Inverse problem of estimating space and time dependent hot surface heat flux in transient transpiration cooling process

In this work, an inverse problem of the transient transpiration cooling is investigated in detail. The hot surface heat flux, which is dependent on time and space, is estimated according to the temperatures measured by thermal sensors. The local thermal non-equilibrium (LTNE) model is used to describe the energy conservation of transpiration cooling process and the thermal dispersion of coolant fluid in considered. The conjugate gradient method (CGM) is applied to solve this inverse problem. The accuracy of the inverse solutions is examined by a certain heat flux with given measurement errors. The examination shows that the inverse method presented by this work can obtain satisfactory results. The effect of variable thermal properties on the inverse solutions cannot be neglected since the large temperature gradient close to the hot surface. The suitable measurement times and points should be chose by considering acceptable accuracy, computational time and memory. Meanwhile, it is found out that the location should be close to the hot surface for more accuracy.