Transport phenomena (engineering & physics)
Encyclopedia
In engineering
and physics
, the study of transport phenomena concerns the exchange of mass
, energy
, or momentum
between observed and studied engineering systems. This subject is a fundamental component of disciplines involved with fluid mechanics
, heat transfer
, and mass transfer
. It is now considered to be a part of the engineering discipline as much as thermodynamics
, mechanics
, and electromagnetism
. Momentum, heat (energy), and mass transport share a similar mathematical framework, and a similar analytical mechanism that carries out the exchange process.
Transport phenomena actually encompasses all agents of physical change
in the universe
. Moreover, it is considered to be fundamental building block which developed the universe, and which is responsible for the success of all life on earth
. However, the scope here limits the transport phenomena to its relationship to artificial engineered systems.
, transport phenomena are all irreversible processes
of statistical nature stemming from the random continuous motion of molecules, mostly observed in fluids. They involve a net macroscopic transfer of matter, energy or momentum in thermodynamic systems that are not in statistical equilibrium
.
Examples of transport processes include heat conduction
(energy transfer), viscosity
(momentum transfer), molecular diffusion (mass transfer), radiation
and electric charge
transfer in semiconductors.
Transport phenomena have wide application. 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
. In chemical engineering
, transport phenomena are studied in reactor design
, analysis of molecular or diffusive transport mechanisms, and metallurgy
.
The transport of mass, energy, and momentum can be affected by the presence of external sources:
, as illustrated by the following examples:
The molecular transfer equations of Newton's law
for fluid momentum, Fourier's law
for heat, and Fick's law for mass are very similar. One can convert from one transfer coefficient to another in order to compare all three different transport phenomena .
(Definitions of these formulas are given below).
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. The Reynolds analogy
assumes that the turbulent diffusivities are all equal and that the molecular diffusivities of momentum (μ/ρ) and mass (DAB) are negligible compared to the turbulent diffusivities. When liquids are present and/or drag is present, the analogy is not valid. Other analogies, such as von Karman
's and Prandtl's, usually result in poor relations.
The most successful and most widely used analogy is the Chilton and Colburn J-factor analogy
. 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. All of this information is used to predict transfer of mass.
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"). What is remarkable is the observation that, when both pressure and temperature vary, temperature differences at constant pressure can cause matter flow (as in convection
) and pressure differences at constant temperature can cause heat flow. Perhaps surprisingly, the heat flow per unit of pressure difference and the density
(matter) flow per unit of temperature difference are equal.
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.
can be divided into two branches: fluid statics
(fluids at rest), and fluid dynamics
(fluids in motion).
When a fluid is flowing in the x direction parallel to a solid surface, the fluid has x-directed momentum, and its concentration is υxρ. By random diffusion of molecules there is an exchange of molecules in the z direction. Hence the x-directed momentum has been transferred in the z-direction from the faster- to the slower-moving layer.
The equation for momentum transport is Newton's Law of Viscosity written as follows:
where τzx is the flux of x-directed momentum in the z direction, ν is μ/ρ, the momentum diffusivity z is the distance of transport or diffusion, ρ is the density, and μ is the viscosity. Newtons Law is the simplest relationship between the flux of momentum and the velocity gradient.
This can be compared to Fourier's Law for conduction of heat:
where D is the diffusivity constant.
For other systems that involve either turbulent flow, complex geometries or difficult boundary conditions another equation would be easier to use:
where A is the surface area, :
is the temperature driving force, q is the heat flow per unit time, and h is the heat transfer coefficient.
Within heat transfer, two types of convection can occur:
Forced convection
can occur in both laminar and turbulent flow. In the situation of laminar flow in circular tubes, several dimensionless numbers are used such as Nusselt number, Reynolds number, and Prandtl. The commonly used equation is:
Natural or free convection is a function of Grashof and Prandtl numbers. The complexities of free convection heat transfer make it necessary to mainly use empirical relations from experimental data .
Heat transfer is analyzed in packed beds, reactors and heat exchangers.
