variavel0=<b>MARCOS DE SOUZA</b> - cesuc@cesuc.br CESUC
<b>Humberto Araujo Machado</b> - machado@univap.br UNIVAP
<b>Ricardo Fortes de Miranda</b> - rfmiranda@mecanica.ufu.br UFU
<b>Abstract.</b> Natural convection inside cavities is a classical test case for numerical methods. The well known lid-driven flow  in a square cavity with  sides at different temperature is still a challenge at critical Rayleigh numbers. In recent years,  authors have been dedicated efforts to solve that problem for inclined cavities considering fluids with variable physical  properties. These modifications cause important variations in the flow behavior: circulation cells appea, and stability of  flow is affected. Capturing these cells demands grid refinement and rising processing time. As an alternative, Generalized  Integral Transform Technique (GITT) is an hybrid numerical analytical method that has been applied successfully  to  convection-diffusion problems. In this method, the original potentials are replaced by eigenexpansions series, and the  system of partial differential equations is transformed in an finite system of ordinary differential equations large enough  to obtain the desired accuracy. The method allows to obtain an error controlled solution without needing of any kind of  grid generation. This paper is aimed at the application of the GITT to the transient version of the classical differentially  heated square cavity  problem, considering  fluid properties as functions  of  temperature. The streamfunction-only  formulation of the flow equations and the energy equation under laminar flow are employed in seeking a solution to this  natural convection problem. - The computational procedure is validated comparing results to some previously reported  results for constant fluid properties. The solution for variable fluid properties with partial Boussinesq approximation  (density variation in the body force term only) is presented for several values of inclinations, and for Rayleigh number of  103 and Prandtl number equal  to 0.71, demonstrating GITT capability to capture circulating cells formation and  evolution at low Rayleigh number, and new correlations for angle of inclination  are presented.
<b>Keywords.</b> natural convection, integral transform, variable properties.