The subject of transport phenomena includes three closely related topics: fluid dynamics, heat transfer, and mass transfer. Fluid dynamics involves the transport of momentum, heat transfer deals with the transport of energy, and mass transfer is concerned with the transport of mass of various chemical species. They frequently occur simultaneously in industrial applications like distillation. The basic equations that describe the three modes of transport phenomena are also closely related and can often be analyzed by analogy.[1]

Any chemical process can be studied at three levels:
  • At the macroscopic level, we write macroscopic balance equations which describe how mass, momentum and energy change in a system. It gives insights into the global assessment of the problem, and for many of the industrial engineering cases, this should suffice.
  • At the microscopic level, we study what is happening to the fluid mixture in a small region of space. Mass, momentum, energy balances are this small region of space rather than the whole entity. This gives us valuable information on the temperature, velocity and concentration profiles.
  • At the molecular level, we try to study these three transports by means of molecular structures and intermolecular forces. Intermolecular forces are also responsible for the transport phenomena.
The basic equations for momentum, heat, and mass can be derived directly from the Boltzmann equation of statistical mechanics.[1][2]


Material Balance

Material balances are governed by the physical law of conservation of mass. The total mass entering (in) must equal the total mass leaving (out)-unless there is generation, depletion, or accumulation. Material or a component can be generated or depleted in a controlled volume by means of a chemical or nuclear reaction. Accumulation takes place when the system is not operating at steady state.

Energy Balance

The principle of energy balance is similar to mass balance. The first law of thermodynamics, or the mechanical energy balance is needed to provide the correct relationship of the many terms in the energy balance: molecular (internal) energy, potential energy, kinetic energy, radiant energy, electrical energy, magnetic energy, chemical reaction effects, heat supplied from external sources, and work done.

Basic concepts, upon which the technique for solving engineering problems is based, are the rate equations for the:[3]
  • Conservation of chemical species,
  • Conservation of mass,
  • Conservation of momentum,
  • Conservation of energy.


It is common to formulate a general rate equation as:


A modification of the above equation gives the general one-dimensional flux equation, expressed as:
In order to apply the above equation each term must be carefully substituted with the mode of transfer. The following table gives a good indication of how to substitute each term depending on the mode of transport. Care should be taken to carefully consider the direction of transport as well as the co-ordinate system being employed to study the system.

Representative terms of the one-dimensional equation


In general, any balance can be expressed as:
The general balance is a powerful equation that can be used to solve various systems. This equation is not only true for a chemical system, but for any property in the physical world. Every time you apply the general property balance equation, you must begin by defining the system under consideration and the quantity of interest in the system. The system is a physical space, which is completely enclosed by a hypothetical envelope whose location exactly defines the extent of the system. The parameter φ may be any specified measurable (extensive) property, such as the mass, moles, volume or energy content of one or more components of the system. When the equation is applied to energy balances, the quantity also includes energy transfer across the system envelope as heat and/or work.[4]

A very interesting example would be that of money or wealth being accumulated in a bank account or a treasury. The amount of money being accumulated in a bank account would be the arithmetic sum of the amount of cash withdrawn (out), amount of cash deposited by various sources (in) and the interest being given by the bank on the savings account (generation).


  1. R. Bryon Bird, Warren E. Stewart and Edwin N. Lightfoot (2007), Transport Phenomena, Second Edition, John Wiley & Sons, ISBN 0-470-11539-4.
  2. Robert E. Broadkey and Harry C. Hershey (1988), Transport Phenomena, A Unified Approach, McGraw Hill International Edition, ISBN 0-07-100152-2.
  3. Ismail Tosun (2002), Modelling in Transport Phenomena, A Conceptual Approach, First Edition,Elsevier, ISBN 0-444-51052-4.
  4. Imperial College Press website, Chapter 1: The General Balance Equation.

Publishing Note:

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