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{{for|the textbook titled ''Transport Phenomena''|Transport Phenomena (book)}}
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{{Chemical engineering}}
In [[engineering]], [[physics]] and [[chemistry]], the study of '''transport phenomena''' concerns the exchange of [[mass]], [[energy]], and [[momentum]] between observed and studied [[Physical system|systems]]. 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.<br>
While it draws its theoretical foundation from the principles in a number of fields, most of the fundamental theory on the topic is a simple restatement of basic conservation laws.<br>
The fundamental analyses in all three subfields of<br>
<!-- please remember inserting pilcrow: ¶ when paragraphs start explaining new concepts, thanks.-->
* heat,
* momentum, and
* mass transport
are often grounded in the simple principle that the sum total of the quantity being studied must be conserved by the system and its environment. Then, the different phenomena that lead to transport are each considered individually with the knowledge that the sum of their contributions must equal zero. This analysis is useful for calculating any number of relevant quantities. For example, in fluid mechanics a common use of transport analysis is to determine the [[velocity profile]] of a fluid flowing through a rigid volume.
 
Transport phenomena are ubiquitous throughout the engineering disciplines. Some of the most common examples of transport analysis in engineering are seen in the fields of process, chemical, 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]]. It is now considered to be a part of the engineering discipline as much as  [[thermodynamics]], [[mechanics]], and [[electromagnetism]].
 
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]].<ref name=J-L-Plawsky>{{Cite book| last = Plawsky| first =Joel L.| title =Transport phenomena fundamentals| publisher =CRC Press| date =April 2001| format =Chemical Industries Series| pages =1, 2, 3| url =http://books.google.com/books?id=huwzAAlNxzsC&printsec=frontcover&dq=transport+phenomena&cd=2#v=onepage&q&f=false
  | isbn =978-0-8247-0500-8}}</ref>
 
==Overview==
In [[physics]], '''transport phenomena''' are all [[Reversible process (thermodynamics)|irreversible processes]] of [[statistical mechanics|statistical]] nature stemming from the random continuous motion of [[molecules]], mostly observed in [[fluid mechanics|fluids]]. Every aspect of transport phenomena is grounded in two primary concepts : the [[conservation law]]s, and the [[constitutive equation]]s. The conservation laws, which in the context of transport phenomena are formulated as [[continuity equations]], describe how the quantity being studied must be conserved within the universe of the question. 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 gradient]]s and the relationship between [[fluid dynamics|fluid flux]] and the [[forces]] applied to the fluid. These equations also demonstrate the deep connection between transport phenomena and [[thermodynamics]], a connection that explains why transport phenomena are irreversible. Almost all of these physical phenomena ultimately involve systems seeking their [[second law of thermodynamics|lowest energy state]] in keeping with the [[principle of minimum energy]]. 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. The various aspects of such equilibrium are directly connected to a specific transport: [[heat transfer]] is the system's attempt to achieve thermal equilibrium with its environment, just as mass and [[momentum|momentum transport]] move the system towards chemical and [[mechanical equilibrium]].
 
Examples of transport processes include [[heat conduction]] (energy transfer), [[fluid flow]] (momentum transfer), [[molecular diffusion]] (mass transfer), [[radiant energy|radiation]] and [[electric charge]] transfer in semiconductors.<ref>Plawsky, Joel., "Transport Phenomena Fundamentals." Marcel Dekker Inc.,2009</ref><ref>Alonso & Finn. "Physics." Addison Wesley,1992. Chapter 18</ref><ref>Deen, William M. "Analysis of Transport Phenomena." Oxford University Press. 1998</ref><ref>J. M. Ziman, ''Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford Classic Texts in the Physical Sciences)''</ref>
 
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 [[nuclear reactor|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:
* An odor 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 resistance or [[drag (physics)|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<ref>{{cite book
|title=Fundamentals of momentum, heat, and mass transfer
|edition=2
|first1=James R.
|last1=Welty
|first2=Charles E.
|last2=Wicks
|first3=Robert Elliott
|last3=Wilson
|publisher=Wiley
|year=1976
|url=http://books.google.com/?id=hZxRAAAAMAAJ&cd=3}}
</ref> which can all be transported by [[diffusion]], as illustrated by the following examples:
* Mass: the spreading and [[dissipation]] of odors 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 [[drag (physics)|drag]] experienced by a rain drop as it falls in the atmosphere is an example of [[momentum diffusion]] (the rain drop loses momentum to the surrounding air through viscous stresses and decelerates).
 
