Advertisement

Acta Mechanica

, Volume 151, Issue 1–2, pp 103–114 | Cite as

Free convection from a vertical permeable circular cone with non-uniform surface temperature

  • M. A. Hossain
  • S. C. Paul
Original Papers

Summary

Laminar free convection from a vertical permeable circular cone maintained at nonuniform surface temperature is considered. Non-similar solutions for boundary-layer equations are found to exist when the surface temperature follows the power law variations with the distance measured from the leading edge. The numerical solutions of the transformed non-similar boundary-layer equations are obtained by using three methods, namely, (i) a finite difference method, (ii) a series solution method, and (iii) an asymptotic solution method. Solutions are obtained in terms of skin friction, heat transfer, velocity profile and temperature profile for smaller values of Prandtl number and temperature gradient are displayed in both tabular and graphical forms. Finite difference solutions are compared with the solutions obtained by perturbation and asymptotic techniques and found to be in excellent agreement.

Keywords

Heat Transfer Finite Difference Prandtl Number Finite Difference Method Skin Friction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Merk, E. J., Prins, J. A.: Thermal convection in laminar boundary layer. Appl. Sci. Res.4A, 11–24 (1953) and 195–206 (1954).Google Scholar
  2. [2]
    Braun, W. H., Ostrach, S., Heighway, J. E.: Free convection similarity flows about two-dimensional and axisymmetric bodies with closed lower ends. Int. J. Heat Mass Transfer2, 121–135 (1961).Google Scholar
  3. [3]
    Hering, R. G., Grosh, R. J.: Laminar free convection from a non-isothermal cone. Int. Heat Mass Transfer5, 1059–1068 (1962).Google Scholar
  4. [4]
    Hering, R. G.: Laminar free convection from a non-isothermal cone at low Prandtl numbers. Int. J. Heat Mass Transfer8, 1333–1337 (1965).Google Scholar
  5. [5]
    Roy, S.: Free convection over a slender vertical cone at high Prandtl numbers. ASME J. Heat Transfer101, 174–176 (1974).Google Scholar
  6. [6]
    Na, T. Y., Chiou, J. P.: Laminar natural convection over a slender vertical frustum of a cone. Wärme und Stoffübertragung12, 83–87 (1979).Google Scholar
  7. [7]
    Sparrow, E. M., Guinle, L. D. F.: Daviation from classical free convection boundary layer theory at low Prandtl numbers. Int. J. Heat Mass Transfer11, 1403–1415 (1968).Google Scholar
  8. [8]
    Lin, F. N.: Laminar free convection from a vertical cone with uniform surface heat flux. Letters in Heat and Mass Transfer3, 45–58 (1976).Google Scholar
  9. [9]
    Kuiken, H. K.: Axisymmetric free convection boundary layer flow past slender bodies. Int. J. Heat Mass Transfer11, 1143–1153 (1968).Google Scholar
  10. [10]
    Oosthuizen, P. H., Donaldson, E.: Free convection heat transfer from vertical cones. J. Heat Transfer94 C3, 330–331 (1972)Google Scholar
  11. [11]
    Na, T. Y., Chiou, J. P.: Laminar natural convection over a frustum of a cone. Appl. Sc. Res.35, 409–421 (1979).Google Scholar
  12. [12]
    Alamgir, M.: Over-all heat transfer from vertical cones in laminar free convection: an approximate method. ASME J. Heat Transfer101, 174–176 (1989).Google Scholar
  13. [13]
    Hossain, M. A., Munir, M. S., Takhar, H. S.: Natural convection flow of a viscous fluid about a truncated cone with temperature dependent viscosity and thermal conductivity. Acta Mech.140 (3–4), 171–181 (1999).Google Scholar
  14. [14]
    Hossain, M. A., Takhar, H. S.: Radiation effect on mixed convection along a vertical plate with uniform temperature. J. Heat Mass Transfer31, 243–248 (1996).Google Scholar
  15. [15]
    Hossain, M. A., Alim, M. A., Rees, D. A. S.: The effect of radiation on free convection from a porous vertical plate. App. Mech. And Eng.42, 181–191 (1999).Google Scholar
  16. [16]
    Butcher, J. C.: Implicit Runge-Kutta process. Math. Comp.18, 50–55 (1974).Google Scholar
  17. [17]
    Nachtsheim, P. R., Swigert, P.: Satisfaction of asymptotic boundary conditions in numerical solutions of systems of nonlinear equations of boundary-layer type. NASA TN-D3004 (1965).Google Scholar

Copyright information

© Springer-Verlag 2001

Authors and Affiliations

  • M. A. Hossain
    • 1
  • S. C. Paul
    • 1
  1. 1.Department of MathematicsUniversity of DhakaDhakaBangladesh

Personalised recommendations