13-3] TEMPERATURE 691 



ture and pressure combinations which can be expected to occur in cooling 

 air during various flight conditions. For each combination of temperature 

 and pressure, a value o{ JV^ can be calculated from Equation 13-5. When- 

 ever TVs is less than the number of pounds of water vapor per pound of dry 

 air in the ambient atmosphere, condensation will occur. A cooling system 

 design similar to Fig. 13-3a will then need to be changed, either to provide 

 removal of water, or to avoid combinations of pressure and temperatures 

 which cause frost or water to appear. Closed cooling systems, such as in 

 Fig. 13-3b and 13-3c should operate very well with entrained condensate, 

 unless ice forms and blocks the air passage. The prevention of icing in air 

 passages requires very careful design. 



In many flight conditions, especially with higher-speed aircraft, the 

 steady-state heat transfer condition is never reached. For the transient 

 case, the heat flow may be described by 



W{hout - h,n) + MCM/dO) = ^ + UA{to^t - /.„) (13-6) 



where M = weight of equipment, lb 



Cp = average specific heat of equipment 



/ = average temperature of equipment at an instant of time 



6 = time, in minutes. 



Thus the heat inflow is balanced by the combined efi^ect of the heat 

 removed with the cooling fluid and the heat required to raise the tempera- 

 ture of the equipment. The factor di /dd is proportional to the temperature 

 difference between the equipment and internal environment and can 

 therefore be expected to be an exponential function. The analytical 

 evaluation of this function is not feasible for most practical equipment; 

 it may be obtained, if desired, by experiment. 



To look at the transient heat flow in another way, first integrate Equation 

 13-6 with respect to time between the limits do and 6, letting to be the value 

 of temperature at the initial time ^o-^ Then, solving for /, 



''^MC. 



' I {torU - t,^)dd - W / {hout - hin)dQ\ 



Jeo Jeo J 



^O) + UJ I {to.t - t,n)dd - W \ {h, 



(13-7) 



This equation shows the dependence of equipment temperature upon 

 the components of heat flow and upon its mass and specific heat. The 

 second and third terms in the bracket are exponentials; this variation in 

 temperature with time is therefore often called thermal lag. Full use should 

 be made of this principle when transient conditions exist; otherwise, a 

 cooling system may be designed with unnecessarily large capacity. 



iln the heat flow calculations, Q is used to represent time to avoid confusion with the tem- 

 perature symbols. 



