Spectral Relaxation numerical simulation of boundary layer flow with nanoparticles on a moving surface influenced by induced magnetic field

Abstract

The concept of boundary-layer flow is of utmost importance in the science of fluid dynamics, playing a significant role in a wide variety of engineering applications and natural phenomena. The proliferation of research on heat and mass transfer in boundary layers over perpetually moving surfaces can be attributed to the diverse range of manufacturing processes in which they are used, including paper production, metal extrusion, material-handling conveyors, and glass fibre production. Additionally, the expansion of nanotechnology has spurred researchers to explore the flow behaviour at the boundary layer in nanofluids. A nanofluid is a fluid that contains nanoparticles, which results in a significant enhancement of its heat transfer properties due to the increased thermal conductivity. The ability to boost heat and mass transfer with a low concentration of nano-sized particles, and to regulate the transport processes, have led to a large variety of applications for nanofluids. Furthermore, the interaction of a magnetic field with a nanofluid has numerous potential uses that rely on the potential variation in the fluid perpendicular to both its motion and the magnetic field. This thesis presents numerical studies of boundary-layer flow and heat transfer from a moving flat plate subject to different boundary conditions under the influence of an applied induced magnetic field. The focus is on flows of two-dimensional, stable, viscous, incompressible, laminar, and electrically conducting water-based nanofluids incorporated with different metallic and magnetic nanoparticles. At the beginning of this thesis, a theoretical model is studied for steady magnetohydrodynamic (MHD) viscous flow resulting from the motion of a semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation magnetic induction effects and thermal convective boundary conditions are included. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The second study examines the continuous laminar boundary-layer flow of ������������water and ������������water nanofluids with convective heat transport from an inclined stationary or moving flat plate, with a convective surface boundary condition, when there is an induced magnetic field. Then, we perform a computational analysis of ii the combined impacts of temperature- and space-dependent internal heat generation/absorption across a moving flat surface in the presence of an induced magnetic field with a momentum slip condition on the boundary-layer flow of a nanofluid. Later, we investigate the effects of viscous dissipation on a convective aligned MHD flow of a nanofluid over a semi-infinite moving flat surface, where the vectors of the magnetic field and the flow velocity are parallel far from the plate. Lastly, the influence of an induced magnetic field on the MHD heat transfer flow of waterbased ferrofluids, under the influence of slip, over a moving plate subject to uniform heat flux, is analysed. A transverse magnetic field is applied to the plate. The aforementioned mathematical problems are solved by applying appropriate similarity transformations to convert the governing boundary-layer equations and related boundary conditions into a system of nonlinear coupled ordinary differential equations. The fluid is assumed to be a water-based nanofluid containing metallic and magnetic nanoparticles with Prandtl number �������� ���� ������������, without a slip condition. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. The SRM is a simple iteration scheme for solving a nonlinear system of equations that does not require any evaluation of derivatives, perturbation, or linearization. Throughout this thesis, the profiles of velocity, induced magnetic field, temperature, and nanoparticle concentration are derived numerically and displayed for a range of physical parameter values. The significance of multiple embedded physical parameters, including the sheet velocity parameter, magnetic field parameter, Prandtl number, magnetic Prandtl number, thermal radiation parameter, Lewis number, Brownian motion parameter, thermophoresis parameter, Grashof number, Biot number, angle of inclination, nanoparticle volume function, Eckert number, and slip parameter, on the fluid flow is examined, and the findings are presented graphically. The numerical values of the skin friction coefficient, heat transfer rate, mass transfer rate, and other missing slope characteristics are tabulated. The impacts of different metallic and magnetic nanoparticles on the boundary-layer flow, friction drag, and heat flow rate are also investigated. To determine the validity of the computational results, they are compared with those of earlier studies. Thus, this study yields a conclusion that supports the accuracy and reliability of the SRM outcomes. The significance of the electrical conductivity of nanofluids is that the flow and heat transfer may be controlled by an external magnetic field, which could lead to important applications in areas iii such as electronic packing, mechanical engineering, thermal engineering, aerospace, and bioengineering. Increasing the magnetic body force parameter strongly reduces the flow velocity and suppresses magnetic induction, but increases the temperature due to the extra work expended as heat in dragging the magnetic nanofluid. Temperatures also increase with the nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced by a higher wall velocity, Brownian motion parameter, or Prandtl number. Both the hydrodynamic and magnetic boundary-layer thicknesses are reduced by greater reciprocal values of the magnetic Prandtl number. The nanoparticle (concentration) boundary-layer thickness increases with the thermophoresis parameter and Prandtl number, whereas it decreases with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing. The nanofluid with �������� nanoparticles is found to have remarkably high thermal conductivity, whereas the lowest cooling rate is observed in the ����������������–water nanofluid. Moreover, higher flow resistance and a faster rate of heat transfer are detected in magnetite nanofluids. The magnetic field’s principal effects are to lower the dimensionless velocity and raise the dimensionless surface temperature compared with the hydrodynamic situation, which in turn increases the ferrofluid skin friction and heat transfer rate. In recent times, there has been a growing trend of companies recognizing the potential of nanofluid technology and directing their attention to its specific industrial applications. The utilization of boundary-layer flow over a flat surface coupled with nanofluid has found extensive application for addressing thermal management issues. The interaction of magnetic fields and fluid dynamics is crucial in various applications such as liquid metal cooling, magnetic drug targeting, and MHD power generation. In essence, the investigation of boundary-layer flow involving nanoparticles on an evolving surface subjected to an induced magnetic field is of great importance due to its capacity to enhance heat transfer, diminish friction, and propel advancements in fields such as energy production and medicine.