Transport Phenomena

Introduction Topics

• What are exactly Transport Phenomena? • How do people group these phenomena together? • What does that mean? • How are they related? • General Equation of Transport Phenomena • Basic Equations What are exactly Transport Phenomena?

• Transport phenomena are really just a way that Chemical Engineers group together three areas of study that have certain phenomenological ideas in common. These three areas of study are: – Fluid Mechanics – Heat Transfer – Mass Transfer Why do people group these phenomena together? • They study the transfer of something. – Fluid Mechanics deals with the transfer of momentum in a fluid. – Heat Transfer deals with the transfer of heat. – Mass Transfer deals with the transfer of mass. What does it mean?

• Fluid Mechanics deals with the transfer of momentum in a fluid. – On a molecular scale this means that the molecules banging into each other transfer their momentum (m*v) to other molecules. – On a larger scale, these molecules banging into each other determine how the fluid is going to flow; that is, if it will just flow smoothly (or 'laminar'), or if it will be rough (or 'turbulent'). What does it mean?

• Heat Transfer deals with the transfer of energy (heat). • Conduction: If you touch something hot, you get heat transfer via conduction. • Convection: If you hold your hand above a burner on a stove, the hot air rising from the burner causes heat moving via convection. • Radiation:Expose to the Sun. Then, move to the shade. The warmth that you feel from the sun is heat transferred via radiation. What does it mean?

• Mass Transfer deals with the transfer of mass. • If you take a glass of water and put one drop of red dye in it, even if you don't stir the water, eventually the water is all the same pinkish color. • The study of how a component spreads out is Mass Transfer. How are they all related?

• They all are similar in their behavior (physical mechanism). • They all move a conservative “physical quantity” (Momentum, Heat, or Mass) from a place where there is a lot to a place where there is less “quantity” in order to reach a thermo-dynamical equilibrium. How are they all related?

• In Fluid Mechanics momentum is transferred from a place where we have a lot of momentum to a place where we have less. • If you observe the flow over a flat plate, the slower flow is right next to the plate, and the faster flow is on the surface of the fluid. How are they all related?

• In Heat Transfer, energy moves from a place where there is a lot to a place where there is less. • For example, if you heat up a brick, then drop it into cold water, the brick gets colder and the water gets warmer. Once the brick and the water are at the same temperature, no more energy can be transferred. How are they all related?

• In Mass Transfer mass moves from a place where there is an high concentration to a place where there is less concentration. • Back to the red dye example: the red dye when it is first dropped into the water is at a high concentration and the water is at zero concentration. But, as the dye spreads out, the concentration of the dye slowly increases, until, it is all at the same low concentration everywhere. Once the concentration of the dye in the water is the same everywhere, no more mass transfer can take place. Analogy between all transport phenomena • There is a driving force causing the transfer which becomes smaller as time progresses, and eventually becomes zero when no more transfer of ‘quantity’ (momentum, heat, mass) takes place. The General Mass Balance Equation

Input   Output   Generation    Consumption  Accumulation  (Enters (Leaves        (Produced     (Consumed   (Buildup   through      through       within within within  system     system        system)     the system)   system)  boundaries)   boundaries)  Levels at which transport phenomena can be studied

• Macroscopic level Describe how momentum, energy and mass in the system change because of the introduction (and/or extraction) of different ‘streams’ (inputs/outputs) to the system from surroundings. • Example

m in Process m out Unit (kg Ch4/h) (kg Ch4/h) Levels at which transport phenomena can be studied

• Microscopic level: examine what is happening to the fluid mixture in a small region within the control volume. • Local balances (equations of change) are used to describe how momentum, energy and mass change within this small region. • This level is useful to get information about physical variables profiles (velocity, T, P and concentration) within the system. Levels at which transport phenomena can be studied

• Molecular level: fundamental understanding of the mechanisms of momentum, energy and mass transport in terms of molecular structure and intermolecular forces. • This level is rarely used in Engineering The mechanisms of Transport Phenomena

• Molecular transport is characterized by individual movement of the particles

• Turbulent transport result from the movement of large group of molecules Nature of Flow:

• Viscous (molecular) flow • At low velocities fluids tend to flow without lateral mixing, adjacent layers slide past one another. • The flow conditions is called laminar flow. Nature of Flow (Cont…)

• Turbulent Flow • Erratic motion of the particles within the fluid. • Non streamline flows Velocity Distribution Considerations

• The fluid is constituted by rigid spherical molecules of diameter d; • There are not attraction and repulsion forces between the molecules; • The molecule volume is not significant with respect to the intermolecular space; • The molecules are perfect elastic. Considerations

• Each molecule moves randomly in different directions at the same velocity; • The number of molecules is sufficient large allowing to take statistic averages of the properties which describe the molecules; • The control volume dV has rectangular form and is represented in a rectangular system of coordinates.