Determination of Void Shapes, Sizes, Numbers and Locations Inside an Object with Known Surface Temperatures and Heat Fluxes

During the past several years we have developed an inverse method that allows a thermal cooling system designer to determine proper sizes, shapes, and locations of coolant fluid passages (holes) in, say, an internally cooled turbine blade. The internally cooled object can be made of materials having distinct thermal diffusivities. Thermal expansion has been neglected although, in principle, it could be included. The result is a simple Laplace’s equation for the steady temperature field over a multiply connected domain that is subject to overspecified thermal boundary conditions. This same methodology with minor modifications concerning the type of thermal boundary conditions has been utilized in the nondestructive detection of possible voids in objects with known surface temperature and heat flux distributions.