Abstract
A sequential algorithm is developed to solve an inverse natural convectionproblem of estimating the time-varying strength of a heat source from theknowledge of temperature readings taken inside the domain. The Boussinesqequation is used to model the natural convection induced by the heat source. Thesequential algorithm is based on the Kalman filtering technique. Although thedirect implementation of the Kalman filter for nonlinear partial differentialequations such as the Boussinesq equation is never feasible due to thetremendous requirements of computer time and memory, a practical method ofsequential estimation is devised in the present investigation—by reducing theBoussinesq equation to a minimal set of ordinary differential equations bymeans of the Karhunen–Loève Galerkin procedure. The performance of thepresent technique of inverse analysis is evaluated by means of severalnumerical experiments, and is found to be very accurate as well as efficient.
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