Mixed convection in a trapezoidal enclosure filled with two layers of nanofluid and porous media with a rotating circular cylinder and a sinusoidal bottom wall

Abstract

The laminar two-dimensional mixed convection in a trapezoidal enclosure with a rotating inner circular cylinder and a sinusoidal bottom wall is studied numerically. The fluid inside the enclosure is a CuO–water nanofluid layer in the top space of it, while the bottom space includes a CuO–water nanofluid saturated with a porous medium. Both the right and left sidewalls are assumed adiabatic, while the bottom and the top walls of the enclosure are maintained, respectively, at the hot and cold temperatures. The dimensionless governing equations are expressed for velocity and temperature formulation and modeled by using COMSOL code based on the Galerkin finite element method. Parametric studies on the effects of various significant parameters such as Rayleigh number, Darcy number, the inner cylinder radius, the porous layer thickness, the angular rotational velocity, the solid volume fraction and the number of undulations on the flow and thermal fields together with the heat transfer rate have been performed. The highest value of the stream function for (Ra\u2009=\u2009103 and Ra\u2009=\u2009105) is seen at (R\u2009=\u20090.2 and S\u2009=\u20090.2). The same thing is observed, when the bottom wall is considered wavy. For (Ra\u2009=\u2009103 and N\u2009=\u20090) and (0.5\u2009≤\u2009S\u2009≤\u20090.8), it can be seen that as the inner cylinder radius increases from (R\u2009=\u20090.1) to (R\u2009=\u20090.3), the stream function values increase continuously. It is found that the average Nusselt number increases as the Rayleigh and Darcy numbers, the solid volume fraction, inner cylinder radius and the angular rotational velocity of the cylinder increase, while it decreases as the porous layer thickness and the number of undulations increase. Comparisons with previously published numerical works are performed, and good agreements between the results are observed.