ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Hours of tutorials: 1 Expository Class: 12 Interactive Classroom: 44 Total: 57
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Chemistry Engineering, Applied Mathematics
Areas: Chemical Engineering, Applied Mathematics
Center Higher Technical Engineering School
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
The main objective of this course is to introduce students to transport phenomena through an integrated approach to the transfer of energy, matter and quantity of motion in continuous media. It is intended that they understand the fundamental laws that govern these three phenomena, which are closely interrelated, and that they acquire the ability to formulate mathematical models that represent the essential aspects of real problems in chemical engineering processes. At the end of the course, students should be able to:
• Apply the laws governing the transfer of quantity of motion, energy and matter, interrelating these three phenomena.
• Formulate complex mathematical models representing real systems in both steady state and non-steady state.
• Develop simple analytical models to obtain the individual and global transport coefficients needed to s o l v e real problems.
• To understand the concept of numerical simulation and the scope of this tool for solving engineering problems.
• Understand the fundamentals of the finite element method.
• Numerically approach simplified models for which it is easy to obtain an analytical solution, as well as models of greater complexity for whose resolution the use of numerical simulation is essential.
1. Introduction to numerical simulation
1.1. Finite element method.
1.2. Introduction to Comsol Multiphysics software package
1.3. Analysis and interpretation of numerical simulation results.
2. Transit of movement quantity
2.1. Introduction to transport phenomena. Levels of description of transport phenomena. Nomenclature. Viscosity and mechanisms of transport of quantity of motion: Newton's law of viscosity. Generalization of Newton's law.
2.2. Microscopic level balances of quantity of motion in envelopes. Velocity distributions for one-dimensional flow in laminar regime in steady state. Boundary conditions.
2.3. Conservation equations in isothermal systems: Continuity equation. Equation of motion. Use of conservation e q u a t i o n s to solve problems.
2.4. Transport of quantity of movement in turbulent flow: Introduction to turbulent flow. Average conservation equations. Introduction to individual and global transport coefficients.
2.5. Numerical simulation of single-phase fluids in laminar regime in two and three dimensions.
3. Heat Transfer
3.1. Transport by conduction, thermal conductivity. Fourier's law. Variation equations for non-isothermal systems in steady state. Conduction with generation. Temperature distribution in solids.
3.2. Convective transport. Transport coefficients. Forced and free convection. Temperature distribution in laminar flow.
3.3. Energy equations.
3.4. Numerical simulation: heat transfer in solids; heat transfer in fluids.
4. Mass Transfer
4.1. Fundamentals and general concepts of mass transfer. Fick's law of diffusion. Velocities of species in diffusion. Continuity equations for different geometries. Most common boundary conditions.
4.2. Steady state molecular diffusion with chemical reaction. Heterogeneous chemical reaction. Homogeneous chemical reaction.
4.3. Numerical simulation: diffusion without convection; diffusion with convection; diffusion with chemical reaction.
BIBLIOGRAFÍA BÁSICA
• BIRD R.B STEWART W.E. AND LIGHTFOOT E.N, Transport Phenomena. 2ª ed. Revised, New York: John Wiley & Sons, 2007. ISBN: 978-0-470-11539-8. SINATURA ETSE: SOLICITADO EBOOK
• BIRD R.B STEWART W.E. Y. LIGHTFOOT E.N, Fenómenos de Transporte. Barcelona: Editorial Reverte, 2006 (y ediciones anteriores). ISBN 8429170502. SINATURA ETSE: A111 2 E, A111 2 F
• BIRD R.B. STEWART W.E. y LIGHTFOOT E.N. Transport Phenomena. 2ª ed. New York: John Wiley & Sons, 2007 (y ediciones anteriores). ISBN 0-471-41077-2. SINATURA ETSE: A111 1, 111 20
• COMSOL Multiphysics User’s Guide. Disponible en línea https://www.comsol.com/
BIBLIOGRAFÍA COMPLEMENTARIA
• WELTY J.R. WICKS, C. Fundamentos de transferencia de momento, calor y masa. 2ª ed México: Limusa, 1999. ISBN 968-18-5896-4. SINATURA ETSE: A111 3E
• RASMUSON, ANDERS ET AL. Mathematical Modeling in Chemical Engineering. Cambridge: Cambridge University Press, 2014. ISBN 978-1-107-04969-7. SINATURA ETSE: 010 37
• DOBRE, T.G., SANCHEZ MARCANO, J.G., Chemical Engineering: Modelling, Simulation and Similitude, Wiley-VCH, 2007. ISBN: 9783527306077
• FINLAYSON, B. A., Introduction to chemical engineering computing, USA, John Wiley & Sons, 2006. ISBN-10: 0-471-74062-4. SINATURA ETSE: A012 46.
