Study of Convective heat transfer in a square cavity filled with a viscoplastic fluid by taking into account viscous dissipation

Abstract

The present work is devoted to the numerical study of forced, natural and mixed convective heat transfer inside a square cavity filled with a non-Newtonian viscoplastic fluid described by the Bingham rheological model. The upper and bottom walls of the enclosure are thermally insulated, while the remaining walls are mobile and differentially heated. In order to solve the general coupled equations, a code based on the finite volume method is used and has been validated after comparison of the present results with those from the literature. Viscous dissipation effects on hydrodynamic and thermal properties are analyzed for various values of the Richardson number. The results show that the Richardson number affects the hydrodynamic characteristics as well as heat transfer in a cavity filled with a viscoplastic fluid and leads to a flow structure modification different from that obtained for a Newtonian fluid. The same observation is done concerning the effect of the Brinkman number. Indeed, it has been noted that neglecting the viscous dissipation results in a significant underestimation of heat transfer in an enclosure, especially in the case of natural heat transfer convection