Introduction to transport phenomena

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Continuum Flow Limitations

The transport phenomena are usually modeled in continuum states for most applications – the materials are assumed to be continuous and the fact that matter is made of atoms is ignored. When the characteristic dimension, L, is small compared to the molecular mean free path, λ, which is defined as average distance between collisions for a molecule, the traditional Navier-Stokes equation and the energy equation based on the continuum assumption have failed to provide accurate results. The continuum assumption also fails when the gas is at very low pressure (rarefied).

See Main Article Continuum flow limitations

Momentum, Heat, and Mass Transfer

Transport phenomena include momentum transfer, heat transfer, and mass transfer, all of which are fundamental to an understanding of both single and multiphase systems. It is assumed that the reader has basic undergraduate-level knowledge of transport phenomena as applied to single-phase systems, as well as the associated thermodynamics, fluid mechanics, and heat transfer.

See Main Article Momentum, Heat, and Mass Transfer

Introduction to Momentum Transfer

A fluid at rest can resist a normal force but not a shear force, while fluid in motion can also resist a shear force. The fluid continuously deforms under the action of shear force. A fluid’s resistance to shear or angular deformation is measured by viscosity, which can be thought of as the internal “stickiness” of the fluid. The force and the rate of strain (i.e., rate of deformation) produced by the force are related by a constitutive equation.

See Main Article Introduction to Momentum Transfer

Introduction to Heat Transfer

Heat transfer is a process whereby thermal energy is transferred in response to a temperature difference. There are three modes of heat transfer: conduction, convection, and radiation. Conduction is heat transfer across a stationary medium, either solid or fluid. Convection occurs between a wall at one temperature and a moving fluid at another temperature. The transmission of thermal radiation does not require the presence of a propagating medium and, therefore can occur in a vacuum. Thermal radiation is a form of energy emitted by matter at a nonzero temperature and its wavelength is primarily in the range between 0.1 to 10 μm.

See Main Article Introduction to Heat Transfer

Introduction to Mass Transfer

When there is a species concentration difference in a multicomponent mixture, mass transfer occurs. There are two modes of mass transfer: diffusion and convection. Diffusion results from random molecular motion at the microscopic level, and it can occur in a solid, liquid or gas. Similar to convective heat transfer, convective mass transfer is due to a combination of random molecular motion at the microscopic level and bulk motion at the macroscopic level. It can occur only in a liquid or gas.

See Main Article Mass transfer

Multiphase Systems

A multiphase system is one characterized by the simultaneous presence of several phases, the two-phase system being the simplest case. The term two-component is sometimes used to describe flows in which the phases consist of different chemical substances. For example, steam-water flows are two-phase, while air-water flows are two-component. Some two-component flows (mostly liquid-liquid) technically consist of a single phase but are identified as two-phase flows in which the term “phase” is applied to each of the components. Since the same mathematics describes two-phase and two-component flows, the two expressions will be treated as synonymous. The phases passing through the multiphase systems may be solid, liquid or gas, or a combination of these three.

See Main Article Multiphase Systems

Transport Phenomena in Micro- and Nanoscales

Transport phenomena at dimensions between 1 and 100 μm are different from those at larger scales. At these scales, phenomena that are negligible at larger scales become dominant, but the macroscopic transport theory is still valid. One example of these phenomena in multiphase systemss is surface tension. Transport phenomena in these scales are still regarded as macroscale, because classical theory of transport theory is still valid. As systems scale down even further to the nanoscale, 1-100 nm, or for ultrafast process (e.g., materials processing using picosecond or femtosecond lasers) the fundamental theory used in larger scale systems breaks down because of fundamental differences in the physics.

See Main Article Transport Phenomena in Micro- and Nanoscales

Dimensional Analysis

Dimensional analysis is very important to interpolate the experimental laboratory results (prototype models) to full scale system. Two criteria must be fulfilled to perform such an objective. First, dimensional similarity, in which all dimensions of the prototype to full scale system must be in the same ratio, should be fulfilled. Secondly, dynamic similarity should be met in which relevant dimensionless groups are the same between the prototype model and full scale system.

See Main Article Dimensional Analysis


Scaling, or scale analysis, is a process that uses the basic principles of heat transfer (or other engineering disciplines) to provide order-of-magnitude estimates for quantities of interest. For example, scale analysis of a boundary-layer type flow can provide the order of magnitude of the boundary layer thickness. In addition, scale analysis can provide the order of magnitude of the heat transfer coefficient or Nusselt number, as well as the form of the functions that describe these quantities. Scale analysis confers remarkable capability because its result is within a few percentage points of the results produced by the exact solution.

See Main Article Scaling


Faghri, A., and Zhang, Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, Burlington, MA.

Faghri, A., Zhang, Y., and Howell, J. R., 2010, Advanced Heat and Mass Transfer, Global Digital Press, Columbia, MO.

Further Reading

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