Fourier's Heat Conduction
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Fourier's heat conduction equation is a partial differential equation that describes the change in temperature (T) as a function of time (t) and position (x). The material properties of heat capacity (Cp), density (rho) and thermal conductivity (k) also play a role. Solutions to this equation provides the materials engineer a means to predict the temperature variation in a solid body. This equation is one of several used in understanding transport phenomena in materials systems. The transport of heat, mass and momentum need to be understood and control in order to produce high quality materials for use by people.
To become acquainted with Fourier's equation and other transport processes, you need to see MTGN461 Transport Phenomena and Reactor Design for Metallurgical and Materials Engineers taught by Prof. Anderson.