Temperature due to laser pulse

[Gonzolo]

Hi, I am wondering if anyone here has a way to calculate the surface temperature of an object as it gets hit by a radiation (laser) pulse of known power and duration, (and wavelength...). Thanks.

 

[Tide]

If the pulse is short enough then the temperature is determined by the absorptivity of the material as a function of the material, light frequency, pulse length and intensity distributed over the beam width and skin depth.

 

[Gonzolo]

Cool, I have that data and am pretty well off actually. Is it safe to say that initial temperature at the surface is proportionnal to beam intensity? It seems like so and makes sense, but I cannot find hard confirmation that initial temperature or "applied temperature" is equivalent (proportionnal) to beam intensity. If they are proportionnal, I feel there should be a simple proportionnality constant, containing the data you mentioned, between the two quantities I and Tinitial. Am I missing something simple here?

 

[Tide]

You're right on the mark. The intensity is the power flow of light energy per unit area so that multiplying the intensity (assuming it's constant or, say, the average value) by the duration of the pulse and its area will give the energy delivered by the light. Multiply also by the absorption coefficient to find the amount of energy deposited.

 

[Gonzolo]

... and T is proportionnal to energy deposited through Boltzmann's constant? (and 3/2, or 1/2 or whatever)?.

 

[rayjohn01]

Actually Gonzo you are right on the mark -- you CANNOT know the exact temerature without knowing the ejecta which carry away a certain amount of energy -- I think that you can see that this is an extremely complex question -- rather like asking how deep is a crater from an impact.
Only in the simplest cases of known object surface , light freqency , etc could you answer this .
It is well known that intensity alone CANNOT answer your question , light impinging on a metal surface of ANY intensity may not eject a single thing
but of the right frequency may release a wealth of electrons -- similarly if the light is simply reflected then there is no temperature change
Ray.

 

[Gonzolo]

Extremely complex is right. The question can so simply be stated, yet I'm finding that Fourier spent a great deal of his research working on this (it's what lead him to create his series), and this was way before lasers, the photoelectric effect etc. I suppose I want to be extra sure there isn't a shortcut or simple approximations I'm not aware of (even empirical formulas). The entire general theory on the subject of inding T as a function of all beam and material variables seems to be more than what could fit a single book.

 

[fair001]

A little direction

I am registered in an introductory course and have been given the following information:
Time of laser pulse - 1 ns
Energy - 1 J
Area - 1 cm^2
Thickness - 0.0005 m
Thermal Diffusivity - 0.1 cm^2/s
Wavelength - 0.37 um
Absorption Coefficient - 8000 cm^-1

I need to find the peak temp but am having trouble figuring out what to do with this information. There is no textbook for my course, any suggestion would be appreciated.

 

[Astronuc]

No density?

Is one familiar with the relationship between thermal diffusivity, heat capacity and thermal conductivity?

This would be a time dependent thermal conduction problem. The laser pusle puts some much energy in at the surface of the material, which then conducts.

See this example - http://www.calce.umd.edu/general/Facilities/laser_flash/Results.pdf

A laser flash technique is used to measure thermal diffusivity of a material.

 

[fair001]

There is no density given and the type of metal is not specified. The question says that the sheet metal is mounted on a copper block which is held at constant room temperature.