OCEAN TEMPEBATUEES 



355 



page 339, and the solution of the new equation will give the tem- 

 perature under the new conditions. The rate of change of heat due 

 to a horizontal flow H of the water can be readily derived as follows : 

 consider a rectangular element of volume (fig. 2) of unit length per- 

 pendicular to the direction of flow and of breadth dz measured in the 

 direction of flow and thickness dy normal to the direction of flow. 



Fig. 2. 



Then the rate at which heat enters into the element less the rate at 

 which it is removed will be 



HaOdy Ha(0 + d6) dy = HadBdij = H<r^- dzdy (44) 



oz 



which is the time rate of change of heat in the element due to the flow 

 of water. Multiplying equation (3) by dz to make it apply to the 

 element of volume now considered and adding the above expression 

 for rate of change of heat gives the new equation 



a-dydz'= 

 ot 



Ha-dydz 

 oz 



(45) 



Dividing through by adydz and substituting the value of Q and 

 from page 341 we have 



a z x] cos at + a 3 x + 1] fc(0 0J H 



which is the same as the temperature equation (10) with the term 



