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

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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.

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Abbreviations

∇:

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

d o :

a/d

K :

coefficient of thermal conductivity

h :

heat transfer coefficient of the surface

References

  1. J. T. Holden, Quart. J. Mech. and A. Math.15 (1962).

  2. A. Singh andH. Singh,Thermal Deformations of a Sphere by Radiation from a Point Source, To appear in Proc. Ind. Acad. Sci.

  3. B. A. Boley andJ. H. Weiner,Theory of Thermal Stresses, (John Wiley and Sons Inc., 1962).

  4. A. Gray, G. B. Mathews andT. B. MacRobert,A Treatise on Bessel Functions and Their Applications to Physics, (Macmillan and Co. Ltd. London).

  5. L. Y. Luke,Integrals of Bessel functions, (McGraw-Hill Book Co. Inc., 1962).

  6. J. N. Goodier, Phil. Mag.23 (1962).

  7. N. Fox, Proc. Lon. Math. Soc.11 (1961).

  8. R. C. L. Bosworth,Heat Transfer Phenomenon, (Ass. Gen. Publ. Phy. Ltd.).

  9. W. H. Mc-Adams,Heat Transmission, (McGraw-Hill Book Co. Inc.).

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Authors and Affiliations

  1. Mathematics Department, Khalsa College, Amritsar, India

    Harinder Singh (Lecture)

  2. Methematics Department, Punjabi University, Patiala, India

    A. Singh (Reader)

Authors
  1. Harinder Singh
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  2. A. Singh
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Singh, H., Singh, A. Quasi-static thermal deformations of a sphere by radiation from a point source. PAGEOPH 101, 10–27 (1972). https://doi.org/10.1007/BF00876770

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  • DOI: https://doi.org/10.1007/BF00876770

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