Radiative Transfer of Energy in the Core of a Heated Tube

Abstract

WHILE investigating the temperature distribution along a thin-walled tube heated by passing an electric current through it in vacuowe had naturally to calculate the radiative transfer of energy occurring in the hollow core of the tube1. Taking the tube to be a circular cylinder of diameter D, and considering an annular ring of width dx, the net gain in energy by the ring due to radiative transfer can be readily calculated. If the ring is not too near the ends, this is found to be equal to : which may be expressed in the form: where σ is Stefan's constant of radiation, and the emissivity of the walls is taken to be unity. It is as though the hollow core had a thermal conductivity of magnitude :

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References

  1. 1

    Proc. Roy. Soc. (in the press).

  2. 2

    Bosworth, R. C. L., “Heat Transfer Phenomena”, 60 (John Wiley, New York, 1952). The expression given by Bosworth corresponds to 4/3 σl0T 3, which is due to his taking the density of radiational energy per unit volume as σT 4/c, whereas actually it should be four times this.

  3. 3

    Casimir, H. B. G., Physica, 5, 595 (1938).

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    Berman, R., Simon, F. E., and Ziman, J. M., Proc. Roy. Soc., A, 220, 176 (1953).

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    Maxwell, J. C., Phil. Trans. Roy. Soc., Part 1, 332 (1879); or “The Scientific Papers of James Clerk Maxwell”, 708.

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KRISHNAN, K., SUNDARAM, R. Radiative Transfer of Energy in the Core of a Heated Tube. Nature 188, 483–484 (1960). https://doi.org/10.1038/188483a0

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