Transient heat flux function estimation utilizing the variable metric method

A new method is presented to solve inverse heat conduction problems (IHCPʹs). The method belongs to the whole domain type of IHCP and utilizes the variable metric method (VMM) instead of the conjugate gradient method (CGM) in order to minimize the function of sum of square errors. Appropriate formulations for sensitivity coefficients, objective function and its gradient are set up in a manner suitable for computer programming of VMM. Numerically simulated data are utilized to assess the effectiveness of the method in comparison with the conjugate gradient method in estimation of space and time varying heat flux. Results indicate that the presented method is quite faster and more accurate than the conjugate gradient method in estimation of unknowns in the whole domain inverse problems.