Recovery of the transient heat transfer coefficient in the nonlinear boundary value problem for the heat equation

AbstractThe problem of numerical identification of the transient heat boundary coefficient for the one-dimensional heat equation in a finite slab under nonlinear boundary conditions is examined on the basis of additional information regarding the solution. After measuring the temperature and the heat flux at the non-active boundary, the inverse heat conduction problem is solved using a fully explicit and stable space marching scheme based on a finite difference implementation of the Mollification Method, and the transient heat boundary coefficient is then approximately determined. Stability bounds are derived an several numerical examples to validate the technique provided