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Engineering Heat and Mass Transfer

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This book is thoroughly upgraded and improved to incorporate the syllabi of various universities and competitive examinations. It is especially designed to serve as a basic text for undergraduate course in Heat and Mass Transfer for students of Mechanical/ Chemical/ Aeronautic/ Production/ Metallurgical Engineering. The book follows the straight forward presentation of an extensive discussion of basic topics, classical pattern treating the subject analytically and numerically. Throughout the text, the emphasis has been laid on clear understanding of the theoretical concepts followed by the pertinent applications. Addressing the need of students, the book enumerates the required steps towards the solution of numerical problems by the use of systematic procedure characterized by a prescribed format.

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16 Chapters

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1

Concepts and Mechanisms of Heat Flow

1.1. What is Heat Transfer ? 1.2. Modes of Heat Transfer. 1.3. Physical Mechanism of Modes of Heat Transfer—Conduction

—Convection—Radiation. 1.4. Laws of Heat Transfer—Law of conservation of mass : Continuity equation—Newton’s second law of motion—Laws of thermodynamics—Fourier law of heat conduction—Newton’s law of cooling—The Stefan Boltzmann law of thermal radiation. 1.5. Combined Convective and Radiation Heat Transfer—Equation of state. 1.6. Thermal

Conductivity—Variation in thermal conductivity—Determination of thermal conductivity—Variable thermal conductivity.

1.7. Isotropic Material and Anisotropic Material. 1.8. Insulation Materials—Superinsulators—Selection of insulating materials—The R-Value of insulation—Economic thickness of insulation. 1.9. Thermal Diffusivity. 1.10. Heat Transfer in

Boiling and Condensation. 1.11. Mass Transfer. 1.12. Summary—Review Questions—Problems—Multiple Choice Questions.

Objective of this chapter is to:

• give an introduction to heat transfer rate, heat flux,

 

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Conduction—Basic Equations

2

2.1. Generalised One Dimensional Heat Conduction Equation. 2.2. Three Dimensional Heat Conduction Equation—For the cartesian coordinates—Three dimensional heat conduction equation in cylindrical coordinates—Three dimensional heat conduction equation in spherical coordinates. 2.3. Initial and Boundary Conditions—Prescribed temperature boundary conditions—Prescribed heat flux boundary conditions—Convection boundary conditions : Surface energy balance—Radiation boundary condition—Interface boundary condition. 2.4. Summary—Review Questions—Problems.

The objective of this chapter is to provide a good understanding of the heat conduction equations and boundary conditions for the use in mathematical formulation of heat conduction problems.

2.1.

GENERALISED ONE DIMENSIONAL HEAT

CONDUCTION EQUATION

For the thermal analysis of the bodies having shapes such as slab, rectangle, the cartesian coordinates are used, while for cylindrical and spherical bodies, the polar and spherical coordinate systems are used.

 

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3

Steady State Conduction Without

Heat Generation

3.1. Plane Wall. 3.2. Electrical Analogy of Heat Transfer Rate Through a Plane Wall. 3.3. Multilayer Plane Wall—Plane slabs in series—Heat conduction through parallel slabs—Composite wall in series and parallel—Overall heat transfer coefficient.

3.4. Thermal Contact Resistance. 3.5. Long Hollow Cylinder—Electrical analogy for hollow cylinder—Multilayer hollow cylinders—

Overall heat transfer coefficient—Log mean area. 3.6. Critical Thickness of Insulation on Cylinders—Effect of thermal resistances.

3.7. Hollow Sphere—Electrical analogy for hollow sphere—Multilayer hollow sphere—Overall heat transfer coefficient—Critical radius of insulation on sphere. 3.8. Summary—Review Questions—Problems.

Objective of this chapter is to:

• obtain steady state temperature distribution without heat generation in slab, hollow cylinders and spheres.

• obtain heat conduction rate from differential heat conduction equation without heat generation in solids.

• study concept of thermal resistance in series and parallel.

