Flow and Heat Exchange in Engineering

Flow and Heat Exchange in Engineering

Engineering Flow and Heat Exchange

By

Jaideep Devgan

Flow and Heat Exchange in Engineering

Jaideep Devgan

ISBN - 9789361520037

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Preface

Welcome to the world of Engineering Electromagnetics! This book is designed to provide students and professionals with a comprehensive understanding of the fundamental principles and applications of electromagnetics in engineering.

Electromagnetics is a cornerstone of modern technology, underlying the operation of countless devices and systems that shape our daily lives. From wireless communication to power generation, electromagnetics plays a crucial role in enabling the technologies that drive our interconnected world.

This book is structured to provide a solid foundation in the theory of electromagnetics, starting with basic concepts such as electric and magnetic fields, electromagnetic waves, and Maxwell's equations. Through clear explanations, illustrative examples, and practical applications, readers will develop the skills necessary to analyze and design electromagnetic systems.

Whether you are a student delving into the field for the first time or a practicing engineer seeking to deepen your understanding, this book aims to be your guide through the intricacies of electromagnetics. It is my hope that the material presented here will inspire curiosity, foster understanding, and empower readers to tackle real-world engineering challenges with confidence.

I would like to express my gratitude to all those who have contributed to this book, whether directly or indirectly. Special thanks to my colleagues, students, and mentors whose insights and feedback have enriched its content. I also extend my appreciation to the publishers and editors who have helped bring this project to fruition.

I invite you to embark on this journey through the fascinating realm of Engineering Electromagnetics. May this book serve as a valuable resource in your quest for knowledge and mastery of this essential discipline.

