Meshless Local Petrov-Galerkin Simulation of Buoyancy-Driven Fluid Flow and Heat Transfer in a Cavity with Wavy Side Walls
A. Arefmanesh; M. Najafi; and M. Nikfar;

doi:10.3970/cmes.2010.062.113
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 62, No. 2, pp. 113-149, 2010
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Keywords meshless, Petrov-Galerkin, buoyancy-driven, cavity, wavy wall
Abstract As some new applications of the meshless local Petrov-Galerkin method (MLPG) with unity as the test function, a number of buoyancy-driven fluid flow natural convection heat transfer problems in cavities with differentially-heated wavy side walls were analyzed. Cavities with a single wavy wall on one side as well as two wavy walls erected on both sides were considered. For the cases of the double wavy walls, two different configurations in terms of the two walls facing each other on the two sides of the cavities symmetrically or non-symmetrically were investigated. All the simulations performed in this work were based on the stream function-vorticity formulation. The work of this study is focused on the cavities filled with incompressible and laminar flow of air with a Prandtl number of 0.71. The moving least-squares interpolations of the field variables were employed in these MLPG numerical calculations. Appropriate parametric and characteristic studies were carried out on all the wavy wall-cavities considered. The analysis focused on the effects of the dimensionless amplitudes, wall's number of undulations, and different Rayleigh numbers on the fluid flow and natural convection heat transfer within the considered enclosures. The results of the MLPG-new applications show smooth Nusselt number distributions and the occurrences of the distributions maxima and minima in the close proximity of the crests and troughs, respectively, as they were supposed to. The logical behavior of the streamlines and the isotherms affected by the appropriate parameters and geometrical characters prove the total validity and feasibility of the code for the new considered applications.
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