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Some boundary-value problems for nonlinear (N) diffusion and pseudo-plastic flow

Published online by Cambridge University Press:  17 February 2009

C. Atkinson  and
C. R. Champion
C. Atkinson
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ
C. R. Champion
Affiliation:
Department of Mathematics, Imperial College, London SW7 2AZ
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Abstract

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In this article, exact and approximate techniques are used to obtain parameters of interest for two problems involving differential equations of power-law type. The first problem is related to non-linear steady-state diffusion, and is investigated by means of a hodograph transformation and an approximation using a path-independent integral. The second problem involves Poiseuille flow of a pseudo-plasticfluid, and a path-independent integral is derived which yields an exact result for the geometry under consideration.

Type
Research Article
Information
The ANZIAM Journal , Volume 33 , Issue 3 , January 1992 , pp. 255 - 268
Copyright
Copyright © Australian Mathematical Society 1992

References

[1] Amazigo, J. C., “Fully plastic crack in an infinite body under longitudinal shear”, Int. J. Solids Structures 10 (1974) 1003–1015.Google Scholar
[2] Atkinson, C., “Steady temperature field associated with a moving rod in a medium with nonlinear thermal conductivity”, Int. J. Engng. Sci. 26 (1988) 1071–1085.CrossRefGoogle Scholar
[3] Atkinson, C. and Bouillet, J. E., “Some qualitative properties of a generalised diffusion equation”, Math. Proc. Camb. Phil. Soc. 86 (1979) 495–510.CrossRefGoogle Scholar
[4] Atkinson, C. and Champion, C. R., “Some boundary value problems for the equation ”, Q. Jl. Mech. Appl. Math. 37 (1984) 401–419.Google Scholar
[5] Atkinson, C. and Champion, C. R., “A boundary integral equation formulation for problems involving nonlinear power-law materials”, IMA Journal Appl. Math. 35 (1985) 23–38.Google Scholar
[6] Atkinson, C. and Jones, C. W., “Similarity solutions in some nonlinear diffusion problems and in boundary layer flow of a pseudo-plastic fluid”, Q. Jl. Mech. Appl. Math. 27 (1974) 193–211.Google Scholar
[7] Atkinson, F. V. and Peletier, L. A., “Similarity solutions of a nonlinear diffusion equation”, Arch. Rat. Mech. Anal. 54 (1974) 373–392.CrossRefGoogle Scholar
[8] Bouillet, J. E. and Atkinson, C., “Qualitative properties of a generalised diffusion equations radial symmetric and comparison results”, J. Math. Anal. 95 (1983) 37–68.CrossRefGoogle Scholar
[9] Eshelby, J. D., “The elastic energy-momentum tensor”, J. Elasticity 5 (1975) 321–335.Google Scholar
[10] Hill, J. M., “Similarity solutions for nonlinear diffusion—a new integration procedure”, J. Eng. Math. 23 (1989) 141–155.Google Scholar
[11] Jones, C. W., “On the propagation of shock waves in regions of non-uniform density”, Proc. Roy. Soc. Lond. A. 228 (1955) 82–99.Google Scholar
[12] Philip, J. R., “n-diffusion”, Aust. J. Phys. 14 (1961) 1–13.CrossRefGoogle Scholar
[13] Rice, J. R., “A path independent integral and the approximate analysis of strain concentration by notches and cracks”, ASME J. Appl. Mech. 35 (1968) 379–386.Google Scholar