• FINLAYSON, B. A., Introduction to chemical engineering computing, USA, John Wiley & Sons, 2006. ISBN-10: 0-471-74062-4. Disponible en línea:
https://ebookcentral-proquest-com.ezbusc.usc.gal/lib/buscsp/reader.acti…
• FINLAYSON, B. A. Introduction to Chemical Engineering Computing. Second edition. Wiley, 2014. SINATURA ETSE: A012 46 A
• REDDY, J. N. Introduction to the Finite Element Method, Fourth Edition /. 4th edition. New York, N.Y: McGraw-Hill Education, 2019. Disponible en línea:
https://www-accessengineeringlibrary-com.ezbusc.usc.gal/content/book/97…
• RICE, R. G., Do, D., Applied Mathematics and Modelling for Chemical Engineers, 2nd Ed., John Wiley & Sons, 2012. ISBN-10: 1118024729
Knowledge
(CN02) Acquire advanced knowledge and demonstrate, in a scientific and technological or highly specialized
research context, a detailed and grounded understanding of the theoretical and practical aspects and
methodology of work in one or more fields of study in Chemical Engineering.
Competition
(CP01) Apply knowledge of mathematics, physics, chemistry, biology, and other natural sciences, obtained
through study, experience, and practice, with critical reasoning to establish economically viable solutions to
technical problems.
(CP02) Conceptualize engineering models, apply innovative methods in problem solving and appropriate
computer applications, for the design, simulation, optimization and control of processes and
systems.
(CP03) Design products, processes, systems and services of the chemical industry, as well as the optimization of
others already developed, taking as a technological basis the different areas of chemical engineering, including
processes and transport phenomena, separation operations and engineering o f chemical, nuclear,
electrochemical and biochemical reactions.
Ability
(HD01) Have the ability to solve problems that are unfamiliar, incompletely defined, and have c omp e t i n g
specifications, considering possible solution methods, including the most innovative, selecting the most
appropriate, and be able to correct the i m p l e m e n t a t i o n , evaluating different design solutions.
(HD04) Search, process, analyze and synthesize, in a critical way, information from different sources for the
establishment of the corresponding conclusions.
The subject has been assigned 6 ECTS credits that will be developed over 12 hours of theoretical teaching, 16 hours of interactive seminar teaching and 24 hours of interactive computer classroom teaching and 1 hour of small group tutorials per student. The Virtual Campus (Moodle) will be used as a tool to provide information/announcements about the teaching activity throughout the course and complementary materials for the study of the subject.
Lectures will be used to develop a part of the syllabus. Before starting a topic, the teacher will describe the contents in a generic way, relating them to each other and to previous topics so that the students can appreciate the importance of the topic. At the end of the subject, a small balance of what has been seen will be made, emphasizing the aspects that may present more difficulties to the student.
The seminar classes will be basically dedicated to problem solving and case studies related to the theoretical concepts. Both in the expository and interactive classes, the aim will be to raise real issues and questions to arouse interest and clarify concepts. Different activities will be proposed throughout the development of the subject that will be associated with the delivery through the Virtual Campus of written documents or the realization of oral sessions (face-to-face or telematic), evaluable in both cases.
The computer classroom classes will have an eminently practical character but without losing sight of the basic fundamentals of the numerical methods used. For each of the examples considered, a brief description of the underlying real problem and the mathematical model used to approach it will be made, as well as the simplifications adopted to approach its numerical resolution. We will proceed to its resolution by means of the Comsol Multiphysics software package, carrying out a critical analysis of the results obtained, which will also allow validating the models.
A compulsory group work will consist of applying the microscopic balances of matter, energy and quantity of movement to a real industrial process and its simulation with the Comsol Multiphysics software. The work will be presented and defended in the group tutorial on the date officially marked in the calendar.
During all these activities, and given the eminently practical nature of the classes, students are expected to develop the competencies associated with the methodology used:
Lectures: CN02
Seminar classes: CN02, CP01, CP02, CP03, HD01
Computer classroom classes: CN02, CP01, CP02, CP03, HD01
Group work: CN02, CP01, CP02, CP02, CP03, HD01
Group Tutoring: HD04
A visit will be made to a company related to the subject's content, depending on the available financial resources and aiming, as far as possible, for integration with the content of other subjects in the module. The purpose of the visit is to connect theoretical content with the reality of the industrial environment. If the visit cannot be carried out, an attempt will be made to replace it with an alternative activity that brings students closer to the industrial world, such as a seminar led by a professional specialized in the sector.
The evaluation of the course is based on three mandatory and graded activities: a final exam, a group project, and its oral presentation. These will assess, separately, the competencies acquired in the two parts of the course: Modeling with Transport Phenomena (MTP) and Simulation with Numerical Methods (SNM).
1. Mandatory and Graded Activities
1.1 Final Exam (70% of the final grade)
Composed of two independent sections:
• A theoretical-practical test on MTP.
