An inverse natural convection problem of estimating the strength of a heat source. (English) Zbl 0986.76084
Summary: We consider the inverse problem of determining the time-varying strength of a heat source, which causes natural convection in a two-dimensional cavity. The Boussinesq equation is used to model the natural convection induced by the heat source. The inverse natural convection problem is posed as a minimization problem of least-square criterion, which is solved by a conjugate gradient method employing the adjoint equation to determine the descent direction. The present method solves the inverse natural convection problem accurately without a simplification of the governing Boussinesq equation.
MSC:
76R10 | Free convection |
80A20 | Heat and mass transfer, heat flow (MSC2010) |
35R30 | Inverse problems for PDEs |
80A23 | Inverse problems in thermodynamics and heat transfer |