Numerical solution of nonlinear inverse heat conduction problem with a radiation boundary condition

A finite difference solution for the transient nonlinear heat conduction equation in a finite slab with a radiation boundary condition is proposed. An implicit finite difference approximation is used which enables accurate estimation of the surface temperature as well as prevention of oscillation of computed values at the surfaces. A two-time level implicit method is used, while Taylor's forward projection method is employed for taking account of the nonlinearities. An iterative method is described which predicts unknown surface conditions. An example is illustrated which is typical of those that arise in practical applications. The results demonstrate that the method is remarkable in its stability to predict surface conditions without debilitation.