Studies on a probable correlation between thermal conductivity, kinetics of devitrification and changes in fiber radius of an aluminosilicate ceramic vitreous fiber on heat treatment

Degradation in heat insulation properties of vitrified ceramic fiber blankets has commonly been observed during prolonged use in heat treatment furnaces The associated physico-chemical property changes during such a heat treatment process has been studied under laboratory conditions with systematic time–temperature variations. Alumino-silicate ceramic fiber blanket .samples were subjected to temperature variations from 1100 to 1350 °C and soaking time variations from 1 to 4 h. Additionally, scanning electron microscopic studies of the fibers were undertaken to study progressive shrinkage of the fibers with rise in time and temperature. Quantitative estimation of mullite formation from devitrified fiber was made through an X-ray diffraction (XRD) study. Association of these two concurrent phenomenon made kinetics of devitrification process study difficult and established mathematical kinetics relationship valid for cylindrical (fiber) samples namely (1−α)0.5=(1−kt/r) (where, α, fraction reacted in time t, r, fiber radius and k, reaction rate constant, yielded wide variation in k values. A modification in fiber radius was thus made taking its n th relationship (where n is an empirical constant), such that the factor n took care of the concurrent phenomenon of mullitization associated shrinkage behavior. Plots were made between ln (1−(1−α)0.5) vs. ln kt. The slope gave the value of n ln r. A value of n=1.7–1.8 was consistent for all the data points with fiber diameter varying between 1.0 and 3.5 μ. The modified equation for this type of reaction can thus be established as (1−(1−kt/r1.7–1.8). The radiant energy heat transfer at higher temperature which characterizes different varieties of ceramic blankets is disclosed in a relationship kT=a Tb (where k=thermal conductivity, T=temperature and a, b are constants). Log–log plot of kT vs. T yields values of b=1.3–1.5 and the equation connecting quantity of heat transfer, Q, temperature, T, and fiber blanket thickness Z, can be correlated as Q ∝ (a (T1b−T2b)/Zb. This indicates that the use of a common temperature (T1+T 2)/2 and an average k at that temperature leads to misleading results unless a correction in Z as Zb is brought into the equation. The value of Z modified as Zb finds favor on our observation of b=1.3–1.5≈n=1.3–1.5 as mentioned earlier and appears to have given rise to a correlation between thermal conductivity and kinetic parameters involving kinetics of mullitization reaction, reaction rate constant and shrinkage in fiber radius with heat treatment.