Mr Wilson, On Convection of Heat. 411 



Consequently the temperature due to a continuous point 

 source at the origin must be given by 



yypcifC /*0 



ux r 2 +w 2 £ 2 



Consequently 



dt. 



„ itx a . / j r ur 



*>* 8 (*#)* r 



p'2/c 



;(a-r) 



4>7rk'r 



as before. 



I shall now consider the distribution of temperature due to a 

 straight line source of heat of strength Q per unit length, coin- 

 ciding with the axis of z when v = w = and u has a positive 

 value. 



This problem can easily be solved by the first method employed 

 for the point source. This method has however the disadvantage 

 that it is necessary to know the form of solution of the differential 

 equation to assume in order to solve the problem. It is interesting 

 therefore to solve the problem by means of Lord Kelvin's point 

 source method which enables the solution to be obtained by a 

 direct process of integration. 



In a medium at rest if a quantity of heat q is instantaneously 

 generated at a point P, then at any subsequent time the rise of 

 temperature due to this is given by 



oe 4 *'^ 



S ^ = 8(7r^' 



k 

 where k' = — , r is the distance from P, and t is the time since the 

 sp 



heat was generated at P. 



The temperature due to an instantaneous line source of heat 

 coinciding with the axis of z of strength q per unit length will 

 therefore be given by 



**-L 



qe -wt dz q J*gp 



8 {irk'tf birk't 



When the medium is in motion so that v = w = and u is positive 

 then the distribution of temperature due to an instantaneous 

 line source coinciding with the axis of z will be obtained by 



27—2 



