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X11 Plate, G = 0 (Dirichlet) at x = 0 and x = L.

 GX11(x  x) =

X12 Plate, G = 0 (Dirichlet) at x = 0 and G/x = 0 (Neumann) at x = L.

 GX12(x  x) =

X13 Plate, G = 0 (Dirichlet) at x = 0 and kG/x + hG = 0 (Neumann) at x = L. Note where B2 = h2L/k

 GX13(x  x) =

X21 Plate, G/x = 0 (Neumann) at x = 0 and G = 0 (Dirichlet) at x = L.

 GX21(x  x) =

X22 Plate, G/x = 0 (Neumann) at both sides.

 GX22(x  x) =

X23 Plate, G/x = 0 (Neumann) at x = 0 and kG/x + h2G = 0 (convection) at x = L.

 GX23(x  x) = same asGX32(x  x) with

 For  x < x, GX23(x  x) = For  x < x, GX23(x  x) =

X31 Plate, - kG/x + h1G = 0 (convection) at x = 0 and G/x = 0 (Neumann) at x = L. Note B1 = h1L/k.

 For  x < x, GX31(x  x) = For  x < x, GX31(x  x) =

X32 Plate, - kG/x + hG = 0 (convection) at x = 0 and G/x = 0 (Neumann) at x = L. Note B1 = h1L/k .

 For  x < x, GX32(x  x) = For  x < x, GX32(x  x) =

X33 Plate, - kG/x + h1G = 0 (convection) at x = 0 and kG/x + h2G = 0 (convection) at x = L. Note B1 = h1L/k and B2 = h2L/k.
 For x < x, GX33(x  x) = x (m2L2 + B1mL - B2mL - B1B2)em(x + x) + (m2L2 + B1mL + B2mL + B1B2)em(x - x + 2L) + (m2L2 + B1mL - B2mL + B1B2)e-m(x - x) + (m2L2 - B1mL + B2mL - B1B2)e-m(x + x - 2L) ÷ Qe2mL - m2L2 + B1mL + B2mL - B1B2 For x > x, GX33(x  x) = x (m2L2 + B1mL - B2mL - B1B2)em(x + x) + (m2L2 + B1mL + B2mL + B1B2)em(x - x + 2L) + (m2L2 + B1mL - B2mL + B1B2)e-m(x - x) + (m2L2 - B1mL + B2mL - B1B2)e-m(x + x - 2L) ÷ Qe2mL - m2L2 + B1mL + B2mL - B1B2

where Q = (m2L2 + B1mL + B2mL + B1B2).

Next: Helmholtz Equation: Steady-Periodic Up: Rectangular Coordinates. Helmholtz Equation. Previous: Semi infinite body, steady
Kevin D. Cole
2002-12-31