 20, Changwondaehak-ro, Uichang-gu, Changwon, 51140, Korea

    Yong Gap Park

Authors
  1. Sudhanshu Pandey
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  2. Yong Gap Park
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Corresponding author

Correspondence to Man Yeong Ha.

Additional information

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

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