This paper deals with the use of the Conjugate Gradient Method of function estimation with Adjoint Problem for the simultaneous identification of two boundary conditions in natural convection inverse problems in two-dimensional irregular cavities. The unknown boundary conditions are estimated with no a priori information about their functional forms. Irregular geometries in the physical domain are transformed into regular geometries in the computational domain by using an elliptic scheme of numerical grid generation. Therefore, the proposed formulation can be applied to the solution of inverse problems in different geometries. The methodology is applied to cases involving an annular cavity, where the position- and time-dependent heat fluxes are unknown at the inner and outer surfaces. The effects of the number and position of temperature sensors on the inverse problem solution are also addressed in the paper. (C) 2003 Elsevier Ltd. All rights reserved.