The total thermal conductivity Ctotal of an open celled foam actually consists of four components as noted below:
Ctotal = Csolid ligaments + Cgas + Cgas convection + Cradiant
Csolid ligaments = the conductivity of the three-dimensional array of solid ligaments or struts that form the foam structure. This term is also often referred to as the "bulk thermal conductivity" of the foam. In most applications, particularly for metal foams used as heat exchangers, this is the quantitatively largest and most thermally dominant of the four components and has the following simplified equation form:
Csolid ligaments = Csolid × relative density × .33
Csolid ligaments = direct thermal conductivity or bulk conductivity of the ligament array
Csolid = conductivity of the solid material of the struts
Relative density = % relative density in decimal form, i.e. 10% = .1
.33 = coefficient representing the foam structure geometric or "tortuosity" factor.
It should be noted that the .33 coefficient is derived both from conductivity tests and conceptual analysis wherein the foam can be analogized to a three-dimensional orthogonal pin fin array. In this case is it obvious that one third of the pins or pin mass are oriented in each of the orthogonal x, y, and z directions.
It should also be noted that this equation is somewhat simplified, but is reasonably accurate, slightly conservative, and is more easily understood from a conceptual standpoint than some of the empirical equations that have been developed from various tests.
Cgas = the bulk conductivity of any gas contained within the open-celled foam. It is usually a small contributor for metal foams, but can be a significant contributor with carbon or ceramic foams that have inherently low ligament material conductivity. Refer to the chart of carbon (RVC) foam conductivity to see a typical example of this effect.
Cgas convection = the conductivity of any gas contained within the cells and which can circulate within the foam or within the individual foam cells. Again, this is also a small contributor for metal foams, but can become significant when dealing with carbon or ceramic foams used as insulation. In such cases, small pore size 80 − 100 PPI foams are used to suppress this effect simply by increasing the foam specific surface area and gas flow pressure drop to the point where convection flow is effectively prevented.
Cradiant = the Infra-red electromagnetic radiation that transmits through the open apertures of the foam. This conductivity element is only of importance if the temperatures are very high and typically does not come into play unless the foam is being used as high temperature insulation. In such cases, the smallest pore size foam is typically used to suppress the view factor and increase the optical opacity of the foam.