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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 k G/ x + h2G = 0 (Neumann) at x = L Note 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. Note that this geometry requires a pseudo GF, denoted H. The temperature solution found from a pseudo GF requires that the total volumetric heating sums to zero and the spatial average temperature in the body must be supplied as a known condition.

 HX22(x x  ) =   X23 Plate, G/ x = 0 (Neumann) at x = 0 and k G/ x + h2G = 0 (convection) at x = L. Note B2 = h2L/k

 GX23(x x  ) =   X31 Plate, - k G/ x + h1G = 0 (convection) at x = 0 and G = 0 (Dirchlet) at x = L. Note B1 = h1L/k

 GX31(x x  ) =   X32 Plate, - k G/ x + h1G = 0 (convection) at x = 0 and G/ x = 0 (Neumann) at x = L. Note B1 = h1L/k

 GX32(x x  ) =   X33 Plate, - k G/ x + h1G = 0 (convection) at x = 0 and k G/ x + h2G = 0 (convection) at x = L. Note B1 = h1L/k and B2 = h2L/k
 GX33(x x  ) = ; forx < x = ; forx > x    Next: Rectangular Coordinates. Finite Bodies, Up: Rectangular Coordinates. Steady 1-D. Previous: Semi infinite body, steady
Kevin D. Cole
2002-12-31