(Difference between revisions)
 Revision as of 17:41, 30 November 2009 (view source) (Created page with '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 tempera…')← Older edit Revision as of 21:53, 10 December 2009 (view source)Newer edit → Line 1: Line 1: - 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. + 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. $\rho {c_p}\frac{{\partial T}}{{\partial t}} = \nabla \cdot (k\nabla T) + q'''$ from [[Basics of heat conduction]], should be solved. If the thermal conductivity is independent from the temperature, the energy equation is reduced to eq. $\frac{1}{\alpha }\frac{{\partial T}}{{\partial t}} = {\nabla ^2}T + \frac{{q'''}}{k}$ 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. + + ==References== + + ==Further Reading== + + ==External Links==

## Revision as of 21:53, 10 December 2009

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. $\rho {c_p}\frac{{\partial T}}{{\partial t}} = \nabla \cdot (k\nabla T) + q'''$ from Basics of heat conduction, should be solved. If the thermal conductivity is independent from the temperature, the energy equation is reduced to eq. $\frac{1}{\alpha }\frac{{\partial T}}{{\partial t}} = {\nabla ^2}T + \frac{{q'''}}{k}$ 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.