Table of Contents

Introduction to Fluid Mechanics and Heat Transfer1

1.1 Importance of Fluid Mechanics and Heat Transfer1

1.2 Fundamental Concepts and Definitions2

1.3 Dimensions and Units4

1.4 Continuum Hypothesis4

1.5 Properties of Fluids5

1.6 Modes of Heat Transfer6

Fluid Statics8

2.1 Pressure and Pressure Measurement8

2.2 Hydrostatic Pressure9

2.3 Manometry10

2.4 Buoyancy and Archimedes’ Principle11

2.5 Surface Tension12

2.6 Capillary Effects13

Fluid Kinematics16

3.1 Flow Visualization16

3.2 Lagrangian and Eulerian Descriptions17

3.3 Streamlines, Pathlines, and Streaklines18

3.4 Vorticity and Circulation20

3.5 Deformation and Strain Rate22

3.6 Rotational and Irrotational Flow23

Conservation Laws for Fluid Flow26

4.1 Mass Conservation (Continuity Equation)26

4.2 Momentum Conservation

(Navier-Stokes Equations)28

4.3 Energy Conservation (Energy Equation)30

4.4 Bernoulli’s Equation32

4.5 Applications of Bernoulli’s Equation34

4.6 Dimensional Analysis and Similarity36

Viscous Flow in Pipes39

5.1 Laminar and Turbulent Flow39

5.2 Reynolds Number40

5.3 Hagen-Poiseuille Flow41

5.4 Darcy-Weisbach Equation43

5.5 Major and Minor Losses44

5.6 Pipe Networks45

External Flow and Boundary Layers48

6.1 Boundary Layer Concept48

6.2 Laminar Boundary Layer49

6.3 Turbulent Boundary Layer49

6.4 Separation and Drag51

6.5 Lift and Aerodynamic Forces52

6.6 Computational Fluid Dynamics (CFD)53

Heat Conduction56

7.1 Fourier’s Law of Heat Conduction56

7.2 Steady-State Conduction57

7.3 Transient Conduction59

7.4 Thermal Resistance and Thermal Circuits61

7.5 Numerical Methods for Conduction63

7.6 Extended Surfaces (Fins)66

Convection Heat Transfer69

8.1 Convection Mechanisms69

8.2 Newton’s Law of Cooling69

8.3 Forced Convection70

8.4 Natural Convection71

8.5 Correlations for Convection Coefficients74

8.6 Heat Transfer in Boundary Layers75

Radiation Heat Transfer78

9.1 Blackbody Radiation78

9.2 Planck’s Law and Stefan-Boltzmann Law80

9.3 View Factors and Radiative Exchange81

9.4 Radiation Heat Transfer in Enclosures82

9.5 Radiation Heat Transfer in

Participating Media83

9.6 Radiation Shielding and

Surface Properties85

Heat Exchangers89

10.1 Types of Heat Exchangers89

10.2 Overall Heat Transfer Coefficient90

10.3 Log Mean Temperature Difference

(LMTD)91

10.4 Effectiveness-NTU Method92

10.5 Heat Exchanger Analysis and Design93

10.6 Fouling and Maintenance94

Boiling and Condensation97

11.1 Boiling Mechanisms97

11.2 Pool Boiling98

11.3 Flow Boiling99

11.4 Critical Heat Flux101

11.5 Condensation Mechanisms102

11.6 Film Condensation104

Compressible Flow107

12.1 Isentropic Flow107

12.2 Normal Shock Waves108

12.3 Oblique Shock Waves109

12.4 Nozzles and Diffusers110

12.5 Supersonic Flow and Shock Tube112

12.6 Compressible Flow with Heat Transfer114

Turbomachinery117

13.1 Centrifugal Pumps117

13.2 Axial Flow Pumps118

13.3 Fans and Blowers120

13.4 Compressors121

13.5 Turbines123

13.6 Cavitation and Pump Performance125

Measurement and Instrumentation128

14.1 Pressure Measurement128

14.2 Temperature Measurement130

14.3 Flow Measurement132

14.4 Thermal Anemometry135

14.5 Laser Doppler Anemometry (LDA)137

14.6 Particle Image Velocimetry (PIV)139

Glossary142

Index144

CHAPTER 1 Introduction to Fluid Mechanics and Heat Transfer

1.1 Importance of Fluid Mechanics and Heat Transfer

Fluid mechanics and heat transfer are two closely related disciplines that play a crucial role in various engineering fields, including mechanical, chemical, aerospace, and civil engineering. These subjects are essential for understanding and designing systems that involve the flow of fluids (liquids and gases) and the transfer of thermal energy.

Fluid mechanics deals with the study of fluids at rest (fluid statics) and in motion (fluid dynamics). It encompasses the analysis of forces acting on fluids, fluid flow patterns, pressure and velocity distributions, and the behavior of fluids in various situations. Understanding fluid mechanics is vital for designing and optimizing systems such as pipelines, hydraulic systems, aerodynamic bodies, and turbomachinery.

Heat transfer, on the other hand, focuses on the study of the movement of thermal energy from one location to another. It governs many natural phenomena and engineering applications, including heating, cooling, power generation, and thermal management systems. Heat transfer occurs through three fundamental modes: conduction (transfer of energy through a stationary medium), convection (transfer of energy between a solid surface and a moving fluid), and radiation (transfer of energy by electromagnetic waves).

The importance of fluid mechanics and heat transfer can be illustrated through numerous practical applications:

1. Heating, Ventilation, and Air Conditioning (HVAC) systems: Fluid mechanics and heat transfer principles are essential for designing efficient HVAC systems that control indoor air quality, temperature, and humidity levels in buildings.

2. Aerospace engineering: Understanding aerodynamics, which is a branch of fluid mechanics, is crucial for designing aircraft, missiles, and spacecraft. Heat transfer plays a vital role in thermal management systems, propulsion systems, and high-speed flight applications.

3. Chemical processing: Many chemical processes involve fluid flow and heat transfer, such as reactors, distillation columns, heat exchangers, and piping systems. Proper design and optimization of these systems require a thorough understanding of fluid mechanics and heat transfer principles.

4. Power generation: Fluid mechanics and heat transfer are fundamental to the design and operation of power plants, including steam turbines, condensers, boilers, and cooling systems.

5. Biomedical engineering: These disciplines are essential for understanding and designing biomedical devices, such as artificial hearts, blood flow systems, and thermal therapy systems.

