The jacketed vessel in Fig. E6.21 is used to heat a liquid

Chapter 6, Problem 6.21

(choose chapter or problem)

The jacketed vessel in Fig. E6.21 is used to heat a liquid by means of condensing steam. The following information is available: (i) The volume of liquid within the tank may vary, thus changing the area available for heat transfer. (ii) Heat losses are negligible. (iii) The tank contents are well mixed. Steam condensate is removed from the jacket by a steam trap as soon as it has formed. (iv) Thermal capacitances of the tank and jacket walls are negligible. (v) The steam condensation pressure Ps is set by a control valve and is not necessarily constant. (vi) The overall heat transfer coefficient U for this system is constant. Condensate Figure E6.21 (vii) Flow rates qF and q are independently set by external valves and may vary. Derive a dynamic model for this process. The model should be simplified as much as possible. State any additional assumptions that you make. (a) Find transfer functions relating the two primary output variables h (level) and T (liquid temperature) to inputs qF, q, and Ts. You should obtain six separate transfer functions. (b) Briefly interpret the form of each transfer function using physical arguments as much as possible. (c) Discuss qualitatively the form of the response of each output to a step change in each input.