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pure and applied geophysics

, Volume 101, Issue 1, pp 10–27 | Cite as

Quasi-static thermal deformations of a sphere by radiation from a point source

  • Harinder Singh
  • A. Singh
Article
  • 31 Downloads

Summary

In this paper the quasi-static temperature and stress distributions set up in an elastic sphere by radiation from a point source at a finite distance from the centre of the sphere and out-side it, have been discussed. The temperature boundary condition has been taken in the general form involving an arbitrary function of time. The final solutions have been obtained in terms of series involving Legendre polynomials. Numerical calculations have been done on IBM 1620 Computer and a desk calculator. The results have been represented in graphs.

Keywords

Radiation Boundary Condition Numerical Calculation Stress Distribution Point Source 
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.

Notation

the del operator

u

the displacement vector

T

the excess of temperature over that at state of zero stress and strain

λ, μ

Lamé's constants

ν

λ/2(λ+μ) Poisson's ratio

α

coefficient of linear expansion

β

2(1+ν)α

a

radius of the sphere

d

distance of the point source from the centre of the sphere

do

a/d

K

coefficient of thermal conductivity

h

heat transfer coefficient of the surface

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References

  1. [1]
    J. T. Holden, Quart. J. Mech. and A. Math.15 (1962).Google Scholar
  2. [2]
    A. Singh andH. Singh,Thermal Deformations of a Sphere by Radiation from a Point Source, To appear in Proc. Ind. Acad. Sci.Google Scholar
  3. [3]
    B. A. Boley andJ. H. Weiner,Theory of Thermal Stresses, (John Wiley and Sons Inc., 1962).Google Scholar
  4. [4]
    A. Gray, G. B. Mathews andT. B. MacRobert,A Treatise on Bessel Functions and Their Applications to Physics, (Macmillan and Co. Ltd. London).Google Scholar
  5. [5]
    L. Y. Luke,Integrals of Bessel functions, (McGraw-Hill Book Co. Inc., 1962).Google Scholar
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    J. N. Goodier, Phil. Mag.23 (1962).Google Scholar
  7. [7]
    N. Fox, Proc. Lon. Math. Soc.11 (1961).Google Scholar
  8. [8]
    R. C. L. Bosworth,Heat Transfer Phenomenon, (Ass. Gen. Publ. Phy. Ltd.).Google Scholar
  9. [9]
    W. H. Mc-Adams,Heat Transmission, (McGraw-Hill Book Co. Inc.).Google Scholar

Copyright information

© Birkhäuser Verlag 1972

Authors and Affiliations

  • Harinder Singh
    • 1
  • A. Singh
    • 2
  1. 1.Mathematics DepartmentKhalsa CollegeAmritsarIndia
  2. 2.Methematics DepartmentPunjabi UniversityPatialaIndia

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