STUDY ON MHD FREE-CONVECTIVE FLOW IN MICRO-CHANNELS
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STUDY ON MHD FREE-CONVECTIVE FLOW IN MICRO-CHANNELS
ABSTRACT
This study investigates the steady natural convection flow of a viscous, incompressible, electrically conducting fluid in vertical parallel plate microchannels with the combined effects of a transverse magnetic field and suction/injection in the presence of velocity slip and temperature jump at the microchannel surfaces.
Analytical solutions for velocity, temperature, volume flow rate, skin friction, and rate of heat transfer, represented as a Nusselt number, are obtained. The velocity solution was used to compute the skin friction, and the temperature was utilised to get the Nusselt number.
Line graphs are used to discuss the effects of various flow characteristics such as suction/injection, Hartmann number, rarefaction, and fluid-wall interaction. During numerical simulations, results demonstrate that when suction/injection,
rarefaction, and fluid-wall contact increase, so does the volume flow rate, while it decreases as the Hartmann number increases. This means that the gas velocity near the wall will drop.Chapter One: General Introduction
1.0 Introduction.
Microflow has received a lot of attention in recent study because of its novel applications in microfluidic system devices including biomedical sample injection, biochemical cell response, microelectric ship cooling, and so on.
The technological demands necessitate a thorough understanding of flow and heat fields, as well as the related microscale properties, which may differ from those at the macroscale.
Gaseous flow in microscale devices has been in the forefront of research efforts and has garnered a lot of attention in recent years, thanks to the rapid rise of applications in micrototal analytic systems and micro electromechanical systems (MEMS).
These applications have sparked an interest in studying the physical characteristics of fluid flow and convective heat transfer in both forced and natural forms via micron-sized channels known as micro-channels.
A magnetohydrodynamic (MHD) flow, the simplest plasma model, has been the focus of numerous empirical and theoretical studies in a variety of industries.
MHD flows associated with heat transfer have received a lot of attention because they have applications in a variety of industries, including electric propulsion for space exploration, crystal growth in liquids, nuclear reactor cooling, electronic packages, microelectronic devices, and so on.
Gravity is the most prevalent type of body force that operates on fluid, and the gravitational acceleration can be used to calculate the body force vector. When an electrically conducting fluid interacts with a magnetic field, it generates an electric current that reduces fluid velocity. As a result, in the case of free convection of an electrically conducting fluid in the presence of a magnetic field, two body forces should exist: buoyancy and Lorentz.
They interact with one another, influencing how heat and mass are transported. Few investigations on MHD free flows have been conducted for confined enclosures. Seki et al. (1979) investigated mercury’s laminar natural convection in a rectangular container with a magnetic field parallel to gravity.
The numerical results were derived and compared to their experiment in the case of a partially heated vertical wall using a uniform heat generator. Rudraiah et al. (1995) conducted a numerical simulation of natural convection in a two-dimensional cavity filled with an electrically conducting fluid in the presence of a magnetic field aligned with gravity.
They used the Grashof and Hartmann numbers as control variables to investigate the influence of a magnetic field on free convection and heat transfer. Some research was conducted on natural convection in a vertical micro-channel. Examples are Yu and Ameel (2001), Cheng and Weng (2005), and Jha et al. (2013). Details are included in the literature review.
1.1 Aim and Objectives of the Study
The goal of this research is to investigate a fully developed natural convection flow of viscous, incompressible, electrically conducting fluid in micro-channels formed by two vertical parallel plates under the effects of a transverse magnetic field and suction/injection. This is accomplished through the following objectives:
i. Examine how an external transverse magnetic field affects the natural convection flow of fluid in vertical parallel plate micro-channels. ii. Examine how suction/injection and an external transverse magnetic field affect the same flow.
1.2 Research Methodology
The methodology used in this thesis to attain the given objectives is to divide the work into five stages. In the first stage, we examined some existing literature and expanded it to incorporate new factors.
The second stage focuses on solving the mathematical model to provide analytical solutions. In the third stage, the numerical values of the analytical solutions to the generated equations are produced using a computer package (MATLAB).
The fourth stage is the graphical representation of the problems, and the final stage is the interpretation of the graphs to discuss the impact of each controlling parameter and provide conclusions.
1.3 Thesis Structure
A five-chapter thesis on MHD free-convective flow in vertical parallel plate micro-channels was written to achieve the work’s aims. Chapter one introduces the study’s objectives and the strategy used to attain them.
Chapter two primarily evaluates existing material. The third chapter provides a mathematical study and solutions to the governing equations, including their non-dimensionalisation. Chapters four and five provide a discussion of the results/graphs, summary, concluding remarks, and recommendations.
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