Editing Thermal conduction (section)

===Splat cooling===

[[Splat cooling]] is a method for quenching small droplets of molten materials by rapid contact with a cold surface. The particles undergo a characteristic cooling process, with the heat profile at <math>t=0</math> for initial temperature as the maximum at <math>x=0</math> and <math>T = 0</math> at <math>x = -\infin</math> and <math> x = \infin </math>, and the heat profile at <math>t=\infin </math> for <math>-\infin \le x \le \infin</math> as the boundary conditions. Splat cooling rapidly ends in a steady state temperature, and is similar in form to the Gaussian diffusion equation. The temperature profile, with respect to the position and time of this type of cooling, varies with:
<math display="block"> T(x,t) - T_i = \frac{T_i \Delta X}{2 \sqrt{\pi \alpha t}} \exp \left ( -\frac{x^2}{4 \alpha t} \right ) </math>

Splat cooling is a fundamental concept that has been adapted for practical use in the form of [[thermal spraying]]. The [[thermal diffusivity]] coefficient, represented as <math>\alpha</math>, can be written as <math> \alpha =\frac{k}{\rho C_p} </math>. This varies according to the material.<ref name="ZhangZhao2012">{{cite book|author1=Sam Zhang|author2=Dongliang Zhao| title=Aeronautical and Aerospace Materials Handbook|url=https://books.google.com/books?id=PJQmI7hix8kC&pg=PA304|access-date=7 May 2013| date=19 November 2012|publisher=CRC Press|isbn=978-1-4398-7329-8|pages=304–}}</ref><ref name="Eein2002">{{cite book| author=Martin Eein|title=Drop-Surface Interactions.|url=https://books.google.com/books?id=qecltbmIbC4C&pg=PA174|access-date=7 May 2013| year=2002|publisher=Springer|isbn=978-3-211-83692-7|pages=174–}}</ref>