Five types of boundary conditions are defined at physical boundaries, and
a ``zeroth'' type designates those cases with no physical boundaries. In the
equations below the coordinate at the boundary is denoted
r_{i}
and i indicates one of the boundaries.
Type 1. Prescribed temperature (Dirichlet condition):
T(r_{i}, t ) = f_{i}(r_{i}, t )
Type 2. Prescribed heat flux (Neumann condition):
k
= f_{i}(r_{i}, t )
Here n_{i} is the outward-facing normal vector on the body surface.
Type 3. Convective boundary condition (sometimes called the Robin
condition):
k
+ h_{i}T(r_{i}, t ) = f_{i}(r_{i}, t )
Here h_{i} is the heat transfer coefficient and specified function f_{i}
is usually equal to
h_{i}T_{} where
T_{} is a fluid
temperature.
Type 4. Thin, high-conductivity film at the body surface:
k
= f_{i}(r_{i}, t ) - (cb)_{i}
Here product
(cb)_{i} are properties of the surface film (density,
specific heat, and thickness), and the surface film must have a negligible
temperature gradient across it (``lumped'').
Type 5. Thin, high-conductivity film at the body surface, with the
addition of convection heat losses from the surface:
k
+ h_{i}T(r_{i}, t ) = f_{i}(r_{i}, t ) - (cb)_{i}
Type 0. No physical boundary. The number 0 (zero) is used
where
there is no physical boundary, which arises in several body shapes. For
example, a semi-infinite body has ``boundary condition'' of type 0 at
x
. Another ``boundary'' of type 0 occurs at
the center of a solid
cylinder (or sphere), for which the coordinate has a limiting value (r = 0)
but there is no physical boundary.
Next:GF Numbering System. Up:Organization of the GF Previous:Organization of the GFKevin D. Cole 2003-07-21