1. Aram Nasih Muhammad
1 | P a g e
Soran University - Faculty of Engineering
Chemical Engineering Department, 3rd Stage
Module Title: Engineering Analysis II
Module Leader: Mahfouz Rostamzadeh Name of Student:
Date of Final Assessment: 20/06/2020
Date and Time for Report Uploading: from 09:00, 20.06.2020 to 09:00, 24.06.2020.
(Duration: 4 days=96 hours)
1st
Attempt
]ATTEMPT
11. Aram Nasih Muhammad
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Chemical Engineering Department, Faculty of Engineering
Soran University
Modeling with Differential Equations in Chemical
Engineering
Prepared by: Aram Nasih Muhammad
Module Leader: Dr. Mahfouz Rostamzadeh
June 19, 2020
This report submitted in fulfillment of the requirements for Course Engineering Analysis II, 3rd stage,
Department of Chemical Engineering, Faculty of Engineering, Soran University, for the final assessment
in 2nd semester of academic year 2019-2020.
12. Aram Nasih Muhammad
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Abstract
In this report, we briefly discuss mathematical modeling and it’s uses within the engineering fields.
We also indicate the uses of differential equations in chemical engineering and see where said equations
are applied within such field. We show some of the applications within the field and provide a practical
example of using the equation within the Chemical Engineering field. Showcasing the importance of
mathematical modeling and differential equations briefly.
Introduction
Modelling with Differential Equations in Chemical Engineering' covers the modelling of charge
procedures of engineering in phrases of differential equations. While it consists of the purely
mathematical aspects of the answer of differential equations, the major emphasis is on the derivation and
solution of major equations of engineering and applied science. Methods of solving differential equations
via analytical and numerical means are introduced in element with many solved examples, and troubles
for answer through the reader. Emphasis is positioned on numerical and laptop strategies of solution. A
key chapter in the e book is devoted to the ideas of mathematical modelling. These concepts are utilized
to the equations in necessary engineering areas. The foremost disciplines included are thermodynamics,
diffusion and mass transfer, warmth transfer, fluid dynamics, chemical reactions, and automatic control.
These topics are of particular fee to chemical engineers, but also are of interest to mechanical, civil, and
environmental engineers, as well as applied scientists. The cloth is also appropriate for undergraduate and
commencing graduate students, as nicely as for evaluation via practising engineers.
1. Definitions and Main Concept
Partial differential equations: involve more than one independent variable and are much more difficult
to solve than ODEs.
ordinary differential equations: when all the quantities are functions of a single independent variable.
Main concept:
A partial differential equation (PDE) is an equation involving one or greater partial derivatives of an
(unknown) function, name it u, that depends on two or extra variables, often time t and one or quite a few
variables in space. The order of the best spinoff is called the order of the PDE. Just as used to be the case
for ODEs, second-order PDEs will be the most important ones in applications.
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1. Applications
There are many applications for differential equations in chemical engineering:
Process engineering: Solution of this equation yields the concentration-time profile for the reactant A in
the reaction, which offers the groundwork for the layout of the reactor. Higher-order differential
equations are very common in chemical engineering systems
fluid flow: The differential equations of fluid flow are based totally on the standards of conservation of
mass, momentum and energy and are recognised as the Navier-Stokes equations.
heat transfer: the heat equation is a partial differential equation that describes how the distribution of
some quantity (such as heat) evolves over time in a solid medium
mass transfer: The differential equations of mass transfer are general equations describing mass transfer
in all directions and at all conditions.
control systems: modeled by partial differential equations. The hope is that the controller has the desired
effect on the original system.
reactor design, Mathematical modeling of chemical reactors is of immense interest and of enormous use
in the chemical industries.
wave equation: The wave equation is an vital second-order linear partial differential equation for the
description of waves as they manifest in classical physics such as mechanical waves (e.g. water waves,
sound waves and seismic waves) or mild waves. It arises in fields like acoustics, electromagnetics, and
fluid dynamics.
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Note: These above four sections must be at least 2 pages and at most 6
pages!
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References
[1] Stanley M. Walas, “Modeling with Differential Equations in Chemical Engineering (Butterworth-
Heinemann Series in Chemical Engineering)”, 1991.
[2] Erwin Kreyszig, “Advanced Engineering Mathematics, 8th Edition” 10th Edition, John Wiley & Sons,
2011
[3] M. N. Barreira et al., “Use of Different Numerical Solution Approaches for a Three-Phase Slurry
Catalytic Reactor Model,” Int. J. Chemical Eng., vol. 1, 2003.
[4] N. K. Madsen and R. F. Sincovec, General software for partial differential equations. In Numerical
Methods for Differential Systems (Edited by L. Lapidus and W. E. Schiesser), pp. 229-242. Academic
Press, New York (1976).
[5] H. H. Klein, Computer modeling of chemical process reactors. 1st Engineering Conf. Chemical
Reaction Engineering, Miramar Hotel, Santa Barbara, CA (1985).
[6] L. Lapidus and G. F. Pinder, Numerical Solution of Partial Differential Equations in Science and
Engineering. Wiley-Interscience, New York (1982).
[7] ] M. J. Balas. Active control of flexible systems. J. Optim. Theory Appl., 23(3):415–436, 1976.
![Aram Nasih Muhammad
1 | P a g e
Soran University - Faculty of Engineering
Chemical Engineering Department, 3rd Stage
Module Title: Engineering Analysis II
Module Leader: Mahfouz Rostamzadeh Name of Student:
Date of Final Assessment: 20/06/2020
Date and Time for Report Uploading: from 09:00, 20.06.2020 to 09:00, 24.06.2020.
(Duration: 4 days=96 hours)
1st
Attempt
]ATTEMPT](https://image.slidesharecdn.com/aram-201130215058/85/Aram-1-320.jpg)
