Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T08:07:36.507Z Has data issue: false hasContentIssue false
  • English
  • Français

An axially symmetric forced convection problem

Published online by Cambridge University Press:  09 April 2009

J. A. Belward
J. A. Belward
Affiliation:
University of Queensland, St. Lucia, Qld, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A simple diffusion-convection heat transfer model is formulated which leads to an axially symmetric partial differential equation. The equation is shown to be closely related to a second one which is adjoint to the original equation in one variable can and be interpreted as a description of another diffusion-convection model. Fundamental solutions of the original equation are constructed and interpreted with reference to both models. Some boundary value problems are solved in series form and integral representations of the solutions are also given. The boundary value problems are shown to be equivalent to an integral equation and the correspondence between the two formulations is understood in terms of the two diffusion-convection problems. A Péclet number is defined in one of the boundary value problems and the behaviour of the solutions is studied for large and small values of this parameter.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 1 , August 1975 , pp. 1 - 17
Copyright
Copyright © Australian Mathematical Society 1975

References

Arscott, F. M. (1964), Periodic Differential Equations (Pergamon Press, London, 1964).Google Scholar
Belward, J. A. (1969), ‘The solution of a Fredholm integral equation on a finite interval’, Quart. AppI. Math. 27, 313–321.CrossRefGoogle Scholar
Belward, J. A. (to appear), ‘On the relationship of some Fredholm integral equations of the first kind to a family of boundary value problem's, J. Math. Anal. and Applics.Google Scholar
Burns, J. C. (1967), ‘The iterated equation of generalised axially symmetric potential theory’, J. Austral. Math. Soc. 7, 263–300.CrossRefGoogle Scholar
Campbell, R. (1955), Théorie générale de l'équation de Mathieu (Masson et cie, Paris, 1955).Google Scholar
Carrier, G. F., Krook, M., and Pearson, C. E. (1966), Functions of a complex variable (McGraw-Hill, New York, 1966).Google Scholar
Colton, D. (1969), ‘Uniqueness theorems for axially symmetric partial differential equations’, J. Math. Mech. 18, 921–930.Google Scholar
Erdélyi, A. et al. (1954), Higher Trancendental Functions, Volumes I, II, III, (McGraw-Hill, New York, 1954).Google Scholar
Koroniev, B. G., ‘On a plate lying on an elastic half-space whose modulus of elasticity is a power of the depth’, Dokl. Akad. Nauk. SSR, 112.Google Scholar
Meixner, J. and Schäfke, F. W. (1954), Matheiusche Funktionen und Sphäroidfunktionen (Springer-Verlag, Berlin, 1954).CrossRefGoogle Scholar
Pillow, A. F. (1970), ‘Diffusion and convection in viscous in viscous flow’, Bull. Austral. Math. Soc. 2, 145–164.CrossRefGoogle Scholar
Weinstein, A. (1953), ‘Generalised axially symmetric potential theory’, Bull. Amer. Math. Soc. 59, 20–38.CrossRefGoogle Scholar