11. Variation of Temperature with Distance

Constant Wall Temperature :

\(T_w\) is constant.

\[\frac{T_w-T_m(x)}{T_w-T_{m,i}} = \exp\left[-\left(\frac{Ph}{\dot{m}C_P}\right)x \right]\]

\[q = hA\Delta T_{\text{lm}}\] where \[\Delta T_{\text{lm}} = \text{Log Mean Temperature Difference (LMTD)} = \frac{\Delta T_o-\Delta T_i}{\ln(\Delta T_o/\Delta T_i)}\]

Note: in all equations evaluate fluid properties at the film temperature (\(T_f\)) defined as the arithmetic mean of the surface and free-stream temperatures unless otherwise stated. \[T_f = \frac{T_S + T_\infty}{2} = \frac{T_w+T_m}{2}\]