408 Mr Wilson, On Convection of Heat. 



This equation is applicable to solid or liquid media and to gaseous 

 media at constant pressure. 



7)0 



When a steady state has been attained ^- = 0, and the equa- 

 tion becomes 



Jr790 I W dd d0\ . 

 kV 2 -sp(u—+v~- + w—) = Q. 



All the cases considered in this paper are cases in which a steady 

 state has been attained. 



The first problem that will be considered is that of an infinite 

 uniform plane source of heat in a medium moving perpendicularly 

 to it with constant velocity u. Let the initial temperature of 

 the medium be zero, and take the plane yz as the source of heat so 

 that v — w = 0. Then the differential equation which has to be 



satisfied is k ^- — spu — = 0. This equation on integrating gives 



7)0 

 k^ spuO = C where is a constant. Let Q be the amount of 



heat given out by unit area of the plane source in unit time. 

 Then it is easy to see that when x is negative C = 0, provided u is 

 positive, and that when a; is positive C = — Q. When x is negative 



therefore log 6 = ~— x + A, where J. is a constant, and when x is 

 positive spud = Q, so that A = log ( — ) . Hence when x is negative 



log e= s ^+ log f-fi.) iflr .^4 J?; 



° k ° \spuj spu 



and when x is positive 6 = — . If the initial temperature of the 

 1 spu 



Q —x 

 medium is 6 then these equations become 6 — 6 = — e k and 



n spu 



— O = — respectively. 



SOU 



It is easy to see that the time t required to reach the steady 



ntil 

 Qk 



SQll^ 



state near the plane must be such that ~- t is a large quantity 



compared with — , or t must be large compared with 

 Thus the time necessary varies inversely as u 3 . 



The next problem that will be considered is that of a point 



