﻿598 Prof. 0. W. Richardson : Some Applications 

 The electric current density is 



J = 47r <? 1 ^ 2 ^{7")r 2 dr s= ~ e \ r 4 %(r) dr 

 Jo ^ Jo 



o 



«• ... (6) 



remembering that 



I e- x x?dx = T(p + 1) =i?r(j9). 



*/0 



The specific electrical conductivity <j is <?/??* times the 

 coefficient of X in (6) when -=— and -^- are zero. Thus 



(^•) 



*= 4 ?k--^- ^A. ..... 



/r a 

 The thermal current density is 



W = 2irm I g 2 x(r)r*dr = — m I r 6 x(r)dr 



tt 7 r (7=T +3 /r 07 _ dA/2 i0 \.ldh-] 



718 . . . (8) 



To find the coefficient & of thermal conductivity, we have 



to substitute in (8) the condition that the electric current J 



is zero, or 







2hAX-~ = 

 ax 



\5 — 1 / h dx' 





We also have 







ldh 



IdO 





h dx 



~ 6 dx 





The coefficient T of thermal conductivity is therefore 





rp ir km 

 3 T 



"T 1 ; a 



(9) 



