Theory for Lumped Isothermal Domain
The Isothermal Domain feature considers the temperature to be homogeneous in space but not necessarily in time. This is an approximation adapted to situations where a domain is nearly at the average temperature and with small fluctuations, for instance, solid objects made of conductive material immersed in water, or global temperature of a heated and well insulated room adjacent to a cold environment.
Recalling Equation 4-16 given previously in the Theory for Heat Transfer in Fluids section, without pressure-volume work and viscous dissipation, the equation to be solved reduces to:
Integrating this equation over the domain leads to:
(4-32)
where the domain mass and the heat capacity at constant pressure are
The exterior boundaries of each Isothermal Domain need the heat exchange to be specified.
Figure 4-2: Interfaces at exterior boundaries of each Isothermal Domain.
COMSOL Multiphysics provides several types of interfaces: thermal insulation, continuity, ventilation, convective heat flux, and thermal contact.
Thermal Insulation
The Thermal insulation condition prevents any heat transfer between both adjacent domains.
Continuity
The Continuity condition ensures equal temperature at both sides of the interface.
Ventilation
The Ventilation condition is used for cases when an isothermal domain is considered fluid and has an adjacent domain containing the same fluid. An opening lets the fluid going from one domain to another with a determined mass flux, denoted by or , respectively, along or opposite to the geometrical normal vector. The Ventilation condition is written
(4-33)
Convective Heat Flux
The Convective heat flux condition is adapted to cases when an isothermal domain is considered solid and is adjacent to a fluid. Convection occurs at the interface with a specified heat transfer coefficient, h. The interface condition reads
(4-34)
Thermal Contact
When an isothermal domain is considered solid and is adjacent to another solid, thermal contact occurs and is characterized by a given thermal resistance, Rt. At the interface, the condition Thermal contact reads
(4-35)