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X11 Plate, G = 0 (Dirichlet) at x = 0 and x = L.
X12 Plate, G = 0 (Dirichlet) at x = 0 and
G/x = 0 (Neumann) at x = L.
X13 Plate, G = 0 (Dirichlet) at x = 0 and
kG/x + h_{2}G = 0 (Neumann) at x = L Note
B_{2} = h_{2}L/k
X21 Plate,
G/x = 0 (Neumann) at x = 0
and G = 0 (Dirichlet) at x = L.
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.
X23 Plate,
G/x = 0 (Neumann) at x = 0
and
kG/x + h_{2}G = 0 (convection) at x = L. Note
B_{2} = h_{2}L/k
X31 Plate,
 kG/x + h_{1}G = 0
(convection) at x = 0 and G = 0 (Dirchlet) at x = L. Note
B_{1} = h_{1}L/k
X32 Plate,
 kG/x + h_{1}G = 0
(convection) at x = 0 and
G/x = 0 (Neumann) at x = L.
Note
B_{1} = h_{1}L/k
X33 Plate,
 kG/x + h_{1}G = 0
(convection) at x = 0 and
kG/x + h_{2}G = 0 (convection) at x = L. Note
B_{1} = h_{1}L/k and
B_{2} = h_{2}L/k
G_{X33}(x x^{}) 
= 
; forx < x^{} 


= 
; forx > x^{} 

Next: Rectangular Coordinates. Finite Bodies,
Up: Rectangular Coordinates. Steady 1D.
Previous: Semi infinite body, steady
Kevin D. Cole
20021231