Mixed Convection of a Bingham Fluid in Differentially Heated Square Enclosure with Partitions

Abstract

This paper reports a two-dimensional numerical investigation of mixed convection inside a liddriven square enclosure, completely filled with a non-Newtonian fluid obeying the Bingham model, having two rectangular adiabatic partitions mounted in different dispositions. Due to the problem’ complexity, the latter is solved using finite volume method when the SIMPLER algorithm is adopted for the pressure-velocity coupling. In order to investigate the yield stress effects on flow field and heat transport, we maintain the Richardson number (Gr/Re²) as 0.01, 1 and 10, respectively, which generates a good simulation of forced, mixed and natural convection dominated flow. The Prandtl and Grashof numbers are fixed at 50 and 10⁴, respectively, while the Bingham number covers the range from 0 to 30. The validity of the computing code was ascertained by comparing our results with the numerical ones already available in the literature and that for both cases: Newtonian and non-Newtonian fluid. The phenomenon is analyzed through the streamlines, the isotherms and the Nusselt numbers with special attention to the partitions’ arrangement and its size. It is found that all parameters related to the geometrical dimensions of the partitions play a crucial role on the temperature distribution, flow field and heat transfer enhancement. For all values of the Bingham number, the mean Nusselt number is found as an increasing function of the decrease Richardson number. Thus, the heat transfer improves.