13-3] TEMPERATURE 689 



Let ^ = heat production rate of equipment, Btu/min (approximately 

 equal to input power) 



U = heat transfer coefficient of equipment enclosure for combined 

 radiation and conduction, Btu/sq ft-min-°F 



A = area of equipment housing, sq ft 



tout = external temperature of equipment housing, °F 



tin = temperature inside equipment housing, °F 



JV = flow rate of cooling fluid, Ib/min 



hin = specific enthalpy of entering fluid, Btu/lb 



hout = specific enthalpy of fluid at exit, Btu/lb. 



Then the steady-state heat flow can be expressed by equating the heat 

 removed by the cooling fluid to the total heat load: 



lV{hout - h..n) = ^+UA {tout - tin). (13-2) 



If the cooling fluid undergoes no change of state, the equation becomes: 



lVC^^t = Si+UA {tout - frn) (13-3) 



where Cp = average specific heat of cooling fluid over the operating 

 temperature range Btu/lb-°F 



A/ ^ temperature rise in cooling fluid, °F 



Equation 13-2 applies to any system using fluids for cooling. If applied 

 to a system similar to Fig. 13-3d, JV would still represent the flow rate 

 of cooling fluid in Ib/min although the flow would be only that of the 

 evaporated fluid. The h^n would be the specific enthalpy of the saturated 

 liquid; therefore, hout — hin would equal hfg, the latent heat of vaporization. 



Equation 13-3 is useful for obtaining a preliminary estimate of the 

 required rate of flow of cooling fluid in any proposed system similar to those 

 of Fig. 13-3a, b, or c. In such a study, the quantities on the right-hand 

 side would be calculated. The value for A/ would be the result of an 

 estimate of the difi^erential temperature required between the hottest 

 component and the cooling fluid. This is often obtained by assuming a 

 heat-transfer efficiency 77 defined as follows 



^^ (13-4) 



/max - // 



^here/niiix = maximum allowable component surface temperature 

 // = temperature of entering cooling fluid. 



