A heat exchanger used to heat a glycol solution with a hot oil is known to exhibit first-order-plus-time-delay behavior, G₁(s) = T?(s)/Q?(s), where r is the outlet temperature deviation and Q? is the hot oil flow rate deviation. A thermocouple is placed 3 m downstream from the outlet of the heat exchanger. The average velocity of the glycol in the outlet pipe is 0.5m/s. The thermocouple also is known to exhibit first-order behavior; however, its time constant is expected to be considerably smaller than the heat exchanger time constant.

(a) Data form a unit step test in Q? on the complete system are shown in Figure. Using a method of your choice, calculate the time constants of this process from the step response.

(b) From your empirical model, find transfer functions for the heat exchanger, for the pipe, and for the thermocouple. Think of the model as the product of three transfer functions process, pipe flow, and sensor. What assumptions do you have to make to obtain these individual transfer functions from the overall transfer function?

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10.0 8.0 6.0 T"C) 4.0 2.0 10 15 Tirme (min) 20 25