Inverse heat conduction: ill-posed problems
Here is the only commercially published work to deal with the engineering problem of determining surface heat flux and temperature history based on interior temperature measurements. Provides the analytical techniques needed to arrive at otherwise difficult solutions, summarizing the findings of the last ten years. Topics include the steady state solution, Duhamel's Theorem, ill-posed problems, single future time step, and more.
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EXACT SOLUTIONS OF THE INVERSE HEAT
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approximation ature Beck boundary conditions calculated Chapter constant heat flux control volume curve derivative difference equations digital filter dimensionless time step direct problem domain regularization method Duhamel's integral Duhamel's theorem exact matching exact solution example filter coefficients finite difference first-order regularization function specification method future temperatures future time steps gain coefficients geometry given by Eq heat conduction equation heat conduction problem heat flux components heat flux error heat flux history heat transfer coefficient heated surface IHCP algorithm ill-posed problems initial temperature integral inverse heat conduction Inverse Problem least squares matrix measured temperatures measurement errors node nonlinear obtained one-dimensional partial differential equation semi-infinite body sensitivity coefficients sequential regularization method shown in Figure solving surface heat flux surface temperature Taylor series temperature distribution temperature error temperature measurements temperature rise thermal properties triangular heat flux values variance vector volumetric heat capacity whole domain regularization