Code Manual for CONTAIN 2.0 - Federation of American Scientists

The interface temperature Oihas still not been defined at this point. All interface temperatures can
be eliminated from the equation by imposing the assumption that the heat flux on both sides of the ~
interface between two nodes must be equal. If this is done, the temperature gradient at the interface
in Equation (10-124) can be expressed in terms of differences between the node-center temperatures
alone. The discretized conduction equation for a given node is then given by
Ki+lAi+lAt
T:+l-Tf = c(T;;’ -T;+l) - ‘iAiAtc (T:+’-T;;’) + ~ (10-125)
micP,i m.c
1P,]
.
micp,i
The quantity ~ is the effective conductance between node i and i+l, derived by applying the flux
continuity condition at the interface. This quantity depends upon the thermal conductivity of the two
regions on either side of the interface, and the distances to the center of each node. This parameter
is geometry-dependent because the distances to the node centers and the interface areas are both
geometry-dependent. It can readily be shown that the conductance 1$ and the half-node thicknesses
~ri for the three geometries are given by
Ki .
ki+l ‘1
i5ri,~
[$l-l;[ 1
The 8ri and ~ri, ~depend on the structure geometry.
For the slab geometry
ihi = ~ri+l = ‘i+l - ‘i
2
For the cylindrical geometry
where
[1 i
5ri = ri in –
r.1
[1
?ki+l = ri+l in v
r
;=
[1
112
ri~, + ri2
2
(10-126)
(10-127)
(10-128)
(10-129)
(10-130)
Rev O 10-62 6/30/97