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### Semi-infinite body, transient 1-D.

X10 Semi-infinite body, 0 < x < , with G = 0 (Dirichlet) at x = 0.

 GX10(x, t | x,) = [4(t - )]-1/2exp - - exp -

X20 Semi-infinite body, with G/x = 0 (Neumann) at x = 0.

 GX20(x, tx, ) = [4(t - )]-1/2exp - + exp -

X30 Semi-infinite body, with - kG/x + h2G = 0 (convection) at x = 0.
 GX30(x, tx, ) = [4(t - )]-1/2 x exp - + exp - - exp(t - ) + (x + x) x erfc + [(t - )]1/2

X40 Semi-infinite body, with - kG/x + (cb)1G/t = 0 (thin film) at x = 0.
 GX40(x, tx, ) = [4(t - )]-1/2 x exp - - exp - + exp - x rerf + where P = and rerf (z) = exp(z2)erfc(z)

X50 Semi-infinite body, with - kG/x + hG + (cb)1G/t = 0 (thin film) at x = 0.
 GX50(x, tx, ) = [4(t - )]-1/2 x exp - - exp - + exp - x (1 + A)rerf + (1 + A) - (1 - A)rerf + (1 - A) where P = , B = hb/k, A = (1 - 4BP)1/2 for 4BP < 1 rerf (z) = exp(z2)erfc(z)

Next: Plate, transient 1-D. Up: Rectangular coordinates. Transient 1-D. Previous: Infinite body, rectangular coordinate
Kevin D. Cole
2002-12-31