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Unformatted text preview: Page - 1 - of 2 Inclass Heat Loss CHE 361 Done Thur Week 2 Exercise 4.10 pg. 71 -- Physical example of input/output relationship and transfer
function. Review Section 2.4 = Dynamic Models of Representative Processes,
2.4.1 Stirred-Tank Heating Process (Constant Holdup).
Assumptions from SEMD3:
1. Perfect mixing, T of product stream = T in tank
2. Inlet and outlet flow rates are equal, thus liquid holdup V is constant.
3. Density ρ and mass heat capacity C of liquid are constant, independent of T.
4. Heat losses are negligible - here we “relax” this assumption,
they are not negligible.
The contents of the stirred-tank heating system shown in Figure E4.10 are heated
at a constant rate of Q (Btu/h) using a gas-fired heater. The mass flow rate
w (lbm/h) and volume V (ft3) are constant, but the heat loss to the surroundings QL
(Btu/h) varies with the wind velocity v (ft/s) according to the expressions = UA (T − Ta )
U (t ) =where U * = coefficient at v =
U * +bv(t ),
where U *, A, b, and Ta are positive constants (>0).
Derive the transfer function between exit temperature T and wind velocity v. Page - 2 - of 2 G (s) = T '( s )
= process transfer function model desired
v '( s ) Modified energy balance (new QL term for Eqn. 2-36 on page 22 of SEMD3). dT
V ρ C = wC (Ti − T ) + Q − QL
= wC (Ti − T ) + Q − UA(T − Ta )
= wC (Ti − T ) + Q − (U * +bv ) A(T − Ta )
Linearize using the “all at once” approach for output T and input v (all other
independent “variables” held constant) and derive the transfer function. V ρC dT ' ∂RHS ∂RHS =
RHS + T' + v' dt ∂T at steady-state ∂v at steady-state ∂RHS = ∂T at steady-state ∂RHS = ∂v at steady-state ...
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This note was uploaded on 03/01/2012 for the course CHE 361 taught by Professor Staff during the Winter '08 term at Oregon State.
- Winter '08