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### Solid Sphere, transient 1-D.

RS01 Solid sphere, 0 < r < b, with G = 0 (Dirichlet) at r = b. a. Best convergence for (t - )/b2 small:
 GRS01(r, t  r, ) = x exp - - exp -

b. Best convergence for (t - )/b2 large:

 GRS01(r, t  r, ) = exp - m2(t - )/b2sin(m)sin(m)

RS02 Solid sphere, 0 < r < b, with G/r = 0 (Newmann) at r = b. a. Approximate relation for (t - )/b2 0.022 (here B2 = - 1):

 GRS02(r, t  r, ) = exp - - exp - +exp - - expB2 + B22 x erfc +

b. Best convergence for (t - )/b2 large:
 GRS02(r, t  r, ) = + exp - (t - )/b2 x sin()sin()

The eigenvalues are given by the positive roots of

 cot = 1

RS03 Solid sphere, 0 < r < b, with kG/r + hG = 0 (convection) at r = b.
a. Approximate relation for (t - )/b2 0.022 (here B2 = hb/k - 1):

 GRS03(r, t  r, ) = exp - - exp - +exp - - expB2 + B22 x erfc +

b. Best convergence for (t - )/b2 large:
 GRS03(r, t  r, ) = exp - (t - )/b2 x sin()sin()

where B2 = hb/k - 1 and where the eigenvalues are given by the positive roots of

 cot = - B2

Next: Hollow Sphere, transient 1-D. Up: Radial-spherical coordinates. Transient 1-D. Previous: Infinite body with a
Kevin D. Cole
2002-12-31