The molecular transfer equations of [[Newtonian fluid|Newton's law]] for fluid momentum, [[Heat conduction|Fourier's law]] for heat, and [[Fick's laws of diffusion|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.<ref>"Thomas, William J. "Introduction to Transport Phenomena." Prentice Hall: Upper Saddle River, NJ, 2000.</ref>
 
<center>
{|class=wikitable style="text-align: center; width: 40%;"
|+Comparison of diffusion phenomena
!Transported quantity
!Physical phenomenon
!Equation
|-
|[[Momentum]]
|[[Viscosity]]<br/>([[Newtonian fluid]])
|<math>\tau=-\nu \frac{\partial \rho\upsilon }{\partial x}</math>
|-
|[[Energy]]
|[[Heat conduction]]<br/>([[Fourier's law]])
|<math>\frac{q}{A}=-k\frac{dT}{dx}</math>
|-
|[[Mass]]
|[[Molecular diffusion]]<br/>([[Fick's law]])
|<math>J=-D\frac{\partial C}{\partial x}</math>
|}
(Definitions of these formulas are given below).
</center>
 
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 (D<sub>AB</sub>) 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 [[Theodore von Kármán|von Karman]]'s and [[Ludwig Prandtl|Prandtl]]'s, usually result in poor relations.
 
The most successful and most widely used analogy is the [[Chilton and Colburn J-factor analogy]].<ref>{{cite book
|title=Transport Phenomena
|edition=1
|publisher=Nirali Prakashan
|year=2006
|isbn=81-85790-86-8
|page=15-3
|url=http://books.google.com/books?id=co4_XmXJddgC&pg=SA15-PA3}}, [http://books.google.com/books?id=co4_XmXJddgC&pg=SA15-PA3 Chapter 15, p. 15-3]
</ref> This analogy is based on experimental data for gases and liquids in both the [[Laminar flow|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===
{{main|Onsager reciprocal relations}}
 
In fluid systems described in terms of [[temperature]], [[density|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"). 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.<ref name="onsager">[http://prola.aps.org/abstract/PR/v37/i4/p405_1 Reciprocal Relations in Irreversible Processes. I., Phys. Rev. 37, 405 - 426 (1931)]</ref>
 
== Momentum transfer ==
 
In momentum transfer, the fluid is treated as a continuous distribution of matter. The study of momentum transfer, or [[fluid mechanics]] 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 ''υ''<sub>x</sub>ρ. 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:
 
:<math>\tau_{zx}=-\nu \frac{\partial \rho\upsilon_x }{\partial z}</math>
 
where τ<sub>zx</sub> 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:<ref name="Griskey, Richard G 2006">"Griskey, Richard G. "Transport Phenomena and Unit Operations." Wiley & Sons: Hoboken, 2006. 228-248.</ref>
 
* 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:
 
:<math>J_{Ay}=-D_{AB}\frac{\partial Ca}{\partial y}</math>
 
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:
 
:<math>\frac{q}{A}=-k\frac{dT}{dx}</math>
 
For other systems that involve either turbulent flow, complex geometries or difficult boundary conditions another equation would be easier to use:
 
:<math>q = h\cdot(A)\cdot {\Delta T}</math>
 
where A is the surface area, :<math>{\Delta T}</math> 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:
 
:<math>Nu_{a}=\frac{h_{a}D}{k}</math>
Natural or [[free convection]] is a function of [[Grashof number|Grashof]] and [[Prandtl number]]s. The complexities of free convection heat transfer make it necessary to mainly use empirical relations from experimental data.<ref name="Griskey, Richard G 2006"/>
 
Heat transfer is analyzed in packed beds, reactors and heat exchangers.
 
== See also ==
* [[Constitutive equation]]
* [[Continuity equation]]
* [[Wave propagation]]
* [[Pulse]]
* [[Action potential]]
* [[Bioheat transfer]]
 
== Resources ==
*{{cite web
  | title = Some Classical Transport Phenomena Problems with Solutions - Fluid Mechanics
  | url= http://www.syvum.com/eng/fluid/
  }}
*{{cite web
  | title = Some Classical Transport Phenomena Problems with Solutions - Heat Transfer
  | url= http://www.syvum.com/eng/heat/
  }}
*{{cite web
  | title = Some Classical Transport Phenomena Problems with Solutions - Mass Transfer
  | url= http://www.syvum.com/eng/mass/
  }}
 
== External links ==
* [http://teaching.matdl.org/ Transport Phenomena Archive] in the Teaching Archives of the Materials Digital Library Pathway
 
== References ==
{{reflist|colwidth=35em}}
 
{{Chemical engg}}
 
{{DEFAULTSORT:Transport Phenomena (Engineering and Physics)}}
[[Category:Transport phenomena| ]]
[[Category:Chemical engineering]]

Latest revision as of 00:46, 17 March 2014

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