Editing Thermal conduction (section)

==Applications==

===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>

===Metal quenching===

Metal [[quenching]] is a transient heat transfer process in terms of the [[Isothermal transformation diagram|time temperature transformation]] (TTT). It is possible to manipulate the cooling process to adjust the phase of a suitable material. For example, appropriate quenching of steel can convert a desirable proportion of its content of [[austenite]] to [[martensite]], creating a very hard and strong product. To achieve this, it is necessary to quench at the "nose" (or [[Eutectic system|eutectic]]) of the TTT diagram. Since materials differ in their [[Biot number]]s, the time it takes for the material to quench, or the [[Fourier number]], varies in practice.<ref name="Abdulkarim dalhatu krb2006">{{cite book|author1=Rajiv Asthana|author2=Ashok Kumar|author3=Narendra B. Dahotre|title=Materials Processing and Manufacturing Science|url=https://books.google.com/books?id=oWRXvrgFhqUC&pg=PA158|access-date=7 May 2013|date=9 January 2006|publisher=Butterworth–Heinemann|isbn=978-0-08-046488-6|pages=158–}}</ref> In steel, the quenching temperature range is generally from 600&nbsp;°C to 200&nbsp;°C. To control the quenching time and to select suitable quenching media, it is necessary to determine the Fourier number from the desired quenching time, the relative temperature drop, and the relevant Biot number. Usually, the correct figures are read from a standard [[nomogram]].{{Citation needed|date=May 2013|reason=Where is this nomogram published?}} By calculating the heat transfer coefficient from this Biot number, one can find a liquid medium suitable for the application.<ref name="Totten2002">{{cite book|author=George E. Totten|title=Handbook of Residual Stress and Deformation of Steel| url=https://books.google.com/books?id=_a9UEHk4cOwC&pg=PA322|access-date=7 May 2013|year=2002|publisher=ASM International| isbn=978-1-61503-227-3|pages=322–}}</ref>