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

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