Abstract
A generalized function-specification approach in the full time domain is presented for solving linear inverse heat conduction problems involving an unknown time-varying uniform applied condition at one of the boundary surfaces. The formalism allows unified treatment of such problems in the 1-D,2-D and 3-D domains in rectangular, cylindrical and spherical coordinates. A wide variety of smooth time variations of the boundary condition as well as variations with an abrupt change can readily be accommodated with the present method. A statistical analysis is performed to establish confidence bounds for the error involved in the determination of boundary quantities. The application of the method is illustrated with specific examples in cylindrical geometry.
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