The heat transfer from the reactor to the coolant is

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. The heat transfer from the reactor to the coolant is given by Q = UA ( T r - T c ). The reaction enthalpies Δ H 1 and Δ H 2 are based on per kmol of A reacted. The values of all parameters and feed values are listed in the table below: Variable Unit Value V r m 3 0.23 V c m 3 0.21 ρ r kg m - 3 1020 ρ c kg m - 3 998 c P r kJ kg - 1 m - 3 4.02 c P c kJ kg - 1 m - 3 4.18 E 1 /R K 9850 E 2 /R K 22019 UA kJ min - 1 K - 1 64.6 c ai kmol m - 3 4.22 c bi kmol m - 3 0 T ri K 300 T ci K 285 q r m 3 min - 1 0.015 q c m 3 min - 1 0.004 Δ H 1 kJ kmol - 1 -6,500 Δ H 2 kJ kmol - 1 -2,500 k 10 min - 1 1 . 5 × 10 12 k 20 min - 1 5 . 0 × 10 26 1
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c are molar concentrations, T are temperatures, V are volumes, ρ are densities, c p are specific heat capacities, q are volumetric flow rates. The subscripts r and c represent reactor and cooling jacket, respectively, and i represents inlet. (a) Identify the control objective, and define the inputs (controlled, disturbance), state variables, and outputs (measured,unmeasured) for this system. (5 pts) (b) As a first step, ignore heat effects, and assume an isothermal reaction (at 300 K) with no cooling necessary. At steady state, what are the concentrations of A and B in the outlet stream? (10 pts) Hint: Use ’fsolve’ in MATLAB to solve a set of non-linear algebraic equations. (c) In reality, the reaction is non-isothermal, and needs cooling. Therefore, based on full mass and energy balances, determine the steady state concentrations of A and B, as well as the steady state reactor and coolant temperatures. How do c a and c b compare with the isothermal case? (10 pts) (d) In this steady state, for the given parameters and inputs, is the control objective satisfied? Are there
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