Krishnan, K. S. ; Jain, S. C.
(1954)
*Temperature distribution in an electrically heated filament*
Nature, 173
(4409).
pp. 820-821.
ISSN 0028-0836

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Official URL: http://www.nature.com/nature/journal/v173/n4409/ab...

Related URL: http://dx.doi.org/10.1038/173820a0

## Abstract

The distribution of temperature in a filament electrically heated in vacuo has been studied by several previous authors. The differential equation defining the steady state is: d^{2}T/dx^{2} + 5/2a (Tm^{4}-T^{4}) = 0, in which T is the temperature at a distance x from one of the ends, T_{m} is the value to which the temperature T_{L} at the centre tends as the length 2l of the filament is increased indefinitely, keeping the heating current the same, and a is a constant determined by the cross-section of the filament, its thermal conductivity and the emissivity of its surface. Using the boundary conditions T = θ when x = 0, and dT/dx = 0 when x = l, one obtains x = ∫^{T}_{θ} [5aTm^{4}(T_{1}-T) -a(T_{1}^{5}- T^{5}]- ^{i} dT, (2) the value of T_{l} occurring in (1) being determined by the condition that, when the upper limit of the integral is made equal to T_{l}, x should become l.

Item Type: | Article |
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ID Code: | 28439 |

Deposited On: | 15 Dec 2010 12:02 |

Last Modified: | 04 Jun 2011 04:36 |

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