• A computer-based practical test on SNM.
1.2 Group Project (25% of the final grade)
This involves applying microscopic balances of mass, energy, and momentum to a chemical engineering process, as well as simulating it using COMSOL Multiphysics software.
1.3 Oral Defense of the Project (5% of the final grade)
• The project will be presented and defended orally in a group tutorial, on the date officially set in the academic calendar.
• The defense will be individual within the group and is mandatory for the project grade to be valid.
A minimum score of 3 out of 10 in each part (MTP and SNM) of the mandatory graded activities is required in order to pass the course.
2. Grading Criteria
To calculate the final course grade, two cases are distinguished depending on whether the minimum requirements are met:
• CASE A: The student has achieved a minimum score of 3/10 in all mandatory and graded parts.
In this case, the grades are calculated as follows:
CMTP = 0,70 * NE1 + 0,25 * NT1 + 0,05 * NET1
CSNM = 0,70 * NE2 + 0,25 * NT2 + 0,05 * NET2
Where:
-CMTP: Grade for the Modeling with Transport Phenomena part
-CSNM: Grade for the Simulation with Numerical Methods part
-NE1/2: Exam grade for the MTP/SNM part
-NT1/2: Project grade for the MTP/SNM part
-NET1/2: Oral presentation grade for the MTP/SNM part
The final grade (FG) is determined as follows:
1. If CMTP>= 4,0 and CSNM >= 4,0, then: FG = (CMTP + CSNM) / 2.
2.Otherwise: FG = min(4, (CMTP + CSNM) / 2).
If FG>=5, the course is considered passed. Otherwise, it is considered failed.
• CASE B: The student has not achieved the minimum score of 3 in any of the mandatory and graded parts.
In this case, the course is considered failed, and the final grade is calculated a
FG = min(3, (CMFP + CSNM) / 2)
3. Second Assessment Opportunity
If the course is not passed in the first opportunity, it can be retaken in the second opportunity. The student may retake only the parts that were not passed (i.e., those with a grade below 5). To pass in this session, the same minimum requirements as before must be met for each part (exam, project, and presentation in MTP and SNM).
4. Repeating Students
Repeating students must complete all mandatory and graded activities again.
5. Attendance
There is no minimum attendance requirement to be eligible for evaluation, but attending in-person classes is strongly recommended to achieve the course objectives.
Evaluation of activities and competences:
-----------------------------------------------
Examination: CN02, CP01, CP02, CP03, HD01
Group work: CN02, CP01, CP02, CP03, HD01
Group tutoring: HD04
Fraudulent tests:
------------------------
For cases of fraudulent performance of exercises or tests, the provisions of the Regulations on the assessment of students' academic performance and the review of qualifications shall apply.
It is estimated a total of 150 hours (6 ECTS), which are divided between 58 classroom hours and 92 hours of autonomous work of the student. The distribution of classroom hours according to the type of activity will be as follows:
- Theoretical teaching: 12 h
- Interactive seminar teaching / technical visit: 16 h
- Interactive laboratory/computer classroom teaching: 24 h
- Small group tutoring: 1 h
- Examination and review: 5 h
Attendance and active participation in the classes of this subject.
The subject will be taught in Spanish. If necessary, doubts will be answered in English to foreign students.
A visit will be made to a company related to the subject's content, depending on the available financial resources and aiming, as far as possible, for integration with the content of other subjects in the module. The purpose of the visit is to connect theoretical content with the reality of the industrial environment. If the visit cannot be carried out, an attempt will be made to replace it with an alternative activity that brings students closer to the industrial world, such as a seminar led by a professional specialized in the sector.
Maria Dolores Gomez Pedreira
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813186
- mdolores.gomez [at] usc.es
- Category
- Professor: University Lecturer
Eva Rodil Rodriguez
Coordinador/a- Department
- Chemistry Engineering
- Area
- Chemical Engineering
- Phone
- 881816796
- eva.rodil [at] usc.es
- Category
- Professor: University Professor
| Tuesday | |||
|---|---|---|---|
| 09:00-11:00 | Grupo /CLE_01 | Spanish | Classroom A6 |
| Friday | |||
| 09:00-10:00 | Grupo /CLIS_01 | Spanish | Classroom A6 |
| 01.12.2026 10:00-12:00 | Grupo /CLE_01 | Classroom A6 |
| 01.12.2026 10:00-12:00 | Grupo /CLIS_01 | Classroom A6 |
| 01.12.2026 10:00-12:00 | Grupo /CLIL_01 | Classroom A6 |
| 06.15.2026 10:00-12:00 | Grupo /CLIL_01 | Classroom A6 |
| 06.15.2026 10:00-12:00 | Grupo /CLE_01 | Classroom A6 |
| 06.15.2026 10:00-12:00 | Grupo /CLIS_01 | Classroom A6 |