A perfectly stirred tank is used to heat a flowing liquid. The dynamic model is shown in Fig. E14.4. Heater Thermocouple Flow system Tm P'

A perfectly stirred tank is used to heat a flowing liquid. The dynamic model is shown in Fig. E14.4.

where:
P is the power applied to the heater
Q is the heating rate of the system
T is the actual temperature in the tank
T_m is the measured temperature time constants have units of min
A test has been made with P€² varied sinusoidally as
P€² = 0.5 sin 0.2t

For these conditions, the measured temperature is
T€²_m = 3.464 sin (0.2t + Ï•) 

Find a value for the maximum error bound between T€² and T€²_m if the sinusoidal input has been applied for a long time.

Heater Thermocouple Flow system Tm P' Q' " 10 2 5s + 1 0.1s + 1 Figure E14.4