<< [[Heat Transfer]] >[!Definition] >Conduction is the transfer of heat through a material >- across a temperature gradient >- without bulk motion of the material In solids, energy is transferred through lattice vibrations and free electrons. In fluids, energy is transferred through collisions of particles in random motion. ## Generalized conduction equation For [[steady-state]] (nothing is changing in time) and one dimensional (across only one axis) $\dot{Q} = \frac{\Delta T}{R_{cond}}$ > Variables: $\dot{Q}$ [[Heat (Q) is energy transferred between systems at different temperatures|Q]] = [[Heat Transfer]] (W) > - [[what is Q dot?]] >$\Delta T$ = Temperature Difference (K) >$R_{cond}$ = Conductive resistance (K/W), the inverse of [[Thermal conductivity]] ## Differential form $\dot{Q} = -kA\frac{\delta T}{\delta x}$ ![[fourier conduction.jpg]] ### why the negative sign? ![[IMG_0800.jpg|sm]] The temperature gradient (dT) is positive in the direction of increasing temperature. Heat flows in the opposite direction, from hot to cold. ## Relevant properties [[Thermal conductivity]] [Conduction Shape Factors](http://www.engineeringarchives.com/ref_heatxfer_conductionshapefactors.html)