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The temperature profile within a body depends upon the rate of its internally-generated heat, its capacity to store some of this heat, and its rate of thermal conduction to its boundaries (where the heat is transfered to the surrounding environment). Mathematically this is stated by the Heat Equation,
along with its boundary conditions, equations that prescribe either the temperature T on, or the heat flux q through, all of the body boundaries W,
In the Heat Equation, the power generated per unit volume is expressed by qgen. The thermal diffusivity a is related to the thermal conductivity k, the specific heat c, and the density r by,
For Steady State problems, the Heat Equation simplifies to,
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