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pure and applied geophysics

, Volume 69, Issue 1, pp 100–109 | Cite as

Propagator matrices for some geothermal problems

  • Janardan G. Negi
  • Rishi Narain Singh
Article

Summary

In problems of linear flow of heat in inhomogeneous media, the governing equation is a second order ordinary differential equation with variable coefficients. When transformed into a set of first order ordinary differential equations with variable coefficients, the problem becomes amenable to an elegant method of propagator matrices. In this paper the propagator matrices for some steady and unsteady heat conduction problems (including a case of heat generation by an irreversible first order reaction) having conductivity and heat generation functions as piecewise continuous, have been described.

Keywords

Differential Equation Ordinary Differential Equation Heat Conduction Governing Equation Heat Generation 
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.

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References

  1. [1]
    H. N. Pollack,Steady heat conduction in layered mediums: The half space and sphere, J. Geophys. Res.70 (1965), 5645.Google Scholar
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    J. G. Negi andR. N. Singh,Geothermic models of variable thermal conductivities and source functions, under publication (1967).Google Scholar
  3. [3]
    F. Gilbert andG. E. Backus,Propagator matrices in elastic wave and vibration problems, Geophysics31 (1966), 326.Google Scholar
  4. [4]
    H. S. Carslaw andJ. C. Jaeger,Conduction of heat in solids, 2nd Ed. (Oxford University Press, 1959), 406.Google Scholar

Copyright information

© Birkhäuser Verlag 1968

Authors and Affiliations

  • Janardan G. Negi
    • 1
  • Rishi Narain Singh
    • 1
  1. 1.Theoretical Geophysics DivisionNational Geophysical Research InstituteHyderabadIndia

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