Natural convection of fluid and solid conjugate problem inside a complex cavity is studied by using vorticity-stream function method. The influences of material character, geometrical shape and Rayleigh number on the heat transfer in overall concerned region have been investigated. The followings can be concluded under steady state: The flow and heat transfer increase with the increase of the thermal conductivity in solid region; Both geometric shape and Rayleigh number affect the overall flow and heat transfer greatly. (C) 2003 Elsevier Ltd. All rights reserved.