Placzek transient

2012-03-22T18:24:36Z

206.16.32.136: Minor-

{{Infobox laboratory equipment
|name = Laser Flash Apparatus
|image = LFA 427.JPG
|alt = State-of-the-art laser flash apparatus to measure thermal diffusivity of a multiplicity of different materials over a broad temperature range (-125 … 2800°C).
|uses = to measure [[thermal diffusivity]], [[thermal conductivity]], [[specific heat]],
}}

The '''laser flash analysis''' or '''laser flash method''' is used to measure [[thermal diffusivity]] of a multiplicity of different materials. An energy pulse heats one side of a plane-parallel sample. The temperature rise on the backside due to the energy input is time-dependent detected. The higher the thermal diffusivity of the sample, the faster the energy reaches the backside. A state-of-the-art laser flash apparatus ('''LFA''') to measure thermal diffusivity over a broad temperature range, is shown on the right hand side.

In a one-dimensional, [[adiabatic| adiabatic case]] the [[thermal diffusivity]] <math>a</math> is calculated from this temperature rise as follows:
:<math> a = 0.1388 \cdot \frac{d^2}{t_{1/2}} </math>
Where
* <math>a</math> is the thermal diffusivity
* <math>d</math> is the thickness of the sample
* <math>t_{1/2}</math> is the time to the half maximum

==Measurement principle==
[[File:LFA schema.png|thumb|upright|LFA measurement principle: An energy / laser pulse (red) heats the sample (yellow) on the bottom side and a detector detects the temperaure signal versus time on the top side (green).]]

The laser flash method was developed by Parker et al. in 1961.<ref name="Parker">
{{cite journal
|author=W.J. Parker, R.J. Jenkins, C.P. Butler, G.L. Abbott
|title=Method of Determining Thermal Diffusivity, Heat Capacity and Thermal Conductivity
|journal=Journal of Applied Physics
|volume=32 |issue=9|page=1679
|year=1961
|doi= 10.1063/1.1728417
|url= http://dx.doi.org/10.1063/1.1728417
|bibcode = 1961JAP....32.1679P }}</ref>
In a vertical setup a light source (e.g. [[Nd:YAG laser|laser]], flashlamp) heats the sample from the bottom side and a detector on top detects the time-dependent temperature rise. For measuring the thermal diffusivity, which is strongly temperature-dependent, at different temperatures the sample can be placed in a furnace at constant temperature.

Perfect conditions are
* homogenous material,
* a homogenous energy input on the front side
* a time-dependent short pulse - in form of a [[Dirac delta function]]

Several improvements on the models have been made. In 1963 Cowan takes radiation and convection on the surface into account.<ref name="Cowan">
{{cite journal
|author=R.D. Cowan
|title=Pulse Method of Measuring Thermal Diffusivity at High Temperatures
|journal=Journal of Applied Physics
|volume=34 |issue=4|page=926
|year=1963
|doi= 10.1063/1.1729564
|url= http://dx.doi.org/10.1063/1.1729564
|bibcode = 1963JAP....34..926C }}</ref>
Cape and Lehman consider transient heat transfer, finite pulse effects and also heat losses in the same year.<ref name="CapeLehman">
{{cite journal
|author=J.A. Cape, G.W. Lehman
|title= Temperature and Finite-Pulse-Time Effects in the Flash Method for Measuring Thermal Diffusivity
|journal=Journal of Applied Physics
|volume=34 |issue=7|page=1909
|year=1963
|doi= 10.1063/1.1729711
|url= http://dx.doi.org/10.1063/1.1729711
|bibcode = 1963JAP....34.1909C }}</ref>
Blumm and Opfermann improved the Cape-Lehman-Model with high order solutions of radial transient heat transfer and facial heat loss, non-linear regression routine in case of high heat losses and an advanced, patented pulse length correction.<ref>{{US patent|7,038,209}}</ref><ref name="Blumm">
{{cite journal
|author=J. Blumm, J. Opfermann
|title= Improvement of the mathematical modeling of flash measurements
|journal=High Temperatures – High Pressures
|volume=34 |page=515
|year=2002
|doi= 10.1068/htjr061
|url= http://dx.doi.org/10.1068/htjr061
}}</ref>

== See also ==
{{portal|Physics}}
*[[Thermal diffusivity]]
*[[Thermal conductivity]]
*[[Thermal conductivity measurement]]
*[[Thermal physics]]

==References==
{{Reflist}}

{{DEFAULTSORT:Laser Flash Analysis}}
[[Category:Materials testing]]
[[Category:Heat transfer]]
[[Category:Heat conduction]]

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Placzek transient