Transport phenomena

While it draws from fields as diverse as continuum mechanics and thermodynamics, it places a heavy emphasis on the commonalities between the topics covered.

Mass, momentum, and heat transport all share a very similar mathematical framework, and the parallels between them are exploited in the study of transport phenomena to draw deep mathematical connections that often provide very useful tools in the analysis of one field that are directly derived from the others.

The fundamental analysis in all three subfields of mass, heat, and momentum transfer are often grounded in the simple principle that the total sum of the quantities being studied must be conserved by the system and its environment.

Thus, the different phenomena that lead to transport are each considered individually with the knowledge that the sum of their contributions must equal zero.

Some of the most common examples of transport analysis in engineering are seen in the fields of process, chemical, biological,[1] and mechanical engineering, but the subject is a fundamental component of the curriculum in all disciplines involved in any way with fluid mechanics, heat transfer, and mass transfer.

Moreover, they are considered to be fundamental building blocks which developed the universe, and which are responsible for the success of all life on Earth.

However, the scope here is limited to the relationship of transport phenomena to artificial engineered systems.

[2] In physics, transport phenomena are all irreversible processes of statistical nature stemming from the random continuous motion of molecules, mostly observed in fluids.

Every aspect of transport phenomena is grounded in two primary concepts : the conservation laws, and the constitutive equations.

The constitutive equations describe how the quantity in question responds to various stimuli via transport.

Prominent examples include Fourier's law of heat conduction and the Navier–Stokes equations, which describe, respectively, the response of heat flux to temperature gradients and the relationship between fluid flux and the forces applied to the fluid.

As they approach this state, they tend to achieve true thermodynamic equilibrium, at which point there are no longer any driving forces in the system and transport ceases.

For example, in solid state physics, the motion and interaction of electrons, holes and phonons are studied under "transport phenomena".

Another example is in biomedical engineering, where some transport phenomena of interest are thermoregulation, perfusion, and microfluidics.

[8] A great deal of effort has been devoted in the literature to developing analogies among these three transport processes for turbulent transfer so as to allow prediction of one from any of the others.

[9] This analogy is based on experimental data for gases and liquids in both the laminar and turbulent regimes.

Although it is based on experimental data, it can be shown to satisfy the exact solution derived from laminar flow over a flat plate.

In fluid systems described in terms of temperature, matter density, and pressure, it is known that temperature differences lead to heat flows from the warmer to the colder parts of the system; similarly, pressure differences will lead to matter flow from high-pressure to low-pressure regions (a "reciprocal relation").

This equality was shown to be necessary by Lars Onsager using statistical mechanics as a consequence of the time reversibility of microscopic dynamics.

The theory developed by Onsager is much more general than this example and capable of treating more than two thermodynamic forces at once.

Newton's law of viscosity is the simplest relationship between the flux of momentum and the velocity gradient.

Some examples are the heating and cooling of process streams, phase changes, distillation, etc.

In some cases direct analytic solutions can be found from these equations for the Nusselt and Sherwood numbers.

In cases where experimental results are used, one can assume these equations underlie the observed transport.

Where can be used in most cases, which comes from the analytical solution for the Nusselt Number for laminar flow over a flat plate.

The heat and mass analogy may also break down in cases where the governing equations differ substantially.

For example, predicting heat transfer coefficients around turbine blades is challenging and is often done through measuring evaporating of a volatile compound and using the analogy.

[14] Many systems also experience simultaneous mass and heat transfer, and particularly common examples occur in processes with phase change, as the enthalpy of phase change often substantially influences heat transfer.

[16] The study of transport processes is relevant for understanding the release and distribution of pollutants into the environment.

Examples include the control of surface water pollution from urban runoff, and policies intended to reduce the copper content of vehicle brake pads in the U.S.[17][18]