An efficient real-time scheme is developed to estimate the unsteady, spatially varying wall heat flux in a two-dimensional heat conduction system from the temperature measurement inside the domain. The algorithm is based on the Kalman filtering and the Karhunen-Loe`ve Galerkin procedure. Although the employment of the Kalman filtering technique allows the derivation of a set of sequential estimation equations, the real-time implementation of these equations is never feasible due to the tremendous requirement of computer time and memory. In the present scheme, this difficulty is circumvented by means of the Karhunen-Loe`ve Galerkin procedure that reduces the governing partial differential equation to a minimal set of ordinary differential equations. The performance of the present technique of inverse heat conduction problems is evaluated by several numerical experiments, and it is found to be very accurate as well as efficient.

Issue Section:
Conductive Heat Transfer
Keywords:
Computational, Heat Transfer, Inverse, Numerical Methods, heat conduction, inverse problems, temperature measurement, differential equations, sequential estimation, Kalman filters, Karhunen-Loeve transforms, Galerkin method, external flows, flow instability
Topics:
Differential equations, Heat conduction, Heat flux, Temperature measurement, Algorithms, Dynamic models, Computers, Eigenfunctions, Inverse problems, Filtration, Galerkin method
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