A sequential method of solving inverse natural convection problems

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