from a Body cooled by a Stream of Fluid. 



595 



it is convenient to denote the kydrodynamical stream- 

 function by Va, and the velocity-potential by V/3. h\ fig. 1, 



CL+OCL 



AA' and BB' denote adjacent stream-lines, and A'B' and 

 AB denote adjacent equipotential curves. Let 



and let 



Then, by hydrodynamics, 



AA' = d* 2 , 



AB = *i. 



oV£ 



0*2 



= ?> 



(3) 



where g is the velocity of the flow of the liquid at the point 



Consider the flow of heat in the time Dt into a prism 

 having unit length, and having ABB'A' for its cross-section 

 (fig. 1). We suppose that this prism is moving with the 

 liquid, and its velocity is therefore q. Let 6 be the initial 

 temperature of the liquid inside this prism, and let + 1)9 be 

 the temperature at the time J)t. The gain by the flow of heat 

 from AA' to BB / during this interval is 



and the oain by the flow from AB to A'B' is 



o# 



0*2 \ 0*2/ 



where k is the conductivity of the liquid. Hence, if c denote 

 the capacity for heat of the liquid per unit volume, the gain 

 of heat by the element contained by the prism is cd*iO*2 D0. 



2R2 



