How porosity could affect thermal conductivity and coefficient of thermal expansion in carbon fiber reinforced Aluminium matrix composite?
We may possibly want to estimate the thermal conductivity of the porous body as follows:
i) Let the density of a porous material (ρ*) and that of the bulk (compact) material (ρ) be given, in terms of porosity (Ø), by: ρ* = (1 - Ø)·ρ.
ii) Let a comparable expression to the former (considering units) be used to estimate the volumetric heat capacity of the porous solid (ρ*·cp*): ρ*·cp* = (1 - Ø)·ρ·cp, where cp* stands for the (isobaric) specific heat capacity of the porous body, while cp is that of the bulk material.
iii) Let k* be the thermal conductivity of the porous body, while α* = k*/(ρ*·cp*) is its thermal diffusivity. Accordingly, let k be the thermal conductivity of the bulk material, being α = k/(ρ·cp) its thermal diffusivity.
iv) We now obtain, for the thermal conductivity of the porous body: k* = (1 - Ø)·(α*/α)·k.
v) Noticing that the thermal diffusivity accounts for the aptitude to conduct thermal energy relative to the aptitude to store thermal energy, we may want to substitute the dimensionless α*/α ratio by the empirical factor (F), reasonably taken as constant for a rather coarse first guess estimate:
k* = (1 - Ø)·F·k.
In my view the thermal conductivity of the material will be reduced with increasing porosity. The thermal expansion is a pure volumetric effect, the porosity will not influence it (the expansion of a solid sphere is the same as that of a hollow sphere)
pl refer to the attached link
Article Micromechanical analysis of the effect of porosity on the th...
Increasing the porosity levels and reducing the pore sizes reduce the thermal conductivity of the ceramic samples.
The pore size and porosity levels affect the thermal expansion but it can increase or decrease depend on rigidity, as S. Ghabezloo presents in his article (see above)
We may possibly want to estimate the thermal conductivity of the porous body as follows:
i) Let the density of a porous material (ρ*) and that of the bulk (compact) material (ρ) be given, in terms of porosity (Ø), by: ρ* = (1 - Ø)·ρ.
ii) Let a comparable expression to the former (considering units) be used to estimate the volumetric heat capacity of the porous solid (ρ*·cp*): ρ*·cp* = (1 - Ø)·ρ·cp, where cp* stands for the (isobaric) specific heat capacity of the porous body, while cp is that of the bulk material.
iii) Let k* be the thermal conductivity of the porous body, while α* = k*/(ρ*·cp*) is its thermal diffusivity. Accordingly, let k be the thermal conductivity of the bulk material, being α = k/(ρ·cp) its thermal diffusivity.
iv) We now obtain, for the thermal conductivity of the porous body: k* = (1 - Ø)·(α*/α)·k.
v) Noticing that the thermal diffusivity accounts for the aptitude to conduct thermal energy relative to the aptitude to store thermal energy, we may want to substitute the dimensionless α*/α ratio by the empirical factor (F), reasonably taken as constant for a rather coarse first guess estimate:
k* = (1 - Ø)·F·k.
Elsewhere at this forum, I have suggested a mixture rule to estimate the coefficient of thermal expansion for a composite after those of its components: https://www.researchgate.net/post/I_want_to_theoretically_calculate_the_CTE_of_particle_loaded_glass_reinforced_vinyl_ester_composite_Which_relation_will_give_better_results
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