Orientation (computer vision): Difference between revisions
en>AvicBot m Bot: Grouping Multiple Issues together (Report error) |
en>Addbot m Bot: Removing {{Orphan}} (Report Errors) |
||
| Line 1: | Line 1: | ||
{{no footnotes|date=May 2012}} | |||
{{ref improve|date=May 2012}} | |||
In [[physics]] and [[engineering]], the '''Fourier number''' (''Fo'') or '''Fourier modulus''', named after [[Joseph Fourier]], is a [[dimensionless number]] that characterizes heat conduction. Together with the [[Biot number]], it characterizes transient conduction problems. Conceptually, it is the ratio of [[diffusion|diffusive]]/[[conduction (heat)|conductive]] transport rate by the quantity storage rate and arises from non-dimensionalization of the [[heat equation]]. The transported quantity is usually either [[heat]] or [[matter]] (particles). | |||
The general Fourrier number is defined as: | |||
: <math>Fo = \dfrac{ \mbox{diffusive transport rate} }{ \mbox{storage rate} }</math> | |||
The thermal Fourrier number is defined by the conduction rate to the rate of thermal energy storage. | |||
:<math>\mathit{Fo}_h = \frac{\alpha t}{L^2}</math> | |||
where: | |||
* α is the [[thermal diffusivity]] [m<sup>2</sup>/s] | |||
* ''t'' is the characteristic time [s] | |||
* ''L'' is the length through which conduction occurs [m] | |||
For transient mass transfer by diffusion, there is an analogous mass Fourier Number (also denoted Fo) defined as: | |||
:<math>\mathit{Fo}_m = \frac{D t}{L^2}</math> | |||
where: | |||
* "D" is the [[Mass_diffusivity|Diffusivity]] (m<sup>2</sup>/s) | |||
* "t" is the characteristic timescale (s) | |||
* "L" is the length scale of interest (m) | |||
==Using Fourier number== | |||
Together with the [[Biot number]], the Fourier number can be used to solve unsteady state conduction problems. The Fourier number is frequently used as a nondimensional time parameter. If the Biot number is less than 0.1, the following equation derived from the Biot and Fourier numbers can be used to find the time. Where ''T''<sub>0</sub> is the initial temperature and ''T'' is the temperature at the center. | |||
: <math>t = \frac{\rho {{c}_{p}}V}{hA} \ln\frac{{{T}_{0}}-{{T}_{\infty }}}{T-{{T}_{\infty }}}</math> | |||
== References == | |||
* {{cite book | first = Frank P. | last = Incropera | authorlink=Frank P. Incropera | coauthors = DeWitt, David P | title = Fundamentals of Heat and Mass Transfer | edition = 5th Edition | page = | publisher = Wiley}} | |||
== See also == | |||
* [[Biot number]] | |||
* [[Convection]] | |||
* [[Heat conduction]] | |||
* [[Heat equation]] | |||
* [[Molecular diffusion]] | |||
* [[Residence time]] | |||
[[Category:Dimensionless numbers of thermodynamics]] | |||
Latest revision as of 05:02, 13 February 2013
Template:No footnotes Template:Ref improve In physics and engineering, the Fourier number (Fo) or Fourier modulus, named after Joseph Fourier, is a dimensionless number that characterizes heat conduction. Together with the Biot number, it characterizes transient conduction problems. Conceptually, it is the ratio of diffusive/conductive transport rate by the quantity storage rate and arises from non-dimensionalization of the heat equation. The transported quantity is usually either heat or matter (particles).
The general Fourrier number is defined as:
The thermal Fourrier number is defined by the conduction rate to the rate of thermal energy storage.
where:
- α is the thermal diffusivity [m2/s]
- t is the characteristic time [s]
- L is the length through which conduction occurs [m]
For transient mass transfer by diffusion, there is an analogous mass Fourier Number (also denoted Fo) defined as:
where:
- "D" is the Diffusivity (m2/s)
- "t" is the characteristic timescale (s)
- "L" is the length scale of interest (m)
Using Fourier number
Together with the Biot number, the Fourier number can be used to solve unsteady state conduction problems. The Fourier number is frequently used as a nondimensional time parameter. If the Biot number is less than 0.1, the following equation derived from the Biot and Fourier numbers can be used to find the time. Where T0 is the initial temperature and T is the temperature at the center.
References
- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534