Unsteady state heat conduction

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Our discussions thus far have been limited to the case that the temperature is not a function of time. For many applications, it is necessary to consider the variation of temperature with time. In this case, the energy equation for classical heat conduction, eq. <math>\rho {c_p}\frac{{\partial T}}{{\partial t}} = \nabla  \cdot (k\nabla T) + q''' </math> from [[Basics of heat conduction]], should be solved. If the thermal conductivity is independent from the temperature, the energy equation is reduced to eq. <math>\frac{1}{\alpha }\frac{{\partial T}}{{\partial t}} = {\nabla ^2}T + \frac{{q'''}}{k}</math> from [[Basics of heat conduction]]. Analysis of transient heat conduction using lumped (zero-dimensional), one-dimensional, and multidimensional models will be presented in this section.
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*[[Lumped analysis]]
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*[[One-dimensional transient heat conduction in finite slab|finite slabs]]
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*[[One-dimensional transient heat conduction in cylinder|cylinders]]
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*[[One-dimensional transient heat conduction in sphere|spheres]]
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*[[One-dimensional transient heat conduction in semi-infinite body|semi-infinite body]]
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*[[Multidimensional transient heat conduction|multidimensional conduction]]
==References==
==References==

Revision as of 06:49, 3 July 2010

References

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