An inverse natural convection problem of estimating the strength of a heatsource

The inverse problem of determining the time-varying strength of a heat sour ce, which causes natural convection in a two-dimensional cavity, is conside red. The Boussinesq equation is used to model the natural convection induce d by the heat source. The inverse natural convection problem is posed as a minimization problem of the least-square criterion, which is solved by a co njugate gradient method employing the adjoint equation to determine the des cent direction. The present method solves the inverse natural convection pr oblem accurately without any simplification of the governing Boussinesq equ ation. (C) 1999 Elsevier Science Ltd. All rights reserved.