# Diffusion through a non-isothermal spherical film

## Input(s)

P: Pressure (atm)

$$\boldsymbol{D}_{\boldsymbol{A} \boldsymbol{B}}$$: Diffusivity $$\left(\mathrm{cm}^{2} / \mathrm{s}\right)$$

R: Gas Constant $$(\mathrm{J} / \mathrm{mol} \mathrm{K})$$

$$\boldsymbol{T}_{1}$$: Temperature (K)

$$\mathrm{n}$$: Exponent (dimensionless)

$$r_{1}$$: Radius of Gas Film $$(\mathrm{cm})$$

$$\boldsymbol{r}_{\mathbf{2}}$$: Radius of Film $$(\mathrm{cm})$$

$$\boldsymbol{x}_{\boldsymbol{A} 1}$$: Position of Gas (fraction)

$$x_{A 2}$$: Position of Film (fraction)

## Output(s)

$$\boldsymbol{W}_{\boldsymbol{A}}$$: Mass Rate $$(\mathrm{mol} / \mathrm{s})$$

## Formula(s)

$\mathrm{W}_{\mathrm{A}}=\frac{4 * \pi *\left(\frac{\mathrm{P} * \mathrm{D}_{\mathrm{AB}}}{\mathrm{R} * \mathrm{~T}_{1}}\right) *\left(1+\left(\frac{\mathrm{n}}{2}\right)\right)}{\left(\mathrm{r}_{1}^{\frac{\mathrm{n}}{2}}\right) *\left(\left(\frac{1}{\mathrm{r}_{1}}\right)^{1+\frac{\mathrm{n}}{2}}-\left(\frac{1}{\mathrm{r}_{2}}\right)^{1+\frac{\mathrm{n}}{2}}\right)} * \ln \left(\frac{1-\mathrm{x}_{\mathrm{A} 2}}{1-\mathrm{x}_{\mathrm{A} 1}}\right)$

## Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 18, Page: 551 .

## Related

### Diffusion through a stagnant gas film

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