SUMMARYThe inverse problem of determining the time-varying strength of a heat source, which causes natural convection in a two-dimensional cavity, is considered. The Boussinesq equation is used to model the natural convection induced by the heat source. The inverse natural convection problem is solved through the minimization of a performance function utilizing the conjugate gradient method. The gradient of the performance function needed in the minimization procedure of the conjugate gradient method is obtained by employing either the adjoint variable method or the direct di erentiation method. The accuracy and e ciency of these two methods are compared, and a new method is suggested that exploits the advantageous aspects of both methods while avoiding the shortcomings of them.
The inverse problem of determining heat flux at the bottom wall of a two-dimensional cavity from temperature measurement in the domain is considered. The Boussinesq equation is used to model the natural convection induced by the wall heat flux. The inverse natural convection problem is posed as a minimization problem of the performance function, which is the sum of square residuals between calculated and observed temperature, by means of a conjugate gradient method. Instead of employing several fixed sensors, a single sensor is used which is moving at a given frequency over the bottom wall. The present method solves the inverse natural convection problem accurately without a priori information about the unknown function to be estimated.
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