GTU 2180503 Process modeling, simulation & optimization Summer 2025 Question Paper & PDF

Explain the meaning of following terms for optimization: Feasible solution, feasible region, and over determined model.

Consider a batch reactor in which the following first-order consecutive reactions are carried out. Reactant A is charged into the vessel. Steam is fed into the jacket to bring the reaction mass up to a desired temperature. Then cooling water must be added to the jacket to remove the exothermic heat of reaction and to make the reactor temperature follow the prescribed temperature-time curve. This temperature profile is fed into the temperature controller as a set-point signal. Derive the temperature profiles for the process and metal wall for the batch reactor described above.

Derive the equations for the series of isothermal, constant holdup CSTRs. List all the assumptions with their justifications.

Construct the region formed by the following constraints and determine the convexity: 𝑥1 ≤ 6; 𝑥2 ≤ 6; 𝑥1 ≥ 0; 𝑥1 + 𝑥2 ≤ 6; 𝑥2 ≥ 0

Explain the algorithm of steepest descent method for unconstrained multivariable optimization problem.

Minimize 𝑓(𝑥) = 𝑥⁴ − 𝑥 + 1 using Newton’s method for a starting point of 𝑥 = 0.6 (Show 3 iterations, use four decimal point accuracy).

Minimize the quadratic function 𝑥² − 2 = 0 by secant method. Use the range of

• •3 to +3.

Solve the following non-linear function with constraints using Lagrange multiplier method: Minimize:𝑓(x,y)=k𝑥−1 𝑦−2 Subject to: 𝑔(𝑥, 𝑦) = 𝑥² + 𝑦² = 𝑎2