10. Temperature profile for one dimensional heat flow

Temperature profile for one dimensional heat flow (\(T_1>T_2\) and \(b>a\))

Flat plate \[T(x) = (T_2-T_1)\frac{x}{L} + T_1\]


Cylinder: \[\frac{T(r)-T_1}{T_2-T_1} = \frac{\ln(r/a)}{\ln(b/a)}\]


Sphere: \[T(r) = \frac{a}{r}\cdot\frac{b-r}{b-a}\cdot T_1 \, + \, \frac{b}{r}\cdot\frac{r-a}{b-a}\cdot T_2\]