HEATING AND COOLING CURVES
A machine can be considered as a homogeneous body developing heat internally at uniform rate and dissipating heat proportionately to its temperature rise,
Assume that a machine attains a temperature rise after the lapse of time t seconds.
In an element of time “dt” a small temperature rise “d” takes place.
Heat developed = p.dt
Heat developed = Gh.dq
Heat dissipated = Sql. dt
Therefore, total heat developed=heat stored + heat dissipated
Where is called as heating time constant and it has the dimensions of time.
Heating time constant is defined as the time taken by the machine to attain 0.623 of its final steady temperature rise.
The heating time constant of the machine is the index of time taken by the machine to attain its final steady temperature rise.
The value of heating time constant is larger for poorly ventilated machines with large or totally enclosed machines, the heating time constant may reach several hours or even days.
When a hot body is cooling due to reduction of the losses developed in it, the temperature time curve is again an exponential function
If motor where disconnected from supply during cooling, there would be no losses taking place and hence, final temperature reached will be the ambient temperature.
Cooling time constant is, therefore, defined as the time required cooling the machine down to 0.368 times the initial temperature rise above ambient temperature.