Equation Formulation
2D geometries
In 2D geometries, the temperature is assumed to be constant in the out-of-plane direction (z direction with default spatial coordinate names). The equation for heat transfer in solids, Equation 4-14, and in fluids, Equation 4-16, are replaced by:
(4-151)
(4-152)
Here dz is the thickness of the domain in the out-of-plane direction. Here, the conductive heat flux, q, becomes
1D axisymmetric geometries
In 1D axisymmetric geometries, the temperature is assumed to be constant in the out-of-plane direction (z direction with default spatial coordinate names) in addition to the axisymmetry (-coordinate with default spatial coordinate names). The equation for heat transfer in solids, Equation 6-15 is replaced by
(4-153)
where dz is the thickness of the domain in the z direction. The equation for heat transfer in fluids, Equation 6-5, is replaced by
(4-154)
Here, the conductive heat flux, q, becomes
1D geometries
In 1D geometries, the temperature is assumed to be constant in the radial direction. The equation for heat transfer in solids, Equation 6-15 is replaced by
(4-155)
where Ac is the cross section of the domain in the plane perpendicular to the 1D geometry. The equation for heat transfer in fluids, Equation 6-5, is replaced by
(4-156)
Here, the conductive heat flux, q, becomes
Out-of-plane flux conditions would apply to the exterior boundaries of the domain if the 1D geometry was seen as a cylinder. With the geometry reduction process, this heat flux condition is mathematically expressed using the cross section perimeter, Pc, as in:
where q0z is the heat flux density distributed along the cross section perimeter.