Inverse reconstruction of boundary condition coefficients in one-dimensional transient heat conduction

This paper describes the restoration of boundary conditions in one-dimensional transient inverse heat conduction problems (IHCP). In the formulation, convective boundary conditions are represented by linear relations between the temperature and the heat flux, together with an initial condition as a function of space. The temperature inside the solution domain together with the space-dependent ambient temperature or heat transfer coefficient are found from additional boundary temperature or average boundary temperature measurements. The determination of the spacewise dependent ambient temperature is a linear IHCP, whilst the determination of the spacewise dependent heat transfer coefficient is a nonlinear IHCP. For both problems uniqueness theorems are available. Numerical results obtained using the boundary element method are presented and discussed.