Temperature distribution in an electrically heated filament

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


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: d2T/dx2 + 5/2a (Tm4-T4) = 0, in which T is the temperature at a distance x from one of the ends, Tm is the value to which the temperature TL 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 = ∫Tθ [5aTm4(T1-T) -a(T15- T5]- i dT, (2) the value of Tl occurring in (1) being determined by the condition that, when the upper limit of the integral is made equal to Tl, x should become l.

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