10 11/07

1. 7.14. (In terms of class notations, $U$ is now a function $V_0$ of time, not a constant. Diffusion equation is another name for the heat equation. The integration can be done using integration by parts since erfc has an easy derivative.)

2. 7.16. With ``outward velocity,'' the motion of a typical position in the middle of the boundary layer is meant, not a particle velocity.

3. 7.17a. Deduce the suitable forms for $A$ and $\delta$, and and then write the ODE. State the conditions for such flows to be possible.

4. 7.17b. Solve the case $n=\frac12$. To do so, differentiate the ODE for $f$ once and then renotate $f'$ by $g$. Function $g$ satisfies the same equation as the function in Stokes 2nd problem discussed in class, and must therefor have the same general solution: a multiple of erfc plus a constant. Verify it. The final solution is, of course, essentially the same as in 7.14, but must be derived independently.