Direct estimation of time-dependent boundary heat flux

We present a non-iterative direct method to estimate time-varying boundary heat flux in a one-dimensional heat conduction domain with heated and insulated walls. The proposed method relates the temporal variation of the surface heat flux to the temperature variation at the heated surface based on the analytical temperature distribution. Several illustrative examples are examined to verify the performance of the proposed method. The uncertainty analysis of the estimated heat fluxes is discussed. The proposed method may also be useful to make sufficiently accurate initial guesses for more sophisticated method which usually adopt the iterative scheme