# CHEE224 : Transport Phenomena Fundamentals

## Personnel

### Instructor

Carlos Escobedo | Dupuis Hall 209 | ce32@queensu.ca | (613) 533-3095 |

### TAs

Peter Gilbert | DUP240 | peter.gilbert@queensu.ca | 613-533-6000 x75342 |

Srijit Nair | DUP 239 | 14sn22@queensu.ca |

## Course Description

The theory and mathematical framework of transport phenomena are introduced. Mass, energy and momentum balances are developed using the integral and differential methods of analysis. The tools used to formulate and solve the problems include representation of physical entities in vector form, multivariable functions and vector operations in 2D and 3D. Specific topics of Chemical Engineering interest include moments of a force, work done by a force, moments of inertia, control surfaces and control volumes and fluid kinematics (21/0/0/21/0).

## Objectives and Outcomes

This course aims at using the physical theory of transport phenomena to develop an understanding of the underlying mathematical principles. Mathematical tools, including vector calculus, partial derivatives and multiple integrals are implemented to deepen the understanding of physical systems.

Specific course learning outcomes include:

- Calculate centre of mass, moment of inertia and volumes using multiple integrals, to determine hydrostatic forces on surfaces.
- Analyze transport phenomena fundamentals (forces in space, moment of a force, work done by a force) and fluid kinematics (displacement, velocity and acceleration, motion along a curve). Define streamlines, streaklines and pathlines. Tools used include vectors in space, dot product, cross product, areas and determinants in 2D, volumes and determinants in 3D, parametric representation of curves, intersection of a line and a plane.
- Apply the integral relations for a control volume and the Reynolds transport theorem to analyze fluid motion.
- Analyze fluid motion using the differential analysis: Velocity and acceleration fields, linear and angular motion and deformation, differential form of the continuity equation (Cartesian and polar forms), stream function, potential function. Associated mathematical framework: vector fields, divergence and curl.
- Formulate equations for heat and momentum transport using partial derivatives, multivariable functions, differentials, the chain rule for multivariable functions, directional derivatives.
- Development of mathematical skills: (i) the mathematical formulation of engineering transport problems and corresponding analytical solution strategies. (ii) Handling of differential operators in vector calculus and coordinate systems important for engineering applications.

This course develops the following attributes:

Knowledge base for engineering (KB-MATH):

- Selects, locates and orients coordinate systems for transport phenomena problems.
- Formulates and solves ordinary and partial differential equations and integral equations arising in Chemical Engineering using analytical and numerical techniques.

Problem analysis: Selects and applies appropriate quantitative models, analyses, and boundary conditions to solve problems.

## Relevance to the Program

The course introduces fundamental concepts that will be useful for the suite of courses known as “transport courses” (CHEE 223 – Fluid Mechanics, CHEE 330 – Heat and Mass Transfer, CHEE 412-Transport Phenomena in Chemical Engineering), which deal with the transport properties of matter. It lays the mathematical background and deepens student confidence in mathematical techniques and problem solving, needed throughout the curriculum.

The course assumes working knowledge of 1^{st} year mechanics and calculus.

## Course Structure and Activities

2 lecture hours + 2 tutorial hours per week. Refer to Solus for times and locations.

The course emphasizes in-class learning activities during the term, in tutorial/workshop sessions. Assessment will be based on assignments submitted throughout the term and tutorial activities and midterm(s). There will be no final exam.

## Resources

Custom courseware. Pearson-ISBN 1269829432.

All course lecture slides, assignments and tutorials will be posted on the onQ site. If you are registered for the course, you can access this information by logging in at https://onq.queensu.ca