Thermal analysis is used to determine the temperature distribution, heat accumulation or dissipation, and other related thermal quantities in an object. The nodal degrees of freedom (primary unknown data) are the temperatures. The primary heat transfer mechanisms are conduction, convection and radiation. In addition, less dominant phenomena such as change of phase (melting or freezing) & internal heat generation can occur.
Conduction.
Conduction is governed by Fourier's law, which is a differential equation describing the rate of heat transfer as a function of temperature gradient, material thermal capacitance & the rate of internal heat generation. This law describes the temperature within the solid body, but does not account for how heat will flow to & from the component. In order to carry out analyses using a conduction model alone, temperatures must be described as part of the boundary condition description. Heat flows (otherwise known as heat flux) are oftentimes specified along boundaries in addition to temperature BC's.
Radiation.
Radiation type boundary conditions are applied if there is a significant temperature
difference between bodies in an enclosed space, or if there is a far field heat source/sink
(such as the sun or a very cold enviornment).
This heat transfer mechanism occurs
exclusively at the surface and is a function of the fourth power of the absolute
temperatures (Kelvin), the emissivity of the bodies & a value known as the Stefan-Boltzman
constant. The emissivity is dependent on surface properties such as the colour &
finish. Radiation type boundary conditions are highly non-linear due to the difference
between fourth order absolute temperatures. A further complication is due to incidents
where the surfaces of two adjacent radiating bodies are not flat and parallel to
each other. This case is overcome by introducing a shape factor (otherwise known
as a view, angle or interception factor) to the solution.
Convection
The convection heat transfer mechanism is due to the temperature gradient between a fluid and a solid. This mechanism is complex as a boundary layer usually exists within the fluid adjacent to the solid boundary. The heat flux is a function of the temperature difference, DT, and a heat transfer coefficient, h.