6. Environmental engineering: Fluid mechanics and heat transfer concepts are applied in the design of water distribution systems, wastewater treatment plants, and air pollution control systems.

7. Renewable energy systems: The design and optimization of wind turbines, solar thermal systems, and geothermal power plants rely heavily on principles of fluid mechanics and heat transfer.

These examples demonstrate the pervasive nature of fluid mechanics and heat transfer in various engineering applications. A solid understanding of these subjects is essential for engineers to design efficient, safe, and sustainable systems that involve fluid flow and thermal energy transfer.

Fig. 1.2 Heating, Ventilation, and Air Conditioning (HVAC) systems

https://images.app.goo.gl/SPaQzcXq6UmWgjuv9

1.2 Fundamental Concepts and Definitions

Fluid Mechanics:

1. Fluid: A substance that deforms continuously under the application of a shear stress, no matter how small. Fluids can be classified into liquids and gases.

2. Continuum: The assumption that fluids are continuous media, ignoring their molecular structure, which allows the application of classical mechanics to fluid flow problems.

3. Density (ρ): The mass per unit volume of a fluid. It is a important property that affects fluid behavior.

4. Pressure (p): The normal force exerted by a fluid per unit area. Pressure is a scalar quantity and can be expressed in various units, such as pascals (Pa) or pounds per square inch (psi).

5. Viscosity (μ): A measure of a fluid’s resistance to deformation or flow. It represents the internal friction within the fluid. Fluids with high viscosity are more resistant to flow.

6. Shear stress (τ): The tangential force per unit area exerted by one layer of fluid on an adjacent layer due to viscous effects.

7. Laminar flow: A flow regime where fluid particles move in smooth, parallel layers or laminae, with no disruption between the layers.

8. Turbulent flow: A flow regime characterized by irregular, chaotic, and fluctuating motion of fluid particles, resulting in increased mixing and energy dissipation.

9. Reynolds number (Re): A dimensionless quantity that characterizes the flow regime, representing the ratio of inertial forces to viscous forces.

10. Boundary layer: The thin region near a solid surface where the effects of viscosity are significant, and the fluid velocity changes from zero at the surface to the free-stream velocity.

Fig. 1.2 Fluid Mechanics

https://images.app.goo.gl/YEEAMK28guMzauwV8

Heat Transfer:

1. Heat (Q): The form of energy transferred due to a temperature difference. Heat is measured in units of energy, such as joules (J) or British thermal units (Btu).

2. Temperature (T): A measure of the average kinetic energy of the molecules in a substance. Temperature is measured in units such as Celsius (°C), Fahrenheit (°F), or Kelvin (K).

3. Conduction: The transfer of thermal energy through a stationary medium, such as a solid or a fluid at rest, due to molecular interactions and collisions.

4. Convection: The transfer of thermal energy between a solid surface and a moving fluid, involving the combined effects of conduction and fluid motion.

5. Radiation: The transfer of thermal energy by electromagnetic waves, which can occur even in the absence of matter.

6. Thermal conductivity (k): A property that indicates a material’s ability to conduct heat. It is a measure of the rate at which heat flows through a material due to a temperature gradient.

7. Convective heat transfer coefficient (h): A parameter that quantifies the rate of convective heat transfer between a solid surface and a fluid per unit area and temperature difference.

8. Emissivity (ε): A measure of a surface’s ability to emit or absorb thermal radiation, ranging from 0 (a perfect reflector) to 1 (a perfect emitter or absorber).

These fundamental concepts and definitions provide a foundation for understanding and analyzing fluid mechanics and heat transfer phenomena.

Fig. 1.3 Heat Transfer

https://images.app.goo.gl/XzhGqgtzafwjvyC56

1.3 Dimensions and Units

In fluid mechanics and heat transfer, various physical quantities are involved, and it is essential to understand their dimensions and units to ensure consistency and proper interpretation of results.

