22 - Convection - Correlations for Heat Transfer Coefficient

Constant Wall Heat Flux

\[\frac{dT_m}{dx} = \frac{q_wP}{\dot{m}C_P} = \text{ constant}\] where \(P\) is the perimeter of wall. Integrating from \(x=0\), we get \[T_m(x) = T_{m,i} + \frac{q_wP}{\dot{m}C_P}x \qquad \Longrightarrow \quad \text{Linear variation}\]