06_Wk2_HeatLossW12

# 06_Wk2_HeatLossW12 - 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

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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 ) 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. 2-36 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 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.

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