Overlapping Multi-Domain Spectral Method for Conjugate Problems of Conduction and MHD Free Convection Flow of Nanofluids over Flat Plates

Musawenkhosi Mkhatshwa,Precious Sibanda,Sandile Motsa

doi:10.3390/mca24030075

Musawenkhosi Mkhatshwa, Precious Sibanda + Show 1 more

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https://doi.org/10.3390/mca24030075

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Abstract

An efficient overlapping multi-domain spectral method is used in the analysis of conjugate problems of heat conduction in solid walls coupled with laminar magnetohydrodynamic (MHD) free convective boundary layer flow of copper (Cu) water and silver (Ag) water nanofluids over vertical and horizontal flat plates. The combined effects of heat generation and thermal radiation on the flow has been analyzed by imposing a magnetic field along the direction of the flow to control the motion of electrically conducting fluid in nanoscale systems. We have assumed that the nanoparticle volume fraction at the wall may be actively controlled. The dimensionless flow equations are solved numerically using an overlapping multi-domain bivariate spectral quasilinearisation method. The effects of relevant parameters on the fluid properties are shown graphically and discussed in detail. Furthermore, the variations of the skin friction coefficient, surface temperature and the rate of heat transfer are shown in graphs and tables. The findings show that the surface temperature is enhanced due to the presence of nanoparticles in the base fluid and the inclusion of the thermal radiation, heat generation and transverse magnetic field in the system. An increase in the nanoparticle volume fraction, heat generation, thermal radiation, and magnetic field parameter enhances the nanofluid velocity and temperature while reducing the heat transfer rate. The results also indicate that the Ag–water nanofluid has higher skin friction and surface temperature than the Cu–water nanofluid, while the opposite behaviour is observed in the case of the rate of heat transfer. The computed numerical results are compared with previously published results and found to be in good agreement.

Highlights

Conjugate heat transfer (CHT) is the interaction between the conduction and the buoyancy forced flow of fluid along a solid surface
The objective of this study is to extend the work of Yu and Lin [9] by analyzing the conjugate heat transfer in MHD free convective flow of Cu–water and Ag–water nanofluids along the vertical and horizontal plates with internal heat generation and thermal radiation
We further demonstrate the application of efficient overlapping multi-domain bivariate spectral quasilinearisation method in solving a nonlinear system of partial differential equations (PDEs) modeling CHT problems

Summary

Introduction

Conjugate heat transfer (CHT) is the interaction between the conduction and the buoyancy forced flow of fluid along a solid surface. The effect of conduction within the solid wall is significant and must be taken into account Such applications include heat exchangers, heaters, nuclear reactors, and pipe insulation systems. In these applications, the analysis of CHT mechanisms, the coupling of the conduction in the solid body and the convection in the fluid surrounding is important [1]. Miyamoto et al [2] considered CHT problems of free convection from a vertical plate with a uniform temperature or a uniform heat flux on the outside surface of the plate. Yu and Lin [9] analyzed conjugate free convection over a vertical and horizontal plate using Keller’s finite-difference method. The flow equations were solved numerically using the finite difference, Runge–Kutta and Shooting method

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