Inverse Modeling of Heat Transfer with Application to Solidification and Quenching

The inverse modeling of heat transfer involves the estimation of boundary conditions from the knowledge of thermal history inside a heat conducting body. Inverse analysis is extremely useful in modeling of contact heat transfer at interfaces of engineering surfaces during materials processing. In the present work, the one-dimensional transient heat conduction equation was inversely modeled in both cartesian as well as cylindrical coordinates. The model is capable of estimating heat flux transients, chill surface temperature, and total heat flow from the source to the sink for an input of thermal history inside the sink. The methodology was adopted to solve boundary heat transfer problems inversely during solidification and quenching. The response of the inverse solution to measured sensor data was studied by carrying out numerical experiments involving the use of varying grid size and time steps, future temperatures, and regularization techniques.