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. (3.8), should be solved. If the thermal conductivity is independent from the temperature, the energy equation is reduced to eq. (3.10). Analysis of transient heat conduction using lumped (zero-dimensional), one-dimensional, and multidimensional models will be presented in this section.