Inverse Problems in Heat Transfer 1

This chapter presents a stochastic modeling and statistical inference approach to the solution of inverse problems in thermal transport systems. Of particular interest is the inverse heat conduction problem (IHCP) of estimating an unknown boundary heat flux in a conducting solid given temperature data within the domain. Even though deterministic sequential and whole time domain estimation methods have been applied with success over the years for the solution of such problems, we herein introduce stochastic approaches to representing and solving the IHCP. As most engineering systems and processes operate in an uncertain environment, it becomes increasingly important to address their analysis and inverse design in a stochastic manner using statistical data-driven prior and concurrent information on the system response. Recent advances in spectral stochastic modeling, computational Bayesian and spatial statistics enable complete and efficient solution procedures to such problems. Two distinct approaches to the IHCP are presented in this chapter one based on spectral stochastic modeling and the other on Bayesian inference. Although these techniques are discussed in the context of the IHCP, the methodologies presented are general and applicable to design and estimation problems in other more complex problems in thermal transport systems including problems in the presence of convection, radiation and conduction.