Determination and biological application of a time dependent thermal parameter and sensitivity analysis for a conduction problem with superficial evaporation

A boundary value problem, which could represent a transcendent temperature conduction problem with evaporation in a part of the boundary, was studied to determine unknown thermophysical parameters, which can be constants or time dependent functions. The goal of this paper was elucidate which parameters may be determined using only the measured superficial temperature in part of the boundary of the domain. We formulated a nonlinear inverse problem to determine the unknown parameters and a sensitivity analysis was also performed. In particular, we introduced a new way of computing a sensitivity analysis of a parameter which is variable in time. We applied the proposed method to model tissue temperature changes under transient conditions in a biological problem: the hamster cheek pouch. In this case, the time dependent unknown parameter can be associated to the loss of heat due to water evaporation at the superficial layer of the pouch. Finally, we performed the sensitivity analysis to determine the most sensible parameters to variations of the superficial experimental data in the hamster cheek pouch.