Skip to main content
SpringerLink
Log in

Similarity analysis of axisymmetric free convection on a horizontal infinite plate subjected to a mixed thermal boundary condition

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

Summary

Similarity analysis of the problem of axisymmetric free convection on a horizontal infinite plate is considered assuming that the plate is subjected to a mixed thermal boundary condition. It is shown that the thermal boundary condition is characterized by a nonnegative parameterm and the two cases ofm=0 andm=1 correspond to prescribed plate temperature and prescribed surface heat flux respectively. If one has to compute the heat transfer coefficient for various values ofm, there is no need to solve the boundary value problem everytime; it is enough to solve a certain polynomial equation provided the solution is known for any particular value ofm.

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

a 0(r),a 1(r),a 2(r):

coefficients in Eq. (1)

A :

transition parameter used in Eq. (22)

C :

function ofr defined in Eq. (8.1)

f :

dimensionless stream function

F :

dimensionless pressure

g :

acceleration due to gravity

G :

function ofr defined in Eq. (8.2)

m :

mixed thermal boundary condition parameter

N :

normalized heat transfer coefficient in Eq. (26)

Nu r :

Nusselt number

p :

fluid pressure

p e :

ambient pressure

P :

normalized pressure drop at the plate

Pr:

Prandtl number

r :

radial coordinate

S :

normalized stress at the plate

T :

temperature

T e :

ambient temperature

u :

velocity in the radial direction

w :

velocity in the axial direction

z :

axial coordinate

β:

coefficient of thermal expansion

η:

dimensionless similarity variable

θ:

dimensionless temperature

λ:

exponent inC

ν:

kinematic viscosity

ϱ:

ambient fluid density

ψ:

stream function

References

  1. Stewartson, K.: On the free convection from a horizontal plate. ZAMP9, 276–281 (1958).

    Google Scholar 

  2. Gill, W. N., Zeh, D. W., Casal, E. D.: Free convection on a horizontal plate. ZAMP16, 539–541 (1965).

    Google Scholar 

  3. Clarke, J. F., Riley, N.: Natural convection induced in a gas by the presence of a hot porous horizontal surface. Q. J. Mech. Appl. Math.28, 373–396 (1975).

    Google Scholar 

  4. Clarke, J. F., Riley, N.: Free convection and the burning of a horizontal fuel surface. J. Fluid Mech.74, 415–431 (1976).

    Google Scholar 

  5. Schneider, W.: Similarity solution for combined forced and free convection flow over a horizontal plate. Int. J. Heat Mass Transfer22, 1401–1406 (1979).

    Google Scholar 

  6. Merkin, J. H., Ingham, D. B.: Mixed convection similarity solutions on a horizontal surface. ZAMP38, 102–116 (1987).

    Google Scholar 

  7. Lin, H. T., Yu, W. S.: Free convection on a horizontal plate with blowing and suction. J. Heat Transfer110, 793–796 (1988).

    Google Scholar 

  8. Schlichting, H.: Boundary layer theory, 6th edn., pp. 93–96. New York: McGraw-Hill 1968.

    Google Scholar 

  9. Shih, I. Pai.: Viscous flow theory, pp. 67–71. Van Nostrand 1956.

  10. Mahmood, T., Merkin, J. H.: Similarity solutions in axisymmetric mixed convection boundary layer flow. J. Engng. Math.22, 73–92 (1988).

    Google Scholar 

  11. Cheng, P., Chau, W. C.: Similarity solutions for convection of ground water adjacent to horizontal impermeable surfaces with axisymmetric temperature distribution. Water Resour. Res.13, 768–772 (1977).

    Google Scholar 

  12. Merkin, J. H., Pop. I.: Free convection above a horizontal circular disk in a saturated porous medium. Wärme und Stoffunters.24, 53–60 (1989).

    Google Scholar 

  13. Ramanaiah, G., Malarvizhi, G.: Axisymmetric convection on a permeable horizontal surface embedded in a saturated porous medium with prescribed heat flux or temperature. J. Energy Heat Mass Transfer12, 91–100 (1990).

    Google Scholar 

  14. Ramanaiah, G., Malarvizhi, G.: Non-Darcy axisymmetric free convection on permeable horizontal surface in a saturated porous medium. Int. J. Heat Fluid Flow (in press).

  15. Ramanaiah, G., Malarvizhi, G.: Unified treatment of similarity solutions of free, mixed and forced convection problems in saturated porous media. Proc. of Sixth Int. Conf. on Numerical Methods in Thermal Problems, Pineridge, Swansea, U.K.6, 431–439 (1989).

    Google Scholar 

  16. Ramanaiah, G., Malarvizhi, G.: Unified treatment of free and mixed convection on a permeable vertical cylinder. Indian J. Tech.28, 604–608 (1990),

    Google Scholar 

  17. Ramanaiah, G., Malarvizhi, G.: Free convection on a horizontal plate in a saturated porous medium with prescribed heat transfer coefficient. Acta Mech.87, 73–80 (1991).

    Google Scholar 

Download references

Author information

Author notes

  1. G. Malarvizhi &  G. Ramanaiah

    Present address: Department of Mathematics, Anna University, 600025, Madras, India

Authors and Affiliations

    Authors
    1. G. Malarvizhi
      View author publications

      You can also search for this author in PubMed Google Scholar

    2. G. Ramanaiah
      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

    Malarvizhi, G., Ramanaiah, G. Similarity analysis of axisymmetric free convection on a horizontal infinite plate subjected to a mixed thermal boundary condition. Acta Mechanica 90, 53–60 (1991). https://doi.org/10.1007/BF01177399

    Download citation

    • Received:

    • Revised:

    • Issue Date:

    • DOI: https://doi.org/10.1007/BF01177399

    Keywords

    Search

    Navigation