MHD Mixed Convection in a Lid-Driven Cavity with a Bottom Trapezoidal Body: Two-Phase Nanofluid Model

Muhammad Sadiq,Ammar Alsabery,Ishak Hashim

doi:10.3390/en11112943

Muhammad Sadiq, Ammar Alsabery + Show 1 more

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https://doi.org/10.3390/en11112943

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Abstract

The current work examines the effects of a bottom trapezoidal solid body and a magnetic field on mixed convection in a lid-driven square cavity. The Al 2 O 3 -water nanofluid used is assumed to obey Buongiorno’s two-phase model. An isothermal heater is placed on the bottom base of the trapezoid solid body, while the cavity’s vertical walls are kept cold at temperature T c . The top moving wall and the remaining portions of the cavity’s bottom wall are thermally insulated. The Galerkin weighted residual finite element method is employed to solve the dimensionless governing equations. The parameters of interest are the Richardson number ( 0.01 ≤ R i ≤ 100 ), Hartmann number ( 0 ≤ H a ≤ 50 ) , nanoparticle volume fraction ( 0 ≤ ϕ ≤ 0.04 ), and the length of the bottom base of the trapezoidal solid body. The obtained results show that increasing the Richardson number or decreasing the Hartmann number tends to increase the heat transfer rate. In addition, both the thermophoresis and Brownian motion greatly improve the convection heat transfer. It is believed that the current work is a good contribution to many engineering applications such as building design, thermal management of solar energy systems, electronics and heat exchange.

Highlights

Mixed convection mechanism is important for controlling heat transfer in many applications, such as electronic systems and nuclear reactors
We investigated the effects of the Richardson number (Ri), Hartmann number (Ha), nanoparticle volume fraction (φ), and the height of the trapezoidal body (D) on the streamlines, isotherms, nanoparticle distribution, and local and average Nusselt numbers
The current paper investigated the effects of a magnetic field on mixed convective heat transfer in an Al2 O3 –water nanofluid filled lid-driven square cavity with a bottom trapezoidal solid body

Summary

Introduction

Mixed convection mechanism is important for controlling heat transfer in many applications, such as electronic systems and nuclear reactors. Alsabery et al [22] examined the effects of a solid inner insert on the mixed convection of a two-phase nanofluid model in a double lid-driven square cavity They observed various effects on the rate of heat transfer with the augmentation of nanoparticles at a low Reynolds number and high. MHD mixed convection of a nanofluid in a partially-heated wavy-walled lid-driven cavity was considered by Öztop et al [29] They found that the Hartmann and Richardson numbers affected the heat transfer rate with the augmentation of the nanoparticle volume fraction. The MHD mixed convection of a two-phase nanofluid model in a lid-driven square cavity with an inner solid block and corner heater was studied by Alsabery et al [31] They observed that increasing the concentration of the nanoparticles by more than 2% had negative effects on the rate of heat transfer. It is believed that the current work is a good contribution to many engineering applications such as building design, thermal management of solar energy systems, electronics, and heat exchange

Mathematical Formulation

Numerical Method and Validation

Results and Discussion

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Methods