Heat and Mass Transfer

Preface
Contents
About the Author
List of Symbols
	Dimensionless Numbers
	Greek Symbols
	Superscript and Subscript
	Space Coordinates
1 Introduction
	1.1 Introduction
	1.2 Heat Transfer by Conduction
	1.3 Heat Transfer by Convection
	1.4 Heat Transfer by Radiation
	1.5 Simultaneous Heat Transfer
	1.6 Summary
	Review Questions
2 One-Dimensional Steady-State Heat Conduction
	2.1 Introduction
	2.2 Temperature Field and Temperature Gradient
	2.3 Thermal Conductivity
		2.3.1 Thermal Conductivity of Solids
		2.3.2 Thermal Conductivity of Metals and Alloys
		2.3.3 Thermal Conductivity of Construction and Heat-Insulating Materials
			2.3.3.1 R-Values of Insulating Materials
		2.3.4 Thermal Conductivity of Gases
		2.3.5 Thermal Conductivity of Liquids
	2.4 General Heat Conduction Equations
		2.4.1 General Heat Conduction Equation in Cartesian Coordinates
			2.4.1.1 Thermal Diffusivity
		2.4.2 General Heat Conduction Equation in Cylindrical Coordinates
		2.4.3 General Heat Conduction Equation in Spherical Coordinates
	2.5 One-Dimensional Steady-State Heat Conduction
		2.5.1 Composite Plane Wall
		2.5.2 One-Dimensional Steady-State Heat Conduction Through a Plane Homogeneous Wall Considering Film Coefficients
			2.5.2.1 Conduction Heat Transfer Through a Composite Plane Wall Considering Film Coefficients
		2.5.3 One-Dimensional Steady-State Conduction Heat Transfer Through a Plane Homogeneous Wall Considering Heat Transfer by Convection and Radiation from the Wall Surface