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
and physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, the study of transport phenomena concerns the exchange of mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
, energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
, or momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
between observed and studied engineering systems. This subject is a fundamental component of disciplines involved with fluid mechanics
Fluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
, heat transfer
Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...
, and mass transfer
Mass transfer
Mass transfer is the net movement of mass from one location, usually meaning a stream, phase, fraction or component, to another. Mass transfer occurs in many processes, such as absorption, evaporation, adsorption, drying, precipitation, membrane filtration, and distillation. Mass transfer is used...
. It is now considered to be a part of the engineering discipline as much as thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
, mechanics
Mechanics
Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment....
, and electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
. Momentum, heat (energy), and mass transport share a similar mathematical framework, and a similar analytical mechanism that carries out the exchange process.
Transport phenomena actually encompasses all agents of physical change
Physical change
Physical changes are changes affecting the form of a chemical substance, but do not change the chemical composition of that substance. Physical changes are used to separate mixtures into their component compounds, but can not usually be used to separate compounds into chemical elements or simpler...
in the universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
. Moreover, it is considered to be fundamental building block which developed the universe, and which is responsible for the success of all life on earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
. However, the scope here limits the transport phenomena to its relationship to artificial engineered systems.
Overview
In physicsPhysics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, transport phenomena are all irreversible processes
Reversible process (thermodynamics)
In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic...
of statistical nature stemming from the random continuous motion of molecules, mostly observed in fluids. They involve a net macroscopic transfer of matter, energy or momentum in thermodynamic systems that are not in statistical equilibrium
Radiative equilibrium
Radiative equilibrium is one of the several requirements for thermodynamic equilibrium, but it can occur in the absence of thermodynamic equilibrium. There are various types of radiative equilibrium, which is itself a kind of dynamic equilibrium....
.
Examples of transport processes include heat conduction
Heat conduction
In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....
(energy transfer), viscosity
Viscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
(momentum transfer), molecular diffusion (mass transfer), radiation
Radiant energy
Radiant energy is the energy of electromagnetic waves. The quantity of radiant energy may be calculated by integrating radiant flux with respect to time and, like all forms of energy, its SI unit is the joule. The term is used particularly when radiation is emitted by a source into the...
and electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
transfer in semiconductors.
Transport phenomena have wide application. 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
Biomedical engineering
Biomedical Engineering is the application of engineering principles and design concepts to medicine and biology. This field seeks to close the gap between engineering and medicine: It combines the design and problem solving skills of engineering with medical and biological sciences to improve...
, where some transport phenomena of interest are thermoregulation
Thermoregulation
Thermoregulation is the ability of an organism to keep its body temperature within certain boundaries, even when the surrounding temperature is very different...
, perfusion
Perfusion
In physiology, perfusion is the process of nutritive delivery of arterial blood to a capillary bed in the biological tissue. The word is derived from the French verb "perfuser" meaning to "pour over or through."...
, and microfluidics
Microfluidics
Microfluidics deals with the behavior, precise control and manipulation of fluids that are geometrically constrained to a small, typically sub-millimeter, scale.Typically, micro means one of the following features:* small volumes...
. In chemical engineering
Chemical engineering
Chemical engineering is the branch of engineering that deals with physical science , and life sciences with mathematics and economics, to the process of converting raw materials or chemicals into more useful or valuable forms...
, transport phenomena are studied in reactor design
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...
, analysis of molecular or diffusive transport mechanisms, and metallurgy
Metallurgy
Metallurgy is a domain of materials science that studies the physical and chemical behavior of metallic elements, their intermetallic compounds, and their mixtures, which are called alloys. It is also the technology of metals: the way in which science is applied to their practical use...
.
The transport of mass, energy, and momentum can be affected by the presence of external sources:
- An odour dissipates more slowly when the source of the odor remains present.
- The rate of cooling of a solid that is conducting heat depends on whether a heat source is applied.
- The gravitational force acting on a rain drop counteracts the drag imparted by the surrounding air.
