Skip to main content
SpringerLink
Log in

Natural convection of micropolar fluids over a uniformly heated horizontal plate

  • Original Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

Numerical studies were performed to determine the laminar free convection of micropolar fluids along a uniformly heated horizontal plate. The coupled governing equations with boundary conditions were solved for the modified Rayleigh number over the ranges of 103 to 108 and various material parameters characterizing the micropolar fluids. Numerical results indicated that the normalized local Nusselt number attains its highest value at the edge of the heated plate and decreases monotonically along the plate surface, and achieves the lowest value at the center of the plate. The material properties of micropolar fluids have significant influences on both the heat transfer and flow field. In comparison with the Newtonian fluid, the micropolar fluids have considerably different features from the Newtonian fluid in Nusselt number, wall skin friction and wall couple stress.

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

B :

material parameter, L2/j

g :

acceleration of gravity (m/s2)

h :

heat transfer coefficient (W/m2·K)

j :

microinertia per unit mass (m2)

k :

thermal conductivity (W/m·K)

K v :

vortex viscosity (kg/m·s)

L :

plate width (m)

N :

dimensionless angular velocity component,L 2σ/α

Nu:

Nusselt number

Pr:

Prandtl number, ν/α

q :

heat flux from the heat source (W/m2)

Ra:

Rayleigh number,gβqL 4/kαν

r c :

thermal capacity ratio, ϱpCp/ϱC

r k :

thermal conductivity ratio,k p/k

r α :

thermal diffusivity ratio, ϱp/α

s :

ratio of the gyration vector and the fluid shear at the solid's boundary

T :

temperature (K)

T α :

ambient fluid temperature (K)

u :

horizontal velocity component (m/s)

U :

dimensionless horizontal velocity component,u/U e

U e :

characteristic velocity, α/L (m/s)

v :

vertical velocity component (m/s)

V :

dimensionless vertical velocity component,v/U e

x, y :

Cartesian coordinates (m)

X, Y :

dimensionless Cartesian coordinates,X=x/L,Y=y/L

σ:

angular velocity component (s−1)

α:

thermal diffusivity,k/ϱc (m2/s)

β:

coefficient of thermal expansion (K1−)

γ:

spin gradient viscosity (kg·m/s)

Δ:

material parameter,K v/μ

θ:

dimensionless temperature,k(T−T ∝)/(qL)

μ:

dynamic viscosity (kg·m/s)

ν:

kinematic viscosity, μ/ϱ (m2/s)

ψ:

stream function (m2/s)

Ψ:

dimensionless stream function, ψ/α

ω:

vorticity (s−1)

Ω:

dimensionless vorticity, ωL 2/α

p :

plate

∝:

ambient condition

References

  1. McAdams, W. H.: Heat transmission, 3rd ed. New York: McGraw-Hill 1968.

    Google Scholar 

  2. Goldstein, R. J., Sparrow, E. M., Jones, D. C.: Natural convection mass transfer adjacent to horizontal plates. Int. J. Heat Mass Transfer16, 1025–1035 (1973).

    Google Scholar 

  3. Lloyd, J. R., Moran, W. R.: Natural convection adjacent to horizontal surface of various planforms. ASME J. Heat Transf96, 443–447 (1974).

    Google Scholar 

  4. Sparrow, E. M., Carlson, C. K.: Local and average natural convection Nusselt number for a uniformly heated shrouded or unshrouded horizontal plate. Int. J. Heat Mass Transf29, 369–379 (1986).

    Google Scholar 

  5. Chambers, B., Lee, T. Y.: A numerical study of local and average natural convection Nusselt numbers for simultaneous convection above and below a uniformly heated horizontal thin plate. ASME J. Heat Transf119, 102–108 (1997).

    Google Scholar 

  6. Eringen, A. C.: Simple microfluid. Int. J. Engng Sci.2, 205–217 (1964).

    Google Scholar 

  7. Eringen, A. C.: Theory of micropolar fluids. J. Math. Mech.16, 1–18 (1966).

    Google Scholar 

  8. Eringen, A. C.: Theory of thermomicrofluids. J. Math. Analysis Appl.38, 480–496 (1972).

    Google Scholar 

  9. Ahmadi, G.: Self-similar solutions of incompressible micropolar boundary-layer flow over a semiinfinite plate. In. J. Engng Sci.14, 639–646 (1976).

    Google Scholar 

  10. Hassanian, I. A., Gorla, R. S. R.: Heat transfer to a micropolar fluid from a non-isothermal stretching sheet with suction and blowing. Acta Mech.84, 191–199 (1990).

    Google Scholar 

  11. Yucel, A.: Mixed convection in micropolar fluid flow over a horizontal plate with surface mass transfer. Int. J. Engng Sci.27, 1593–1602 (1989).

    Google Scholar 

  12. Rees, D. A. S., Bassom, A. P.: The Blasius boundary-layer flow of a micropolar fluid. Int. J. Engng Sci.34, 113–124 (1996).

    Google Scholar 

  13. Pop, I., Na, T.-Y.: Boundary layer flow of a micropolar fluid due to a stretching wall. Appl. Mech./ Ingenieur-Archiv67, 229–236 (1997).

    Google Scholar 

  14. Rees, D. A. S., Pop, I.: Free convection boundary-layer flow of a micropolar fluid from a vertical flat plate. IMA J. Appl. Math.61, 170–197 (1998).

    Google Scholar 

  15. Jena, S. K., Mathur, M. N.: Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a nonisothermal vertical flat plate. Int. J. Engng Sci.19, 1431–1439 (1991).

    Google Scholar 

  16. Peddieson, J.: An application of the micropolar fluid model to the calculation of turbulent shear flow. Int. J. Engng Sci.10, 23–32 (1972).

    Google Scholar 

  17. Rubin, S. G., Graves, R. A.: Viscous flow solution with a cubic spline approximation. Computers and Fluids1, 1–36 (1975).

    Google Scholar 

Download references

Author information

Author notes

  1. T. H. Hsu & S. P. How

    Present address: Department of Mechanical Engineering, National Kaohsiung, University of Applied Sciences, No. 415, Chien Kung Road, Kaohsiung, Taiwan, Republic of China

Authors and Affiliations

    Authors
    1. T. H. Hsu
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. S. P. How
      View author publications

      You can also search for this author in PubMed Google Scholar

    Rights and permissions

    Reprints and permissions

    About this article

    Cite this article

    Hsu, T.H., How, S.P. Natural convection of micropolar fluids over a uniformly heated horizontal plate. Acta Mechanica 155, 191–202 (2002). https://doi.org/10.1007/BF01176242

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01176242

    Keywords

    Search

    Navigation