Dimensions:

Dimensions represent the fundamental physical quantities that describe a given property or variable. The primary dimensions used in fluid mechanics and heat transfer are:

1. Mass (M)

2. Length (L)

3. Time (T)

4. Temperature (Θ)

Other derived dimensions include:

1. Force (MLT^-2)

2. Energy or Work (ML^2T^-2)

3. Power (ML^2T^-3)

4. Pressure or Stress (ML^-1T^-2)

Units:

Units are the specific measures used to quantify physical quantities. Several systems of units are used in fluid mechanics and heat transfer, with the most common being:

1. International System of Units (SI):

- Mass: kilogram (kg)

- Length: meter (m)

- Time: second (s)

- Temperature: Kelvin (K) or Celsius (°C)

- Force: newton (N)

- Energy or Work: joule (J)

- Power: watt (W)

- Pressure or Stress: pascal (Pa)

2. British Gravitational (BG) System:

- Mass: slug (slug)

- Length: foot (ft)

- Time: second (s)

- Temperature: Rankine (°R) or Fahrenheit (°F)

- Force: pound-force (lbf)

- Energy or Work: foot-pound-force (ft-lbf)

- Power: horsepower (hp)

- Pressure or Stress: pound-force per square inch (psi)

Dimensional Analysis:

Dimensional analysis is a powerful tool used in fluid mechanics and heat transfer to ensure the consistency of equations, derive dimensionless parameters, and facilitate the interpretation of experimental data. The concept of dimensional homogeneity states that all terms in an equation must have the same dimensions.

Dimensionless Parameters:

Dimensionless parameters, such as Reynolds number (Re), Prandtl number (Pr), and Nusselt number (Nu), are widely used in fluid mechanics and heat transfer. These parameters are formed by combining relevant dimensional quantities in a specific way, resulting in dimensionless groups that characterize various flow or heat transfer phenomena.

For example, the Reynolds number (Re) is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid flow:

Re = (ρVL) / μ

Where:

- ρ is the fluid density (ML^-3)

- V is the fluid velocity (LT^-1)

- L is a characteristic length (L)

- μ is the dynamic viscosity of the fluid (ML^-1T^-1)

By understanding dimensions and units, engineers can ensure accurate calculations, interpret experimental data correctly, and communicate results effectively within the field of fluid mechanics and heat transfer.

1.4 Continuum Hypothesis

The continuum hypothesis is a fundamental assumption in fluid mechanics and heat transfer that allows us to treat fluids as continuous substances, ignoring their molecular structure. This assumption simplifies the analysis and modeling of fluid flow and heat transfer phenomena, making it possible to apply the principles of classical mechanics and thermodynamics.

In reality, fluids are composed of molecules that are constantly in motion and interact with each other through intermolecular forces. However, at the macroscopic scale, the behavior of a large number of molecules can be described by averaged properties, such as density, velocity, pressure, and temperature. The continuum hypothesis assumes that these properties vary smoothly and continuously throughout the fluid domain, allowing us to treat the fluid as a continuous medium.

The validity of the continuum hypothesis depends on the scale at which the fluid is being analyzed. It is generally applicable when the length scales of interest are much larger than the mean free path of the fluid molecules. The mean free path is the average distance traveled by a molecule between collisions with other molecules.

For most engineering applications involving gases at atmospheric pressure and liquids, the continuum hypothesis holds true, and the fluid can be considered a continuous medium. However, in situations where the length scales approach the mean free path of the molecules, such as in micro- and nanofluidics or rarefied gas flows, the continuum assumption may break down, and alternative approaches, such as molecular dynamics simulations or kinetic theory, may be required.

The continuum hypothesis allows us to apply the fundamental laws of conservation of mass, momentum, and energy to fluid flow and heat transfer problems. These laws, along with appropriate constitutive equations and boundary conditions, form the basis for the mathematical models used to describe fluid mechanics and heat transfer phenomena.

By treating fluids as continuous media, engineers can analyze and design systems involving fluid flow and heat transfer, such as pipelines, turbines, heat exchangers, and combustion chambers, using well-established computational and analytical techniques.