Commonalities among phenomena
An important principle in the study of transport phenomena is analogy between phenomena.Diffusion
There are some notable similarities in equations for momentum, energy, and mass transfer which can all be transported by diffusionDiffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
, as illustrated by the following examples:
- Mass: the spreading and dissipation of odours in air is an example of mass diffusion.
- Energy: the conduction of heat in a solid material is an example of heat diffusion.
- Momentum: the dragDrag (physics)In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
experienced by a rain drop as it falls in the atmosphere is an example of momentum diffusionMomentum diffusionMomentum diffusion refers to the diffusion, or spread of momentum between particles of matter, usually in the liquid state....
(the rain drop loses momentum to the surrounding air through viscous stresses and decelerates).
The molecular transfer equations of Newton's law
Newtonian fluid
A Newtonian fluid is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.-Definition:...
for fluid momentum, Fourier's law
Heat conduction
In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz....
for heat, and Fick's law for mass are very similar. One can convert from one transfer coefficient to another in order to compare all three different transport phenomena .
| Transported quantity | Physical phenomenon | Equation |
|---|---|---|
| Momentum Momentum In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object... |
Viscosity Viscosity Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity... (Newtonian fluid Newtonian fluid A Newtonian fluid is a fluid whose stress versus strain rate curve is linear and passes through the origin. The constant of proportionality is known as the viscosity.-Definition:... ) |
 |
| Energy Energy In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems... |
Heat conduction Heat conduction In heat transfer, conduction is a mode of transfer of energy within and between bodies of matter, due to a temperature gradient. Conduction means collisional and diffusive transfer of kinetic energy of particles of ponderable matter . Conduction takes place in all forms of ponderable matter, viz.... (Fourier's law) |
 |
| Mass Mass Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:... |
Molecular diffusion (Fick's law) |
 |
(Definitions of these formulas are given below).
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. The Reynolds analogy
Reynolds analogy
Reynolds analogy is popularly known to relate turbulent momentum and heat transfer. The main assumption is that heat flux q/A in a turbulent system is analogous to momentum flux τ, which suggests that the ratio τ/ must be constant for all radial positions....
assumes that the turbulent diffusivities are all equal and that the molecular diffusivities of momentum (μ/ρ) and mass (DAB) are negligible compared to the turbulent diffusivities. When liquids are present and/or drag is present, the analogy is not valid. Other analogies, such as von Karman
Theodore von Karman
Theodore von Kármán was a Hungarian-American mathematician, aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization...
's and Prandtl's, usually result in poor relations.
The most successful and most widely used analogy is the Chilton and Colburn J-factor analogy
Chilton and Colburn J-factor analogy
Chilton–Colburn J-factor analogy is a successful and widely used analogy from heat, momentum, and mass transfer analogies. The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same...
. 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. All of this information is used to predict transfer of mass.
Onsager reciprocal relations
In fluid systems described in terms of temperature, matter density, and pressure, it is known that temperatureTemperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
differences lead to heat
Heat
In physics and thermodynamics, heat is energy transferred from one body, region, or thermodynamic system to another due to thermal contact or thermal radiation when the systems are at different temperatures. It is often described as one of the fundamental processes of energy transfer between...
flows from the warmer to the colder parts of the system; similarly, pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
differences will lead to matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
flow from high-pressure to low-pressure regions (a "reciprocal relation"). What is remarkable is the observation that, when both pressure and temperature vary, temperature differences at constant pressure can cause matter flow (as in convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....
) and pressure differences at constant temperature can cause heat flow. Perhaps surprisingly, the heat flow per unit of pressure difference and the density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
(matter) flow per unit of temperature difference are equal.
This equality was shown to be necessary by Lars Onsager
Lars Onsager
Lars Onsager was a Norwegian-born American physical chemist and theoretical physicist, winner of the 1968 Nobel Prize in Chemistry.He held the Gibbs Professorship of Theoretical Chemistry at Yale University....
using statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
as a consequence of the time reversibility
Time reversibility
Time reversibility is an attribute of some stochastic processes and some deterministic processes.If a stochastic process is time reversible, then it is not possible to determine, given the states at a number of points in time after running the stochastic process, which state came first and which...
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.