 

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Steady State Conduction with Heat Generation

4.1. The Plane Wall—Specified temperatures on both sides—Plane wall without heat generation—Plane wall with insulated and convective boundaries—Plane wall exposed to convection environment on its both boundaries—The maximum temperature in the wall. 4.2. The

Cylinder—Solid cylinder with specified surface temperature—Solid cylinder exposed to convection environment. 4.3. Hollow Cylinder with

Heat Generation and Specified Surface Temperatures—Hollow cylinder insulated at its inner surface—The location of maximum temperature in the cylinder—4.4. The Sphere—Solid sphere with convective boundary—Solid sphere with specified surface temperature—4.5. Summary—

Review Questions—Problems—References and Suggested Reading.

Most of the engineering applications involve heat generation in the solids, such as nuclear reactors, resistance heaters etc. In this chapter, we will consider one dimensional steady state heat conduction with heat generation and determination of temperature distribution and heat flow in solids of simple shapes such as plane wall, a long cylinder and a sphere. Such type of problems cannot be solved with electrical analogy concept presented in previous chapter.

 

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Heat Transfer from

Extended Surfaces

5

5.1. Types of Fins. 5.2. Fin Selection and Applications. 5.3. Governing Equation. 5.4. Fin Performance—Fin effectiveness—Fin efficiency—Overall fin effectiveness—Area weighted fin efficiency. 5.5. Approximate Solution of Fin: Concept of Corrected Fin Length.

5.6. Error in Temperature Measurement by Thermometers. 5.7. Design Considerations for Fins—Space considerations : Condition for use of fins—Weight consideration. 5.8. Summary—Review Questions—Problems.

The term ‘extended surface’ is commonly used in reference to a solid that experiences energy transfer by conduction and convection between its boundary and surroundings. A temperature gradient in x direction sustains heat transfer by conduction internally, at the same time, there is heat dissipation by convection into an ambient at T∞ from its surface at temperature Ts, given as

Q = h As (Ts – T∞) where h = convection heat transfer coefficient, and

As = heat transfer area of a surface.

When the temperatures Ts and T∞ are fixed by design considerations, there are only two ways to increase the heat transfer rate : (i) to increase the convection coefficient h, or (ii) to increase the surface area A. In the situations, in which an increase in h is not practical or economical, the heat transfer rate can be improved by increasing surface area.

 

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Transient Heat Conduction

6

6.1. Approximate Solution—Systems with negligible internal resistance : lumped system analysis—Dimensionless quantities—Thermal time constant and response of thermocouple—The lumped system analysis for mixed boundary conditions—The validity of lumped system analysis. 6.2. Analytical Solution—Criteria for neglecting internal temperature gradients—Infinite cylinder and sphere with convective boundaries—One term approximation. 6.3. Transient Temperature Charts : Heisler and Gröber Charts—Transient temperature charts for slab—Transient temperature charts for long cylinder and sphere. 6.4. Transient Heat Conduction in Semi Infinite Solids—Penetration depth and penetration time. 6.5. Transient Heat Conduction in Multidimensional Systems. 6.6. Summary—Review Questions—Problems—

References and Suggested Reading.

When the heat energy is being added or removed to or from a body, its energy content (internal energy) changes, resulting into change in its temperature at each point within the body over the time. During this transient period, the temperature becomes function of time as well as direction in the body. The conduction occurred during this period is called transient (unsteady state) conduction. Therefore, in unsteady state

 

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Principles of Convection

7

7.1. Mechanism of Heat Convection. 7.2. Classification of Convection. 7.3. Convection Heat Transfer Coefficient. 7.4. Convection

Boundary Layers—Velocity boundary layer—Thermal boundary layer—Significance of boundary layers. 7.5. Laminar and Turbulent

Flow—Laminar boundary layer—Turbulent boundary layer. 7.6. Momentum Equation for Laminar Boundary Layer. 7.7. Energy Equation for the Laminar Boundary Layer. 7.8. Boundary Layer Similarities—Friction coefficient—Nusselt number. 7.9. Determination of

Convection Heat Transfer Coefficient—Dimensional analysis—Exact mathematical solutions—Approximate analysis of boundary layers—