Fig. 1.4 Continuum Hypothesis

https://images.app.goo.gl/4pK1UoWZBh7tUK4Y7

1.5 Properties of Fluids

Fluids exhibit a wide range of properties that influence their behavior and are crucial in understanding and analyzing fluid mechanics and heat transfer phenomena. These properties can be classified into two main categories: intensive properties and extensive properties.

Intensive Properties:

Intensive properties are independent of the mass or volume of the fluid and depend only on the composition and state of the fluid. Some important intensive properties of fluids include:

1. Density (ρ): The mass per unit volume of a fluid. Density can vary with temperature and pressure for compressible fluids like gases.

2. Viscosity (μ): A measure of a fluid’s resistance to deformation or flow. It represents the internal friction within the fluid. Viscosity is influenced by temperature and, in some cases, pressure.

3. Thermal Conductivity (k): A property that indicates a fluid’s ability to conduct heat. It quantifies the rate at which heat flows through the fluid due to a temperature gradient.

4. Specific Heat Capacity (c): The amount of heat required to raise the temperature of a unit mass of a fluid by one degree. Specific heat capacity varies with temperature and pressure for gases.

Extensive Properties:

Extensive properties depend on the mass or volume of the fluid. Some important extensive properties of fluids include:

1. Mass (m): The quantity of matter contained in the fluid.

2. Volume (V): The amount of space occupied by the fluid.

3. Internal Energy (U): The total kinetic and potential energy of the molecules within the fluid.

4. Enthalpy (H): The sum of the internal energy and the product of pressure and volume for a given fluid.

5. Entropy (S): A measure of the disorder or randomness of the molecular motion within the fluid.

Other important fluid properties include surface tension, vapor pressure, and compressibility factor. These properties play crucial roles in various fluid mechanics and heat transfer applications, such as capillary action, phase changes, and compressible flow.

Knowledge of fluid properties is essential for accurate modeling, analysis, and design of fluid systems. These properties can be obtained from experimental data, empirical correlations, or thermodynamic models. Engineers often rely on property tables, equations of state, or specialized software to determine the appropriate values of fluid properties for their specific applications.

1.6 Modes of Heat Transfer

Heat transfer is the process of thermal energy movement from a higher temperature region to a lower temperature region. There are three fundamental modes of heat transfer: conduction, convection, and radiation.

Conduction:

Conduction is the transfer of heat through a stationary medium, such as a solid or a fluid at rest, due to molecular interactions and collisions. In solids, conduction occurs through the vibration of atoms and the transfer of energy from high-energy to low-energy atoms. In fluids, conduction occurs through the random motion and collisions of molecules.

The rate of heat transfer by conduction is given by Fourier’s law:

q = -k A (dT/dx)

Where:

- q is the heat transfer rate (W)

- k is the thermal conductivity of the material (W/m·K)

- A is the cross-sectional area perpendicular to the heat flow (m²)

- dT/dx is the temperature gradient in the direction of heat flow (K/m)

Conduction is the dominant mode of heat transfer in solids and plays a crucial role in the design of heat sinks, insulation materials, and thermal protection systems.

Convection:

Convection is the transfer of heat between a solid surface and a moving fluid, involving the combined effects of conduction and fluid motion. Convection can be classified into two types: natural convection and forced convection.

Natural Convection: This occurs when the fluid motion is caused by buoyancy forces arising from density variations due to temperature differences within the fluid.

Forced Convection: This occurs when the fluid motion is induced by external means, such as a pump or a fan.

The rate of heat transfer by convection is given by Newton’s law of cooling:

q = h A (Ts - T∞)

Where:

- q is the heat transfer rate (W)

- h is the convective heat transfer coefficient (W/m²·K)

- A is the surface area (m²)

- Ts is the surface temperature (K)

- T∞ is the bulk fluid temperature (K)

Convection is the primary mode of heat transfer in many engineering applications, such as heat exchangers, cooling systems, and thermal management of electronic devices.

Radiation:

Radiation is the transfer of thermal energy by electromagnetic waves, which can occur even in the absence of matter. All objects with a temperature above absolute zero emit thermal radiation. The