Momentum transfer
In momentum transfer, the fluid is treated as a continuous distribution of matter. The study of momemtum transfer, or fluid mechanicsFluid mechanics
Fluid mechanics is the study of fluids and the forces on them. Fluid mechanics can be divided into fluid statics, the study of fluids at rest; fluid kinematics, the study of fluids in motion; and fluid dynamics, the study of the effect of forces on fluid motion...
can be divided into two branches: fluid statics
Fluid statics
Fluid statics is the science of fluids at rest, and is a sub-field within fluid mechanics. The term usually refers to the mathematical treatment of the subject. It embraces the study of the conditions under which fluids are at rest in stable equilibrium...
(fluids at rest), and fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
(fluids in motion).
When a fluid is flowing in the x direction parallel to a solid surface, the fluid has x-directed momentum, and its concentration is υxρ. By random diffusion of molecules there is an exchange of molecules in the z direction. Hence the x-directed momentum has been transferred in the z-direction from the faster- to the slower-moving layer.
The equation for momentum transport is Newton's Law of Viscosity written as follows:
where τzx is the flux of x-directed momentum in the z direction, ν is μ/ρ, the momentum diffusivity z is the distance of transport or diffusion, ρ is the density, and μ is the viscosity. Newtons Law is the simplest relationship between the flux of momentum and the velocity gradient.
Mass transfer
When a system contains two or more components whose concentration vary from point to point, there is a natural tendency for mass to be transferred, minimizing any concentration difference within the system. Mass Transfer in a system is governed by Fick's First Law: 'Diffusion flux from higher concentration to lower concentration is proportional to the gradient of the concentration of the substance and the diffusivity of the substance in the medium.' Mass transfer can take place due to different driving forces. Some of them are :- Mass can be transferred by the action of a pressure gradient(pressure diffusion)
- Forced diffusion occurs because of the action of some external force
- Diffusion is caused by temperature gradients (thermal diffusion)
This can be compared to Fourier's Law for conduction of heat:
where D is the diffusivity constant.
Energy transfer
All process in engineering involve the transfer of energy. Some examples are the heating and cooling of process streams, phase changes, distillations, etc. The basic principle is the law of thermodynamic which is expressed as follows for a static system:For other systems that involve either turbulent flow, complex geometries or difficult boundary conditions another equation would be easier to use:
where A is the surface area, :
is the temperature driving force, q is the heat flow per unit time, and h is the heat transfer coefficient.Within heat transfer, two types of convection can occur:
Forced convection
Forced convection
Forced convection is a mechanism, or type of heat transport in which fluid motion is generated by an external source...
can occur in both laminar and turbulent flow. In the situation of laminar flow in circular tubes, several dimensionless numbers are used such as Nusselt number, Reynolds number, and Prandtl. The commonly used equation is:
Natural or free convection is a function of Grashof and Prandtl numbers. The complexities of free convection heat transfer make it necessary to mainly use empirical relations from experimental data .
Heat transfer is analyzed in packed beds, reactors and heat exchangers.
See also
- Constitutive equationConstitutive equationIn physics, a constitutive equation is a relation between two physical quantities that is specific to a material or substance, and approximates the response of that material to external forces...
- Continuity equationContinuity equationA continuity equation in physics is a differential equation that describes the transport of a conserved quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described...
- Wave propagationWave propagationWave propagation is any of the ways in which waves travel.With respect to the direction of the oscillation relative to the propagation direction, we can distinguish between longitudinal wave and transverse waves....
- PulsePulseIn medicine, one's pulse represents the tactile arterial palpation of the heartbeat by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed against a bone, such as at the neck , at the wrist , behind the knee , on the inside of the elbow , and near the...
- Action potentialAction potentialIn physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and...
- Bioheat transferBioheat transferBioheat transfer is the study of heat transfer in biological systems. In simpler terms, it is the study of how heat moves from one compartment, be it within the body or external to the body, to another compartment in the body. Bioheat transfer has its foundations in the engineering discipline of...
External links
- Transport Phenomena Archive in the Teaching Archives of the Materials Digital Library Pathway