| In this dissertation, attention has been focused on the inverse heat conduction problems.; First, a sequential, non-iterative finite element method has been developed for the inverse heat conduction problems. The method takes advantage of the linearity between the computed temperatures and the instantaneous surface heat fluxes. Explicit minimization of the instantaneous error norm results in a linear system of equations in the current set of surface heat fluxes.; Next, solution stabilities of two one-dimensional inverse heat condition problems are studied based on the above method. In this work, the spectral norm analysis provides a proper choice of the computational time steps, and the Friableness norm analysis shows a clear picture of the error propagations of the computed temperatures (and/or surface heat fluxes).; To reduce the sensitivity of the inverse solutions to the input errors, and to obtain the maximum information out of existing data, the above method is then regularized with the use of future temperatures. The improved method offers a number of potential advantageous features over existing methods: non-iterative solution of the inverse problem, explicit determination of sensitivity matrices, future sequential regularized.; The finite element formulation for the above method is based on the continuous Gherkin approach. As an attempt, the local discontinuous Gherkin method is applied for a one-dimensional inverse heat conduction problem.; Finally, as a seperate effort, the effect of the cooling paths on the quenching hardness is studied. |
