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Hollow Sphere, steady 1-D.

RS11 Hollow sphere, a r b, with G = 0 (Dirichlet) at r = a and at r = b.

4GRS11(r  r) =

RS12 Hollow sphere, a r b, with G = 0 (Dirichlet) at r = a and G/r = 0 (Neumann) at r = b.

4GRS12(r  r) =

RS13 Hollow sphere, a r b, with G = 0 (Dirichlet) at r = 0 and kG/r + h2G = 0 (convection) at r = b. Note B2 = h2b/k.

4GRS13(r  r) =

RS21 Hollow sphere, a r b, with G/r = 0 (Neumann) at r = a and G = 0 (Dirichlet) at r = b.

4GRS21(r  r) =

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.

4HRS22(r  r) =

RS23 Hollow sphere, a r b, with G/r = 0 (Neumann) at r = a and kG/r + h2G = 0 (convection) at r = b. Note B2 = h2b/k.

4GRS23(r  r) =

RS31 Hollow sphere, a r b, with - kG/r + h2G = 0 (convection) at r = a and G = 0 (Dirichlet) at r = b. Note B1 = h1a/k.

4GRS31(r  r) =

RS32 Hollow sphere, a r b, with - kG/r + h2G = 0 (convection) at r = a and G/r = 0 (Neumann) at r = b. Note B1 = h1a/k.

4GRS32(r  r) =

RS33 Hollow sphere, a r b, with - kG/r + h1G = 0 (convection) at r = a and kG/r + h2G = 0 (convection) at r = b. Note B1 = h1a/k and B2 = h2b/k.

4GRS33(r  r) =

Next: Helmholtz Equation. Steady with Up: Radial-spherical coordinates. Steady 1-D Previous: Solid sphere,steady 1-D.
Kevin D. Cole
2002-12-31