The following are some of the common terminology and definitions that need to be understood before one can proceed to solve complex chemical engineering problems involving property transport phenomena.

Systems

  • Open system: A system which continuously interacts with its environment. There is exchange of mass and/or energy and/or information through the system boundary.
  • Closed system: A system which is permeable to energy but not to matter.
  • Isolated system: A system which can neither exchange matter or energy with the surroundings. Internal motion within the system of either mass or energy is permitted in isolated systems. In a strict sense, only the universe is truly an isolated system and it is thus a hypothetical concept.

Continuum approximation

One of the important assumptions made in transport phenomena while dealing particularly with momentum transfer problems, is that of continuum. A continuum is a body that can be continually sub-divided into infinitesimal elements with properties being those of the bulk material. The continuum concept in fluid mechanics is an a priori assumption, so it cannot be derived from first principles.This description is an idealization that neglects the molecular structure of real fluids. Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Fundamental physical laws like conservation of mass and energy are still applicable to such systems.

Steady-state

The term steady-state means that, at a particular location in space, the dependent variable does not change as a function of time. A steady-state flow process requires conditions at all points in a system remain constant as time changes. There must be no accumulation of mass or energy over the time period of interest. Thermodynamic properties may vary from point to point, but will remain unchanged at any given point.

The steady-state may be expressed mathematically as:
TP-SteadyState.png
It is also important to distinguish between partial and ordinary derivatives as the conclusions are very different.

Quasi-static process

A quasi-static process is defined as a process which, at any moment, can be assumed to be almost in equilibrium. It is important to know how much time it takes for a system to approach equilibrium. A system is not in equilibrium when the macroscopic parameters (temperature, pressure, etc.) are not constant throughout the system.

Uniform

The term uniform means that, at a particular instant in time, the dependent variable is not a function of position. The variation of a physical quantity with respect to position is called the gradient. Therefore, the gradient of a quantity must be zero for a uniform condition to exist with respect to that quantity.

Equilibrium

A system is in equilibrium if both steady-state and uniform conditions are met simultaneously. An equilibrium system does not exhibit any variations with respect
to position or time. The state of an equilibrium system is specified completely by the pressure, volume and temperature of the system.

Flux

The flux of a certain quantity is defined by the equation below (where the area is normal to the direction of the flow):
TP-Flux.png
The type of fluxes dealt with may be molar flux, mass flux, energy flux or momentum flux.

Inlet/Outlet Rate

A quantity may enter or leave the system by two means:
  • By inlet or outlet streams.
  • By exchange of quantity between the system and its surrounding through the system boundaries.
  • In either case, the rate of input and/or output is expressed in terms of flux.

The rate of a quantity can be expressed as,
Capture6.PNG
Here, the area (A) is perpendicular to the direction of flux.

Further Reading

  • Joel Plawsky (2009), Transport Phenomena Fundamentals, 2nd Edition, Marcel Dekker Inc., ISBN 1-42006-233-6.
  • R. B. Bird, W. E. Stewart and E. N. Lightfoot (2007), Transport Phenomena, Revised Second Edition, John Wiley & Sons, ISBN 0-470-11539-4.
  • William J. Thomson (2000), Introduction to Transport Phenomena, 1st Edition, Prentice Hall, ISBN 0-13-454828-0.
  • W. J. Beek, K. M. K. Muttzall and J. W. van Heuven (2000), Transport Phenomena, 2nd Edition, John Wiley & Sons, ISBN 0-471-99990-3

Publishing Note:

This article was written by Shubham Pinge, a member of this wiki, and uploaded by him. Some minor formatting and editing was then provided by Milton Beychok, the organizer of this wiki.