Natural convection problem in a Bingham fluid using the operator-splitting method

© 2015 Elsevier B.V. In this paper, natural convection in a square cavity with differentially heated vertical sides and filled with a Bingham fluid has been studied without any regularisation. The finite element method (FEM) based on the operator splitting method is utilised to solve the problem. This study has been conducted for the pertinent parameters in the following ranges: Rayleigh number Ra=10³-10⁵ and the Prandtl number between 0.1 and 10. Moreover, the Bingham number is studied in wide ranges for different Prandtl and Rayleigh numbers. Results indicate that the heat transfer increases with the enhancement of the Rayleigh number, with a decrease in the size of the unyielded zones. For specific Rayleigh and Prandtl numbers, the increase in the Bingham number decreases the heat transfer. Furthermore, as expected, the growth of the Bingham number expands the unyielded sections in the cavity. Finally, for fixed Rayleigh and Bingham numbers, the unyielded regions grow with the augmentation of the Prandtl number. Comparisons with the previously published work, based on the augmented Lagrangian method, and the bi-viscosity model respectively are made.