Lattice Boltzmann application for a viscoplastic fluid flow and heat transfer into cubic enclosures

The present work deals with a Tri-dimensional natural convection into a cubical enclosure, completely filled with a yield fluid which obeying the Bingham rheological model. A thermal gradient is governed by a uniform temperature imposed on the right and the left walls, when the other surfaces are kept insulated. To solve the governing equations, a numerical code based on the Lattice Boltzmann method is used. The latter has been validated after comparison between the present results and those of the literature. Regarding the Bingham number effect on heat transfer rate inside the enclosure, the convection phenomenon is analyzed through the isotherm plots and its temperature profiles with special attention to the local Nusselt number of the active walls.