Thermal Resistance

The thermal resistance of the heatsink (RthK) can be found from the curves illustrated for any select working point of the semiconductor. The following relation applies:

RthK =  thermal resistance of the  heatsink (K/W)
RthH =  thermal resistance of the semiconductor (K/W)
Tj = junction temperature (°C)
Tu = ambient temperature (°C)
Ptot = Power loss (W)
Once a suitable shape has been select the anticipated junction temperature Tj of the semiconductor should be checked using Tj = TG + Ptot x RthH as the housing temperature TG can be measured by simple means.
Thermal resistance of random shapes with forced cooling
RthKf ≈  a x RthK
R thKf = Thermal resistance, forced cooling   RthK = Thermal resistance, natural cooling

Principles of Heat Transfer
Heat transfer is a directed transfer of energy between mediums, liquids or gases of different temperatures where the natural flow of heat transfer is from high to low temperature.
Conduction
Conduction is a molecular movement within a medium undergoing a fall in temperature. The conduction and the resultingheat transfer depends on the material involved. The conductivities of materials are expressed as coefficients
λ in [ W/mK].

The thermal resistance of a body is expressed in K/W and is dependent on its coefficient and the area and distance of
heat flow. It describes the temperature rise of the body above the ambient for every Watt of power supplied.

Radiation
Radiation is the transfer of energy through electro-magnetic waves in the wavelength range from 0.8µm to 400µm.
As opposed to conduction, radiation is not bound to a transfer medium. It depends on the temperature and surface of the radiating body. Rough bodies radiate stronger than smooth bodies. Radiation increases with temperature of the radiating body whereby dark bodies absorb and emit more heat than light bodies. The following energy retainment formula applies to radiation:
ϕ = reflected quantity
ϕ + α + J = 1       α = absorptivity quantity
J = transferred quantity
ϕ, α und J depend on the material and the wavelengths of the radiation. Radiation from heat sinks is mainly peripheral as radiation between ribs is practically absorbed. To improve heat emission through radiation with natural convection and high surface temperature it is beneficial to black anodize the heat sink as the heat transfer coefficient depends on the ambient medium (air) and the type of heatsink surface and not on the heatsink material itself.
Convection
Convection is heat exchange within liquids, Vaporize or gases through molecular movement from cool to warm areas.
Free convection is brought about by differences of air density caused by different temperatures. Air layers close to the
surface become specifically lighter than deeper layers due to the heat from the heat sink fins. This causes a static pressure difference between the layers resulting in an upward air flow. If the heat seat fins are too close together they warm each other up and restrict free convection. Forced convection (forced cooling) requires a separate convection source in the form of a fan. To achieve optimal convection the heat sinks should be free-standing with vertical fins.
Laminated flow
Laminated flow is air movement in parallel streams or layers with internal friction but without turbulence
Turbulent flow
Above a so-called critical speed a laminated flow changes to a turbulent flow whereby air currents can develop which
work against the flow direction. Turbulent flow is a major factor in achieving good heat dissipation through convection.
Convection is more important in heat dissipation with heat sinks than radiation.
Thermal transfer Before heat can be transferred from a heatsink to the ambient air a thermal resistance must be overcome. The resistance depends on the thermal coefficient of the material and the contact area, whereby the heat transfer is not proportionally increased by a larger contact area but is influenced by the fin construction of the heatsink. The effectiveness of the fins decreases towards their tips where the temperature fall decreases. Heat dissipation through convection can be improved by increasing the air flow, changing its direction and by producing turbulence.