Analogy between heat and momentum transfer—Numerical analysis. 7.10. Dimensional Analysis—Primary dimensions and dimensional formulae—Dimensional homogeneity—Rayleigh’s method of dimensional analysis—Buckingham π theorem—Dimensional analysis for forced convection—Dimensional analysis for natural convection. 7.11. Physical Significance of the Dimensionless Parameters—Reynolds number—Critical reynolds number Recr—Prandtl number—Grashof number—Nusselt number—Stanton number—Peclet number—Graetz number. 7.12. Turbulent Boundary Layer Heat Transfer—Prandtl mixing length concept—Turbulent heat transfer. 7.13. Reynolds Colburn

 

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External Flow

8.1. Laminar Flow Over a Flat Plate—Approximate analysis of momentum equation—Approximate analysis of energy equation. 8.2. Reynolds

Colburn Analogy : Momentum and Heat Transfer Analogy for Laminar Flow Over Flat Plate. 8.3. Turbulent Flow Over a Flat Plate.

8.4. Combined Laminar and Turbulent Flow. 8.5. Flow Across Cylinders and Spheres—Drag coefficient—Heat transfer coefficient.

8.6. Summary—Review Questions—Problems—References and Suggested Reading.

When a fluid flows over a body such as plate, cylinder, sphere etc., it is regarded as an external flow. In such a flow, the boundary layer develops freely without any constraints imposed by adjacent surfaces. Accordingly, the region of flow, outside the boundary layer in which the velocity and temperature gradients are negligible is called the free stream region.

In an external flow forced convection, the relative motion between the fluid and the surface is maintained by external means such as a fan or a pump and not by buoyancy forces due to temperature gradients as in natural convection.

 

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Internal Flow

9

9.1. Flow Inside Ducts. 9.2. Hydrodynamic Considerations—Mean velocity um—Hydrodynamic entry length—Velocity profile in fully developed region—Friction factor—Pressure drop and friction factor in fully developed flow. 9.3. Thermal Considerations—The mean temperature or bulk temperature. 9.4. The Heat Transfer in Fully Developed Flow. 9.5. General Thermal Analysis—Constant surface heat flux—Constant surface temperature. 9.6. Heat Transfer in Laminar Tube Flow. 9.7. Flow Inside a Non-circular Duct. 9.8. Thermally

Developing, Hydrodynamically Developed Laminar Flow. 9.9. Heat Transfer in Turbulent Flow Inside a Circular Tube—Analogy between heat and momentum transfer in turbulent flow through tube—Correlation for turbulent flow. 9.10. Heat Transfer to Liquid Metal

Flow in Tube. 9.11. Summary—Review Questions—Problems—References and Suggested Reading.

9.1.

FLOW INSIDE DUCTS

The flow of fluid through the tubes and ducts for transporting cooling and heating fluids, etc., is of engineering importance. Most heat exchangers involve the heating or cooling of fluids flowing in the tubes. The fluid in such applications is forced to flow by a fan or pump through a tube that is sufficiently long to accomplish desired heating or cooling. Pressure drop and heat flux are associated with forced flow through the tubes and friction factor and heat transfer coefficient are used to determine the pumping power and length of tube.

 

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Natural Convection

10.1. Physical Mechanism. 10.2. Definitions—Buoyance force—Volumetric expansion coefficient—Grashof number. 10.3. Natural

Convection Over a Vertical Plate. 10.4. Empirical Correlations for External Free Convection Flow—Vertical plate—Horizontal surfaces

—Inclined plates—Free convection on a long cylinders—Free convection on a spheres. 10.5. Simplified Equations for Air. 10.6. Natural

Convection in Enclosed Spaces. 10.7. Summary—Review Questions—Problems—References and Suggested Reading.

10.1.

PHYSICAL MECHANISM

In natural convection, the fluid motion is due to buoyancy forces within the fluid. The buoyancy forces are developed due to density variation in the fluid caused by temperature difference between the fluid and adjacent surface. The larger the temperature difference in adjacent fluid, the larger the buoyancy force and stronger natural convection currents and higher the heat transfer rate. Whenever a heated object for an example a hot egg, is exposed to atmospheric air, the air adjacent to the hot egg gets heated and becomes lighter (less dense) and thus rises up as shown in Fig. 10.1. This motion leads to the formation of the boundary layer on the surface of the egg and the heat is transferred from the warmer boundary layer to outer atmospheric air by natural convection. The velocity of air is zero at the boundary surface and it is significant outside the boundary layer.

