# Consider a vapor condensing on a wall and forming a liquid film. Assume that locally the film

## Question:

Consider a vapor condensing on a wall and forming a liquid film. Assume that locally the film thickness is related to the flow rate per unit transfer area by momentum-transfer considerations.

Then show that the change in mass flow rate is related to the film thickness as per the following equation:

$\frac{d \dot{m}}{d x}=\frac{ho^{2} g \delta^{2}}{\mu} \frac{d \delta}{d x}$

From a heat balance show that the change in mass flow rate is given by

$\hat{h}_{\lg } \frac{d \dot{m}}{d x}=\frac{k_{1}}{\delta}\left[T_{\mathrm{sat}}-T_{\mathrm{w}}\right]$

Equate the two expressions for the change in $$\dot{m}$$ and and derive an expression for $$d \delta / d x$$. Integrate this expression and derive an expression for $$\delta$$ as a function of $$x$$. Verify that the resulting expression is the same as Eq. (18.62). Find an expression for the local heat transfer coefficient and verify that it is proportional to $$x^{-1 / 4}$$.

Find an expression for the average heat transfer coefficient for a wall of height $$L$$ by integration of the local value.

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