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ABSTRACT
In the present paper, the complicated structures of needled C/C-SiC composite materials with random distributions of fibers and pores are reconstructed. A multiple-relaxation-time (MRT) lattice Boltzmann model with off-diagonal elements in the relaxation time matrix is adopted to predict longitudinal and transverse thermal conductivities of needled C/C-SiC composite materials whose constituents are anisotropic. The accuracy of the proposed method is verified by the good agreements between the numerical results and experimental data obtained by the Hot Disk thermal constants analyzer. After validations, the factors that influence the effective thermal conductivities of the composite materials are investigated.
Nomenclature
| c | = | pseudo sound speed, m/s |
| T | = | temperature, K |
| cp, ρcp | = | heat capacity, J/(kg · K), volumetric heat capacity, J/(m3 · K) |
| D | = | thermal diffusivity, m2/s |
| e | = | discrete velocity |
| f, f eq | = | temperature distribution function, equivalent distribution function |
| m, M | = | moment vector, transformation matrix |
| q, T | = | heat flux, W/m2, temperature, K |
| S | = | relaxation time matrix |
| t, δt, δx | = | time, time step, space step |
| Ω | = | collision matrix |
| ε, γ | = | constants, ε = 2γ, and γ = 1/8 |
| δ | = | thicknesses of materials, m |
| ϕ | = | volume fraction |
| λ | = | thermal conductivity, W/(m · K) |
| τ | = | relaxation time coefficient |
| Subscript | = | |
| α | = | direction of the temperature distribution function |
| = | directions opposite to α | |
| c,w | = | nonwoven cloth, short-cut fiber web |
| e | = | effective |
| i, j | = | number index |
| L | = | longitudinal |
| T | = | transverse |
| x, y, z | = | direction index |
| η, ζ | = | principle axis of heat conduction |
Nomenclature
| c | = | pseudo sound speed, m/s |
| T | = | temperature, K |
| cp, ρcp | = | heat capacity, J/(kg · K), volumetric heat capacity, J/(m3 · K) |
| D | = | thermal diffusivity, m2/s |
| e | = | discrete velocity |
| f, f eq | = | temperature distribution function, equivalent distribution function |
| m, M | = | moment vector, transformation matrix |
| q, T | = | heat flux, W/m2, temperature, K |
| S | = | relaxation time matrix |
| t, δt, δx | = | time, time step, space step |
| Ω | = | collision matrix |
| ε, γ | = | constants, ε = 2γ, and γ = 1/8 |
| δ | = | thicknesses of materials, m |
| ϕ | = | volume fraction |
| λ | = | thermal conductivity, W/(m · K) |
| τ | = | relaxation time coefficient |
| Subscript | = | |
| α | = | direction of the temperature distribution function |
| = | directions opposite to α | |
| c,w | = | nonwoven cloth, short-cut fiber web |
| e | = | effective |
| i, j | = | number index |
| L | = | longitudinal |
| T | = | transverse |
| x, y, z | = | direction index |
| η, ζ | = | principle axis of heat conduction |