## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

Appendix H

# Solution of the Problem (Chapter 9)

Using the dimensionless expressions in Eqs. (9.28)(9.38) and the following approximate expressions at interfaces z=0 and z=h3,

${\frac{\partial {p}_{1}^{\prime }}{\partial z}|}_{z={h}_{3}}=\frac{{{p}_{1}-{p}_{1}^{\prime }|}_{z={h}_{3}}}{{h}_{1}/2}\mathrm{and}{\frac{\partial {p}_{2}^{\prime }}{\partial z}|}_{z=0}=\frac{{{p}_{2}^{1}|}_{z=0}-{p}_{2}}{{h}_{2}/2}$

(H.1)

Eqs. (9.8)(9.21) becomes

${\omega }_{1}\frac{\partial {p}_{D1}}{\partial {t}_{D}}-{w}_{1}{\mathrm{\Delta }}_{D}{p}_{D1}+2{k}_{vD1}\left({p}_{D1}-{{p}_{D1}^{\prime }|}_{{z}_{D}=1}\right)=0$

(H.2)

${\omega }_{2}\frac{\partial {p}_{D2}}{\partial {t}_{D}}-{w}_{2}{\mathrm{\Delta }}_{D}{p}_{D2}+2{k}_{vD2}\left({p}_{D2}-{{p}_{D2}^{\prime }|}_{{z}_{D}=0}\right)=0$

(H.3)

${p}_{Dj}\to 0\mathrm{when}{t}_{D}\to 0,j=1,2$

(H.4)

${p}_{Dj}\to 0\mathrm{when}{r}_{D}\to \infty ,j=1,2$

(H.5)

${w}_{j}{\left({r}_{D}\frac{\partial {p}_{Dj}}{\partial {r}_{D}}\right)}_{{r}_{D}=1}=-{q}_{Dj},j=1,2$

(H.6) ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required