The effect of viscous dissipation on entropy production for a gaseous compressible fluid in a microchannel with a rectangular cross-section.

Number of pages: 124 File Format: word File Code: 32345
Year: 2011 University Degree: Master's degree Category: Facilities - Mechanics
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  • Summary of The effect of viscous dissipation on entropy production for a gaseous compressible fluid in a microchannel with a rectangular cross-section.

    Master's Thesis

    Energy Conversion Trend

    Abstract

     

    In this project, we investigate a steady gas flow in a microchannel with a rectangular cross-section. The flow with a certain temperature enters the channel with a constant temperature wall. Momentum and energy equations are discretized and solved numerically. Discretization has been done by FVM method and approximation by TVD method and Van Albada function have been used. Boundary conditions of velocity slip and temperature jump are applied on the wall. The effect of viscous dissipation and Knudsen number on heat transfer in the channel and in the presence of the mentioned boundary conditions have been investigated. Also, entropy generation in the channel has been investigated in detail. It has been observed that an increase in the Brinkman number increases the entropy production and an increase in the Knudsen number decreases the entropy production in the channel. Chapter One: The need for a narrow passageway The need for narrower passages for the passage of flow

    Fluid flow inside channels is seen in many natural and man-made systems. Mass and heat transfer is carried out by the channel wall in biological systems such as brain, lung, kidney, intestine, etc., as well as many man-made systems such as heat exchangers, nuclear reactors, distillation units, air separation units, and the like. In general, the transfer processes are carried out by the walls of the channels, as long as the current is passing through the channel.

    The channel has two basic tasks that must be performed during its operation:

    1. Make the fluid effectively collide with the walls of the channel.

    2. In order for the transfer process to be carried out well, the channel must always send the new fluid towards the wall and remove the fluid that is near the wall and has completed its transfer process away from the view so that the new fluid in the vicinity of the wall replaces it. is linearly proportional to Therefore, the ratio of the internal surface area of ??the channel to the volume will be inversely proportional to the diameter of the channel, it is clear that the ratio of the internal surface area of ??the channel to the volume will increase as the diameter decreases.

    In the human body, two very effective processes of heat and mass transfer occur in the lung and kidney, where the diameter of the channels or in other words, the narrow channels is about four micrometers.

    A range of micro channels with different dimensions by mentioning The type of system in which the micro channel is used

    As the dimensions of the channel get smaller, some of the theories that were used to describe the state of the fluid, energy and mass transfer need more investigation to ensure their validity. There are two basic factors to move away from conventional theories to describe the micro scale, for example, differences in modeling fluid flow inside small diameter channels can arise for the following reasons:

    1. Changes in basic processes such as deviation from the hypothesis of a continuous medium for gas flow, or the double effect of some forces such as electrokinetic forces and the like.

    2. Uncertainty in the application of basic factors obtained by laboratory methods in higher-scale problems, such as drop coefficients, inlet and outlet, fluid flow inside pipes. 3- Uncertainty in micro-scale measurements, such as geometric dimensions and problem parameters. 1-2 Classification of channels.

    1-2 Classification of channels

    The classification of channels based on their hydraulic diameter is a simple and yet effective solution for checking different ranges. Reducing the dimensions of the channel in different processes has different effects and providing a special condition according to the variables of the process may seem like a very inappropriate option at first glance, but if we consider the number of processes and variables governing the transition from normal dimensions to micro-scale phenomena, we see the same simple method of categorizing channels based on their dimensions as a suitable method, which is fully accepted in the scientific works done in this field.

    Abstract

     

    This paper presents a numerical investigation on steady gaseous flow in rectangular microchannel. Fluid flow with known temperature enters microchannel with constant wall temperature. Momentum and energy equation are discretized by FVM using TVD method and Van Albama function. The effect of viscous dissipation and Knudsen number on heat transfer in the presence of velocity slip and temperature jump boundary conditions is presented. Entropy generation is also thoroughly investigated.

  • Contents & References of The effect of viscous dissipation on entropy production for a gaseous compressible fluid in a microchannel with a rectangular cross-section.

    List:

     

    The first chapter. 5

    need for a narrow passage. 5

    1-1 The need for narrower passages to pass the current. 6

    1-2 Classification of channels 8

    1-3 Basic assumptions in heat transfer and pressure drop in micro channels 9

    Chapter two. 14

    Fluid flow in microchannel. 14

    2-1 Preface 15

    2-2 Hydraulic diameter. 16

    2-3 length of flow development. 17

    2-4 modes of heat transfer. 18

    2-5 continuity hypothesis. 19

    2-6 principles of thermodynamics. 21

    2-7 General rules. 22

    2-8 Special rules. 23

    2-9 flow structure. 24

    2-10 thermal inlet length. 25

    The third chapter. 27

    Description and solution of project 27

    3-1 Preface 28

    3-2 Discretization of momentum equations. 30

    3-3 discretization of continuity equation. 37

    3-4 boundary conditions. 39

    3-4-1 applying the slip boundary condition: 40

    3-4-2 boundary conditions for . 42

    3-4-3 boundary conditions for . 43

    3-4-4 boundary conditions for . 44

    3-5 Applying boundary conditions in momentum equations. 45

    3-6 discretization of the energy equation. 46

    3-6-1 How to apply the temperature jump boundary condition on the walls 60

    3-6-2 Boundary conditions for temperature 61

    3-7 Solution algorithm. 63

    3-7-1 steps of SIMPLER. 63

    3-8 General form of solving equations by TDMA method. 66

    Chapter Four. 68

    Results and suggestions. 68

    4-1 checking the correctness of the numerical solution: 69

    4-2 results and explanations: 69

    4-3 suggestions. 80

    Attachments. 81

    Application of boundary conditions in momentum equations. 82

    Application of boundary conditions in momentum equations. 89

    Application of boundary conditions in momentum equations. 98

    Application of boundary conditions in equations. 105

    Applying boundary conditions on energy equation coefficients. 111

    Resources. 120

     

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The effect of viscous dissipation on entropy production for a gaseous compressible fluid in a microchannel with a rectangular cross-section.