 

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11

Condensation and Boiling

11.1. Condensation—Filmwise condensation—Dropwise condensation. 11.2. Laminar Film Condensation on a Vertical Plate.

11.3. Condensation on a Single Horizontal Tube—Condensation on horizontal tube banks—Calculation of reynolds number. 11.4. Turbulent

Filmwise Condensation. 11.5. Condensate Number. 11.6. Dropwise Condensation. 11.7. Film Condensation Inside Horizontal Tubes.

11.8. Boiling—Boiling modes. 11.9. Pool Boiling Regimes—Critical heat flux—Leidenfrost point. 11.10. Mechanism of Nucleate Boiling—

Critical diameter of a bubble. 11.11. Pool Boiling Correlations—Correlation for nucleate boiling—Correlation for critical heat flux—Pool film boiling—Minimum heat flux. 11.12. Forced Convection Boiling. 11.13. Summary—Review Questions—Problems—References and

Suggested Reading.

The condensers and boilers are widely used heat transfer equipments in the industries. The condensation and boiling involve convection processes associated with change of phase of fluid. Because there is a phase change during the process, the fluid transfers the latent heat only at its saturation temperature.

 

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Thermal Radiation:

Properties and Processes

12

12.1. Theories of Radiation—Maxwell’s theory—Max Planck’s theory. 12.2. Spectrum of Electromagnetic Radiation. 12.3. Black body

Radiation. 12.4. Spectral and Total Emissive Power. 12.5. Surface Absorption, Reflection and Transmission. 12.6. Black body

Radiation Laws—Black body spectral emissive power—Wien’s displacement law—Stefan Boltzmann law—Radiation function and band emission. 12.7. Emissivity—Hemispherical and total emissivity—Spectral emissivity—Directional emissivity—Kirchhoff’s law—Gray and diffuse surfaces : Gray Lambert body approximation. 12.8. Radiation From a Surface—Solid angle—Spectral intensity of radiation (Ibλ)—

Radiation intensity (Ib). 12.9. Radiosity. 12.10. Solar Radiation—Solar radiation on the earth—Atmospheric emission—Green house effect—

Selective surfaces. 12.11. Summary—Review Questions—Problems—References and Suggested Reading.

Thermal radiation or radiation heat transfer is a distinct separate mechanism from conduction and convection for transfer of heat energy. It refers to the heat energy emitted by the bodies because of their temperatures. All bodies at a temperature above absolute zero temperature emit energy by a process of electromagnetic radiation. The intensity of such radiation depends upon the temperature and nature of the surface. The energy transfer by radiation does not require any medium between hot and cold surfaces. The energy transfer by radiation is the fastest (at the speed of light) and it does not suffer any attenuation even in the vacuum. In fact, the heat transfer through an evacuated space can occur only by radiation. When a person sits infront of a fire, he gets most of the heat energy by radiation as shown in Fig. 12.1. Further, it is also interesting that the radiation heat transfer can also occur between two bodies separated by a medium that is colder than the both bodies. For an example, the energy emitted by sun reaches the earth surface after travelling through space and extremely cold air layers at high altitudes.

 

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13

Radiation Exchange between Surfaces

13.1. Radiation View Factor—View factor integral—The view factor relations—The cross string method. 13.2. Black body Radiation

Exchange. 13.3. Radiation from Cavities. 13.4. Radiation Heat Exchange between Diffuse, Gray Surfaces—The net radiation exchange by a surface—Radiation exchange between two gray surfaces—Radiation heat exchange between two parallel infinite planes. 13.5. The

Radiation Exchange between Three Surfaces Enclosure. 13.6. Radiation Heat Transfer in Three Surface Enclosure. 13.7. Radiation

Shields. 13.8. Temperature Measurement of a Gas by Thermocouple: Combined Convective and Radiation Heat Transfer

13.9. Summary—Review Questions—Problems—References and Suggested Reading.

In the previous chapter, our discussion was restricted to radiation properties, physical relation, and radiation processes that occur at a single surface. In this chapter, we will consider the radiation heat exchange between two or more surfaces. Such type of radiation exchange depends on the surface geometries, surface orientation as well as their temperatures and radiative properties.

