# Anisotropic Heat Transfer in Plane of Carbon Fabrics Reinforced Geopolymer Composite
## 1 Introduction
### Physical and Thermal Properties of Carbon Fiber Reinforced Geopolymer Composite  
A geopolymer matrix is prepared by mixing a metakaolin binder of 6.88%, aluminosilicate powder of 49%, and alkali activator with the NaOH/KOH of 44.12% in free dissolution. The chemical composition of the geopolymer consists of Al (2.04), Si (31.80), P (0.08), K (15.5), Zr (1.76), Na (0.63), Ca (0.24), and O (48.32). The geopolymer slurry was filled on the surface of carbon fabrics that later stack together in the transverse direction. The stacked piles of fabrics with filled geopolymer matrix were compressed by a roller until the desired thickness of about 3 mm was achieved. The assembled fabric reinforced geopolymer matrix was placed in a vacuum bag and cured at 0.003 MPa at RT for 2 h. The composite underwent curing at 70 \({}^{\circ}\)C for a period of 2 h, with a follow up 20 h at RT. The composite was fabricated in with the fabrics arranged in the plane direction. Thermal conductivity of the composite was measured in the plane direction. The out-of-plane thermal diffusivity of the rectangular composite sample 3 \(\times\) 15 \(\times\) 220 mm\({}^{3}\) was determined by using a laser flash technique (NETZSCH model LFA 447). The specific heat of the composite was determined by using standard Pyroceram 9606. The out-of-plane thermal conductivity of the composite sample was measured by using thermal diffusivity, specific heat capacity, and density of the sample  
\[K=\rho C_{p}\alpha \tag{5}\]  
\(K\) is the thermal conductivity (W m\({}^{-1}\) K\({}^{-1}\)) of the composite, \(\rho\) is the density of the composite (g cm\({}^{-3}\)), \(C_{p}\) is the specific heat capacity of the samples (J g\({}^{-1}\) K\({}^{-1}\)), and \(\alpha\) is the thermal diffusivity (m\({}^{2}\) s\({}^{-1}\)).  
Thermal conductivity of the composites was determined at a temperature range from 25 \({}^{\circ}\)C to 250 \({}^{\circ}\)C. The graphite coating was applied on the samples to increase the absorption of flashlight on the front surface and the emissivity on the back surface. The standard deviation of the thermal conductivity of the composite was achieved by measuring five samples at each temperature.  
The density of the carbon fiber reinforced geopolymer composites was measured as prepared and for samples after exposure to 1000 \({}^{\circ}\)C. Samples having dimensions of 3 \(\times\) 15 \(\times\) 220 mm were used for density measurements. The volume fraction of fiber, geopolymer matrix, and porosity is calculated from composites by the following equations:  
\[V_{f}=\frac{n\rho_{f}}{t\rho_{f}}\cdot 100\% \tag{6}\]  
\[V_{m}=\frac{1}{t\rho_{m}}\left(\frac{m_{c}}{Lb}-n\rho_{w}\right)\cdot 100\% \tag{7}\]  
\[V_{v}=100-\left(V_{f}+V_{m}\right) \tag{8}\]  
where \(V_{f}\), \(V_{m}\), \(V_{v}\) are the volume fractions of fiber, matrix, and void in the geopolymer composites; \(n\) is the number of fabric layers in the composite samples; \(t\), \(L\), \(b\) are the thickness, length, and width of the composite [m], respectively; \(\rho_{w}\) is the density of fiber layer [g/m\({}^{2}\)]; \(\rho_{f}\) is the density of a single fiber [g/m\({}^{3}\)]; and \(\rho_{m}\) is the density of matrix [g/m\({}^{3}\)].  
The surface morphology of the composite was investigated by a scanning electron microscope (SEM, ZEISS) with field emission source using 30 kV acceleration voltages.