** Next:** Helmholtz Equation. Steady with
** Up:** Radial-spherical coordinates. Steady 1-D
** Previous:** Solid sphere,steady 1-D.

RS11 Hollow sphere,
*a*
*r*
*b*, with *G* = 0
(Dirichlet) at *r* = *a* and at *r* = *b*.
RS12 Hollow sphere,
*a*
*r*
*b*, with *G* = 0
(Dirichlet) at *r* = *a* and
*G*/*r* = 0 (Neumann) at *r* = *b*.
RS13 Hollow sphere,
*a*
*r*
*b*, with *G* = 0
(Dirichlet) at *r* = 0 and
*k**G*/*r* + *h*_{2}*G* = 0 (convection) at *r* = *b*. Note
*B*_{2} = *h*_{2}*b*/*k*.
RS21 Hollow sphere,
*a*
*r*
*b*, with
*G*/*r* = 0 (Neumann) at *r* = *a* and *G* = 0 (Dirichlet) at *r* = *b*.
RS22 Hollow sphere,
*a*
*r*
*b*, with
*G*/*r* = 0 (Neumann) at both boundaries. Note that this geometry
requires a pseudo GF, denoted *H*. The temperature solution found from a
pseudo GF requires that the total volumetric heat flow is equal to the
boundary heat flow, and the spatial average temperature in the body must be
supplied as a known condition.
RS23 Hollow sphere,
*a*
*r*
*b*, with
*G*/*r* = 0 (Neumann) at *r* = *a* and
*k**G*/*r* + *h*_{2}*G* = 0
(convection) at *r* = *b*. Note
*B*_{2} = *h*_{2}*b*/*k*.
RS31 Hollow sphere,
*a*
*r*
*b*, with
- *k**G*/*r* + *h*_{2}*G* = 0 (convection) at *r* = *a* and *G* = 0 (Dirichlet) at *r* = *b*.
Note
*B*_{1} = *h*_{1}*a*/*k*.
RS32 Hollow sphere,
*a*
*r*
*b*, with
- *k**G*/*r* + *h*_{2}*G* = 0 (convection) at *r* = *a* and
*G*/*r* = 0
(Neumann) at *r* = *b*. Note
*B*_{1} = *h*_{1}*a*/*k*.
RS33 Hollow sphere,
*a*
*r*
*b*, with
- *k**G*/*r* + *h*_{1}*G* = 0 (convection) at *r* = *a* and
*k**G*/*r* + *h*_{2}*G* = 0 (convection) at *r* = *b*. Note
*B*_{1} = *h*_{1}*a*/*k* and
*B*_{2} = *h*_{2}*b*/*k*.

** Next:** Helmholtz Equation. Steady with
** Up:** Radial-spherical coordinates. Steady 1-D
** Previous:** Solid sphere,steady 1-D.
*Kevin D. Cole*

*2002-12-31*