Natural convection in an enclosed cavity with conjugate effects in the walls was simulated over a broad range of Grashof number and the limits of convergence were investigated. A fuzzy controller was employed to adjust relaxation factors dynamically during code execution. The controller operates with a rule set that mimics human expert decision making on the appropriate choice of relaxation factor. Performance of the controller was compared to that of simulations with fixed relaxation factors. Cases investigated involved conjugate heat transfer in one or more walls of a rectangular cavity. Governing equations of continuity, momentum and energy in laminar flow were solved using a finite difference method. Simulating natural convection is more challenging at higher Grashof numbers and convergence is more difficult to attain. The controller was able to extend the range of convergence in all the cases, typically by 4 orders of magnitude, and in one case, by 6 orders of magnitude. (C) 2009 Elsevier Ltd. All rights reserved.