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Modeliing and math physics, Cheat Sheet of Mathematics

Mathematics

It is about math and modelling

Typology: Cheat Sheet

2014/2015

Uploaded on 10/04/2023

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Modeling, Simulation and Optimisation for Chemical Engineering
CH3133 – CC01, CC02
Homework Assignment
Question. 1
A. Differentiate between lumped system and distributed system.
B. Consider a perfectly insulated, well-stirred tank, as shown in the figure, where a hot liquid
stream at 75°C is mixed with a cold liquid stream at 15°C. Is it a lumped parameter system or
a distributed parameter system? Explain why?
C. Consider a liquid level system as shown in Figure below. Derive the mathematical model.
What type of model is it? Why
Question. 2
Consider a conical receiver shown in figure. The inlet and outlet liquid volume flowrate are F1
and F2, respectively.
a. Develop the model equation with necessary assumption(s) with respect to the height h.
b. What type mathematical model is this?
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Modeling, Simulation and Optimisation for Chemical Engineering

CH3133 – CC01, CC

Homework Assignment Question. 1 A. Differentiate between lumped system and distributed system. B. Consider a perfectly insulated, well-stirred tank, as shown in the figure, where a hot liquid stream at 75°C is mixed with a cold liquid stream at 15°C. Is it a lumped parameter system or a distributed parameter system? Explain why? C. Consider a liquid level system as shown in Figure below. Derive the mathematical model. What type of model is it? Why Question. 2 Consider a conical receiver shown in figure. The inlet and outlet liquid volume flowrate are F 1 and F 2 , respectively. a. Develop the model equation with necessary assumption(s) with respect to the height h. b. What type mathematical model is this?

Use 𝑉 = 1 3 𝜋𝑟^2 ℎ and 𝑟 ℎ

𝑅 𝐻 to get the final form. Question. 3 Consider a mixing Tank which has a solvent flowing in with concentration CAo of a solute A and flowrate Fo. The fluid exits the tank at different concentration C. There is no chemical reaction in the tank. The Tank is full of solvent of with a concentration CA. Assume CA less than CAo. Data: Fo= 0.10 m^3 V the volume of solvent in the tank = 25 m^3 The system is at steady state before the step increase CAo = 0.956 moles/m^3 Built a model for the exit concertation. Question. 4 Consider the Continuous Stirred Tank Reactor (CSTR) shown in Figure. A single irreversible first-order reaction occurs in the reactor, i.e., A → B where the reaction rate is r=kCA (the consumption term in your mole balance equation). Note: in every continuous process, there will be a start-up period in which operation will start with an unsteady state behavior and move towards steady state. One of the applications of the unsteady state model is to predict the start-up period. Other application of the unsteady state model is to predict the process behavior subjected to upstream changes such as disturbances). a. Write the mole balance around the reactor and obtain an unsteady state model for this process (find the ordinary differential equation). Integrate the ordinary differential equation to develop an analytical expression for CA as a function of time (min). b. What is the steady state concentration of A in the reactor?