A process involves a continuous-flow stirred tank with a mass of solid metal. The assumptions for the system are: (i) The tank is well mixed; (ii) The physical properties are constant; (iii) V = constant, F = constant [vol/time]; (iv) The solid metal block contributes a significant portion of the energy storage, and the temperature is uniform throughout the solid; (v) The heat transfer from the liquid to the metal is UA(T Tm); (vi) Heat losses are negligible; (vii) All variables are initially at steady state. (a) Apply unsteady state energy balances over the tank liquid contents and metal block to derive a dynamic model for the system. (b) Derive the transfer function relating the temperature of the metal block (Tm) to the inlet temperature (T0). Note: The temperature of the liquid in the tank, T, should not appear in this expression. (c) Using the data below, determine the response of Tm(t) to a step change in the inlet temperature of 10 C. Plot the response. Data F = 10 m3/min ; V = 5 m3 ; M = 50 kg ; UA = 50 kJ/(min)(K) ; Cp = 4.2 kJ/(kg)(K) ; Cpm = 0.4 kJ/(kg)(K) ; = 1000 kg/m3.

F To v o T Tm M = mass