Chapter 5, Problem 5.21E

Interpretation Introduction

Interpretation:

The transfer function which relates the exiting temperature $T$ to the inlet concentration $c_{Ai}$ is to be derived. All the assumptions made during the derivation are to be stated. Approximate this transfer function by first-order approximation and the validity of this approximation is to be compared with the step responses of both the models, original and approximate.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable $\left(y\right)$ and the original variable $\left(\overline{y}\right)$ is known as deviation variable $\left(y^{\prime }\right)$. It is generally used while modelling a process. Mathematically it is defined as:

$y^{\prime }=y-\overline{y}$

In steady-state process, the accumulation in the process is taken as zero.