	2.6 One-Dimensional Steady-State Heat Conduction Through a Cylindrical Shell
		2.6.1 One-Dimensional Steady-State Heat Conduction Through a Cylindrical Shell Considering Film Coefficients
			2.6.1.1 Overall Heat Transfer Coefficient
		2.6.2 Composite Cylindrical Wall
	2.7 One-Dimensional Steady-State Heat Conduction Through a Spherical Shell
		2.7.1 One-Dimensional Steady-State Heat Conduction Through a Spherical Shell Considering the Film Coefficients
		2.7.2 Composite Spherical Shell
	2.8 Measurement of Thermal Conductivity
		2.8.1 Thermal Conductivity Measurement of Solids
		2.8.2 Thermal Conductivity Measurements of Liquids and Gases
	2.9 Effect of Variable Thermal Conductivity
		2.9.1 Plane Wall
		2.9.2 Cylindrical Shell
		2.9.3 Spherical Shell
	2.10 Critical Thickness of Insulation
		2.10.1 Critical Thickness of Insulation for Cylinders
		2.10.2 Critical Thickness of Insulation for Spherical Vessel
	2.11 Thermal Contact Resistance
	2.12 Summary
	Review Questions
	Problems
	References
3 Extended Surfaces (Fins)
	3.1 Introduction
	3.2 Heat Transfer from a Fin of Uniform Cross-Section
		3.2.1 A Very Long Fin
			3.2.1.1 Comments on Parameter M
		3.2.2 Negligible Heat Transfer from the Fin End as Compared to the Heat Transferred from the Fin Surface (Ac ≪ PL)
		3.2.3 Short Fins (Fin with Heat Loss from the Fin End)
	3.3 Hollow Fins
	3.4 Composite Fins
	3.5 Effectiveness and Efficiency of Fins
	3.6 Heat Transfer from a Finned Wall
	3.7 Intensification of Heat Transfer by Finning
	3.8 Error in Temperature Measurement with Thermometer Well
	3.9 When Fins Are to Be Used?
	3.10 Heat Transfer from a Bar Connected to Two Heat Sources at Different Temperatures
	3.11 Generalized Equation of Fin
	3.12 Fin of Minimum Weight (Isachenko et al.1977)
	3.13 Straight Fin of Triangular Section
	3.14 Straight Fin of Trapezoidal Section
	3.15 Annular Fin
	3.16 Fin Efficiency Plots
	3.17 Summary
	Review Questions
	Problems
	References
4 Conduction with Heat Generation
	4.1 Plane Wall with Uniform Heat Generation
		4.1.1 Case (A) Surfaces at Different Temperatures
			4.1.1.1 The Maximum Temperature and Its Location Within the Wall
		4.1.2 Case (B) Surfaces at the Same Temperature
	4.2 Cylinder with Uniform Heat Generation
	4.3 Solid Sphere with Uniform Heat Generation
	4.4 Heat Transfer Through Piston Crown
	4.5 Summary
	Review Questions
	Problems
5 Steady-State Two-Dimensional Heat Conduction
	5.1 Introduction
	5.2 Analytical Solution of Two-Dimensional Heat Conduction Problems
	5.3 Conduction Through a Flat Semi-infinite Homogeneous Plate
	5.4 Mean Value Theorem
	5.5 Graphical Analysis of Two Dimensional Steady-State Conduction: Thermal Flux Plotting and Shape Factor
	5.6 Experimental Investigation of Conduction Process by Method of Analogy: Electro-Thermal Analogy
	5.7 Numerical Solution Methods
		5.7.1 Finite-Difference Method
		5.7.2 Solution of Nodal Equations
			5.7.2.1 Relaxation Method
			5.7.2.2 Gaussian Elimination
			5.7.2.3 The Gauss–Seidel Iteration Method
	5.8 Two-Dimensional Steady-State Heat Conduction with Heat Generation
	5.9 Summary
	Review Questions
	Problems
6 Unsteady or Transient Heat Conduction
	6.1 Introduction
	6.2 Lumped Heat Capacity Analysis
		6.2.1 Instantaneous and Total Heat Flow
		6.2.2 Applicability of the Lumped Heat Capacity Analysis
	6.3 Lumped Capacitance, Varying Fluid Temperature
	6.4 Multiple-Lumped Capacity Systems
	6.5 Transient Heat Flow in Semi-infinite Solids
	6.6 Transient Heat Conduction in Infinite Plate
	6.7 Heisler and Grober Charts
	6.8 Two- and Three-Dimensional Transient Heat Conduction Systems
		6.8.1 Two-Dimensional Systems
		6.8.2 Three-Dimensional Systems
	6.9 Numerical Method of Solving Transient Conduction Problems
		6.9.1 The Explicit and Implicit Formulations
	6.10 The Schmidt Graphical Method for One-Dimensional Problems
	6.11 Summary
	Review Questions
	Problems
	References
7 Convective Heat Transfer
	7.1 Introduction
		7.1.1 Natural Convective Heat Transfer
		7.1.2 Forced Convection Heat Transfer
	7.2 Flow of Fluid Past a Flat Plate
	7.3 Flow in Tubes
		7.3.1 Laminar Flow Through a Tube
		7.3.2 Turbulent Flow Through a Tube
