Sensitivity Coefficients for Analyzing Interstitial Properties During Phase Change in Porous Media

The sensitivity coefficients for analyzing the interstitial properties during phase change in porous media are presented. Computation of the sensitivity coefficients is the main objective of this study. Experimentally measured temperature data provide an estimate of the phase front locations used as the state variable for this study. The derivations are based on the assumption that the phase front, X, at a given time, t, is a function of interstitial properties τ_t and τ_q with all other parameters remaining constant. The properties τ_t and τ_q are the lag-time in temperature and heat flux, respectively. The analysis includes two types of boundary conditions: prescribed temperature of phase change materials and prescribed temperature for solid matrix. Results for the first case show that for any given ratio τ_t/τ_q, the sensitivity coefficient decreases asymptotically to zero at large times. Furthermore, the sum of the sensitivity coefficients S_t + S_q = 0 when τ_t/τ_q ≈ 1. This is significant information because the variables S_t and S_q have the same magnitude with opposite signs. This implies that these two sensitivity coefficients become linearly dependent and it will be difficult to predict the values of τ_t and τ_q in the neighborhood of τ_t/τ_q ≈ 1. A similar trend but with different sensitivity values are reported for the second case.