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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 StirredTank 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 stirredtank heating system shown in Figure E4.10 are heated
at a constant rate of Q (Btu/h) using a gasfired 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 )
QL
U (t ) =where U * = coefficient at v =
U * +bv(t ),
heat transfer
0
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. 236 on page 22 of SEMD3). dT
V ρ C = wC (Ti − T ) + Q − QL
dt
= 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 steadystate ∂v at steadystate ∂RHS = ∂T at steadystate ∂RHS = ∂v at steadystate ...
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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
 Staff
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