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
and i indicates one of the boundaries.
Type 1. Prescribed temperature (Dirichlet condition):
T(ri, t ) = fi(ri, t )
Type 2. Prescribed heat flux (Neumann condition):
= fi(ri, t )
Here ni is the outward-facing normal vector on the body surface.
Type 3. Convective boundary condition (sometimes called the Robin
+ hiT(ri, t ) = fi(ri, t )
Here hi is the heat transfer coefficient and specified function fi
is usually equal to
T is a fluid
Type 4. Thin, high-conductivity film at the body surface:
= fi(ri, t ) - (cb)i
(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:
+ hiT(ri, t ) = fi(ri, t ) - (cb)i
Type 0. No physical boundary. The number 0 (zero) is used
there is no physical boundary, which arises in several body shapes. For
example, a semi-infinite body has ``boundary condition'' of type 0 at
. 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