Galerkin finite element analysis of magneto-hydrodynamic natural convection of Cu-water nanoliquid in a baffled U-shaped enclosure

Abstract

In this paper, single-phase homogeneous nanofluid model is proposed to investigate the natural convection of magneto-hydrodynamic (MHD) flow of Newtonian Cu–H2O nanoliquid in a baffled U-shaped enclosure. The Brinkman model and Wasp model are considered to measure the effective dynamic viscosity and effective thermal conductivity of the nanoliquid correspondingly. Nanoliquid's effective properties such as specific heat, density and thermal expansion coefficient are modeled using mixture theory. The complicated PDS (partial differential system) is treated for numeric solutions via the Galerkin finite element method. The pertinent parameters Hartmann number (1 ≤ Ha ≤ 60), Rayleigh number (103 ≤ Ra ≤ 106) and nanoparticles volume fraction (0% ≤ ϕ ≤ 4%) are taken for the parametric analysis, and it is conducted via streamlines and isotherms. Excellent agreement between numerical results and open literature. It is ascertained that heat transfer rate enhances with Rayleigh number Ra and volume fraction ϕ, however it is diminished for larger Hartmann number Ha.

Keywords

• Natural convection
• Nanoliquid
• Rayleigh number
• Baffled U-shaped
• Nusselt number
• Galerkin finite element method