Skip to main content
SpringerLink
Log in

Unsteady characteristics of laminar free convection in an enclosure in the presence of power law fluid at Ra = 107

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The present study deals with an unsteady laminar free convection inside the annuli confined between an outer square enclosure and an inner circular cylinder. The annuli are filled with non-Newtonian power law fluids. The inner cylinder is located at three positions along the vertical center line. The unsteadiness arising due to bifurcation of flow from steady state is also reported in this study. The flow characteristics were found to be steady in nature in case of shear thickening fluid. However, most of the cases in the shear thinning fluid regime are found to be unsteady in nature with periodic and non-periodic fluctuations. The bifurcation of the flow from steady to unsteady state is mainly governed by the location of the cylinder as well as the characteristics of non-Newtonian fluid. The Bernard cells arising due to very high convective flow at Ra = 107 are also observed in the flow fields.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

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

ρ :

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

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, \(U = {{Lu} \over \alpha },V = {{Lu} \over \alpha }\)

x, y :

Cartesian coordinates in x and y directions, m

X, Y :

Dimensionless coordinates in x and y directions, \(X = {x \over L},\,Y = {y \over L}\)

2D :

Two dimensional

α :

Thermal diffusivity, m2/s

β :

Thermal expansion coefficient, 1/K

ζ :

Distance of bottom wall from the center of circular cylinder

η :

Effective viscosity, Ns/m2

ρ :

Density, Kg/m3

ϕ :

Angle of internal cylinder

θ :

Dimensionless temperature, \(\theta = {{T - {T_c}} \over {{T_h} - {T_c}}}\)

T :

Dimensionless time, \(\tau = {{t\alpha } \over {{L^2}}}\)

c :

Cold/cooled

h :

Hot/heated

m :

Mean

References

  1. 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 

  2. 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 

  3. 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 

  4. 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 

  5. 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 

  6. 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 

  7. 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 

  8. 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 

  9. 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 

  10. 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 

  11. 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 

  12. P. Meshram, S. Bhardwaj, A. Dalal and S. Pati, Effects of the inclination angle on natural convection heat transfer and entropy generation in a square porous enclosure, Numer. Heat Transfer, Part A: Appl., 70 (2016) 1271–1296.

    Article  Google Scholar 

  13. S. Dutta, A. K. Biswas and S. Pati, Natural convection heat transfer and entropy generation inside porous quadrantal enclosure with non-isothermal heating at the bottom wall, Numer. Heat Transfer, Part A: Appl., 73 (2018) 222–240.

    Article  Google Scholar 

  14. G. C. Pal, N. Goswami and S. Pati, Numerical investigation of unsteady natural convection heat transfer and entropy generation from a pair of cylinders in a porous enclosure, Numer. Heat Transfer, Part A: Appl., 74 (2018) 1323–1341.

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. 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 

  17. 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 

  18. 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 

  19. 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 

  20. M. Lamsaadi, M. Naimi, M. Hasnaoui and M. Mamou, Natural convection in a tilted rectangular slot containing Non-Newtonian Power-Law fluids and subject to a longitudinal thermal gradient, Numerical Heat Transfer, Part A: Applications, 50 (2006) 561–583.

    Article  Google Scholar 

  21. 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 

  22. M. H. Matin, I. Pop and S. Khanchezar, Natural convection of power-law fluid between two-square eccentric duct annuli, Journal of Non-Newtonian Fluid Mechanics, 197 (2013) 11–23.

    Article  Google Scholar 

  23. S. Yigit, R. J. Poole and N. Chakraborty, Effects of aspect ratio on natural convection of Bingham fluids in rectangular enclosures with differentially heated horizontal walls heated from below, International Journal of Heat and Mass Transfer, 80 (2015) 727–736.

    Article  Google Scholar 

  24. 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 

  25. S. Pandey, Y. G. Park and M. Y. Ha, Flow and heat transfer characteristics of non-Newtonian fluid in a square enclosure containing an internal cylinder, Journal of Mechanical Science and Technology, 34(7) (2020) 3079–3094.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1A5A808320111).

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong Gap Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Man Yeong Ha
    View author publications

    You can also search for this author in PubMed Google Scholar

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pandey, S., Park, Y.G. & Ha, M.Y. Unsteady characteristics of laminar free convection in an enclosure in the presence of power law fluid at Ra = 107. J Mech Sci Technol 34, 3457–3470 (2020). https://doi.org/10.1007/s12206-020-0738-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-020-0738-7

Keywords

Search

Navigation