Inverse calculation of local heat transfer coefficient on generic surfaces in OpenFOAM

The inverse heat conduction problem (IHCP) is a classic example from the large family of inverse problems, in which a thermal boundary condition is reconstructed on a surface of a body. When the normal fluxes dominate the heat transfer and the tangential fluxes are small, the problem can be simplified into one dimensional. Often, the opposite is true and a multidimensional problem needs to be solved. This paper presents a universal IHCP solver implemented in the open-source code OpenFOAM, whose main advantages are polyhedral meshes, variety of linear solvers, parallel calculations, being an open-source. The solver is robust, efficient and accurate. The quality of the solver is demonstrated on three examples: (i) jet cooling in the pressure die casting, spray cooling of (ii) a rail and (iii) a tube. Valuable data from experiments were used as an input in all three examples. Additionally, this paper introduces, for the first time, a novel semi-analytical formula for determining the optimal number of future timesteps required to solve the sequential IHCP.