 

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Heat Exchangers

14

14.1. Classification of Heat Exchanger. 14.2. Temperature Distribution. 14.3. Overall Heat Transfer Coefficient. 14.4. Fouling Factor.

14.5. Heat Exchanger Analysis. 14.6. Log Mean Temperature Difference Method—Parallel flow heat exchanger—Counter flow heat exchanger—Condenser—Evaporator. 14.7. Multipass and Cross Flow Heat Exchangers. 14.8. The Effectiveness-NTU Method—Heat exchanger effectiveness—NTU—Capacity ratio—Effectiveness of a parallel flow heat exchanger—Effectiveness of a counter flow heat exchanger. 14.9. Rating of Heat Exchangers. 14.10. Sizing of Heat Exchangers. 14.11. Compact Heat Exchangers. 14.12. Plate Heat

Exchanger (PHE). 14.13. Requirements of Good Heat Exchanger. 14.14. Heat Exchanger Design and Selection. 14.15. Practical

Applications of Heat Exchangers. 14.16. Heat Pipes. 14.17. Summary—Review Questions – Problems – References and Suggested

Reading.

A device used for exchange of heat between the two fluids that are at different temperatures, is called the heat exchanger. The heat exchangers are commonly used in wide range of applications, for example, in a car as radiator, where hot water from the engine is cooled by atmospheric air. In a refrigerator, the hot refrigerant from the compressor is cooled by convection into atmosphere by passing it through finned tubes. In a steam condenser, the latent heat of condensation is removed by circulating water through the tubes. The heat exchangers are also used in space heating and air-conditioning, waste heat recovery and chemical processing. Therefore, the different types of heat exchangers are needed for different applications.

 

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Mass Transfer

15

15.1. Introduction. 15.2. Modes of Mass Transfer. 15.3. Comparison between Heat and Mass Transfer. 15.4. Concentrations, Velocities and Fluxes. 15.5. Fick’s Law of Diffusion. 15.6. General Mass Diffusion Equation. 15.7. Boundary Conditions. 15.8. Mass Diffusion without Homogeneous Chemical Reactions—Steady state diffusion through a plane membrane—Water vapour migration—Equimolar counter diffusion—Diffusion through a stagnant gas: Stefan’s flow. 15.9. Mass Diffusion with Homogeneous Chemical Reactions.

15.10. Convective Mass Transfer—Mass transfer coefficient dimensionless parameters in convective mass transfer—Analogy between heat and mass transfer—Correlation for convective mass transfer. 15.11. Dimensional Analysis of Convective Mass Transfer.

15.12. Evaporation of Water into Air. 15.13. Summary—Review Questions—Problems—References and Suggested Reading.

15.1.

INTRODUCTION

We have so far dealt with conduction, convection and radiation modes of heat transfer, in which energy transfer takes place due to temperature difference in the medium(s). Similarly, if there is a concentration difference within two or more species (components) of a mixture, then mass transfer must occur in order to minimize the concentration difference within the system.

 

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Experiments in

Engineering Heat Transfer

16

Expt. 1 Thermal Conductivity of Metallic Rod. Expt. 2 Thermal Conductivity of Insulating Powder. Expt. 3 Thermal Conductivity of Composite Wall. Expt. 4 Natural Convection Experiment. Expt. 5 Forced Convection Experiment. Expt. 6 Heat Transfer from Pin

Fins. Expt. 7 Stefan Boltzmann Constant. Expt. 8 Measurement of Emissivity of a Test Surface. Expt. 9 Heat Exchanger Experiment.

Expt. 10 Critical Heat Flux. Expt. 11 Heat Pipe. Expt. 12 Thermocouples Calibration Test Rig—Review Questions—References

Engineering education has placed a great emphasis on the ability of an individual to perform experiments along with a theoretical analysis of the problems. The experimental methods have their own importance. They help in better understanding of the basic principles of the subject and to verify the result obtained analytically.

Therefore, in engineering curiculla, the students are expected to devote one laboratory period a week for experimentation. The students are exposed to the basic instruments and get acquainted with the methods used for measuring the physical properties.

 

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