	7.4 Equation of Continuity
		7.4.1 The Displacement and Momentum Thickness
		7.4.2 The Enthalpy and Conduction Thickness
	7.5 Momentum Equation of Laminar Boundary Layer Over a Flat Plate
		7.5.1 Solution of Momentum Equation (Blasius Solution)
	7.6 Integral Momentum Equation of Laminar Boundary Layer Over a Flat Plate: von Karman Solution
	7.7 Energy Equation of Laminar Boundary Layer Over a Flat Plate
		7.7.1 Pohlhausen’s Solution
		7.7.2 von Karman Integral Technique (Integral Analysis of Energy Equation for the Laminar Boundary Layer)
	7.8 Turbulent Boundary Layer Over a Flat Surface
	7.9 Laminar Flow in Tubes
	7.10 Turbulent Flow in Tubes
	7.11 Momentum and Heat Exchange in Turbulent Flow (Eddy Viscosity and Eddy Thermal Diffusivity)
	7.12 Reynolds Analogy for Flow Past a Flat Surface
		7.12.1 Reynolds–Colburn Analogy
		7.12.2 Application of Colburn Analogy to Turbulent Heat Transfer from a Flat Plate
	7.13 Prandtl–Taylor Modification of Reynolds Analogy for Turbulent Flow Over Flat Plates
		7.13.1 von Karman Analogy for Flat Plates
	7.14 Reynolds Analogy for Turbulent Flow in Tubes
		7.14.1 Prandtl–Taylor Modification of Reynolds Analogy for Turbulent Flow in Tubes
		7.14.2 Friction Drag: Flow Over a Flat Plate Parallel to the Flow
			7.14.2.1 Laminar Flow
			7.14.2.2 Turbulent Flow
	7.15 Natural or Free Convection
	7.16 Integral Momentum and Energy Equation of Free Convection on a Vertical Plate
	7.17 Liquid Metal Heat Transfer for Laminar Flow Over a Flat Plate
	7.18 Summary
	Review Questions
	Problems
	References
8 Empirical Relations for Forced Convection Heat Transfer
	8.1 Introduction
	8.2 Dimensional Analysis
	8.3 Dimensional Analysis Applied to Forced Convection
		8.3.1 Rayleigh’s Method
		8.3.2 Buckingham’s Pi-Method
		8.3.3 Physical Significance of Dimensionless Numbers
	8.4 Experimental Determination of Forced Convection Heat Transfer Coefficient
		8.4.1 Uniform Temperature Condition
		8.4.2 Uniform Heat Flux Condition
	8.5 Friction Factor and Heat Transfer Coefficient Correlations for Circular Ducts
		8.5.1 Laminar Flow in Circular Tubes
			8.5.1.1 Friction Factor Correlations
			8.5.1.2 Heat Transfer Coefficient Correlations
		8.5.2 Turbulent Flow in Circular Tubes
			8.5.2.1 Friction Factor Correlations
			8.5.2.2 Heat Transfer Coefficient Correlations
	8.6 Effects of Temperature Varying Properties
	8.7 Heat Transfer and Friction in Concentric Circular Tube Annuli and Parallel Plate Duct
		8.7.1 Laminar Flow
		8.7.2 Turbulent Flow
	8.8 Heat Transfer and Friction in Rectangular Duct
		8.8.1 Laminar Flow
		8.8.2 Turbulent Flow
	8.9 Correlations for External Forced Flow Over a Flat Plate
		8.9.1 Laminar Flow
		8.9.2 Turbulent Flow
	8.10 Forced Convection Laminar and Turbulent Flows Around Submerged Bodies
		8.10.1 Cylinder in Cross Flow
		8.10.2 Flow Around a Sphere
		8.10.3 Flow Across Tube Banks
	8.11 Heat Transfer in Liquid Metals
	8.12 Influence of Duct Wall Roughness in Turbulent Flow
	8.13 Summary
	Review Questions
	Problems
	References
9 Empirical Relations for Natural or Free Convection
	9.1 Introduction
	9.2 Buoyancy Force in Natural Convection
	9.3 Dimensional Analysis Applied to Natural Convection
		9.3.1 Rayleigh’s Method
		9.3.2 Buckingham’s Pi Method
		9.3.3 Physical Interpretation of Grashof Number
	9.4 Experimental Determination of Natural Convection Heat Transfer Coefficient
	9.5 Empirical Relations for Free or Natural Convection
		9.5.1 Vertical Plate and Cylinders
		9.5.2 Inclined Plate
		9.5.3 Horizontal Plate
		9.5.4 Horizontal Cylinder of Diameter D and Length L  greaterthan   greaterthan  d
		9.5.5 Sphere of Diameter d
	9.6 Free Convection in Parallel Plate Channels
		9.6.1 Vertical Channels
		9.6.2 Inclined Channels
	9.7 Empirical Correlations for Enclosed Spaces
	9.8 Combined Free and Forced Convection (Kays and Crawford 1980; Gebhart 1961; Holman 1992; Cengel 2007)
	9.9 Summary
	Review Questions
	Problems
	References
10 Laws of Thermal Radiation
	10.1 Introduction
	10.2 Reflection, Absorption and Transmission of Radiation
	10.3 Emissivity and a Perfect Blackbody
	10.4 Planck’s Spectral Distribution of Emissive Power
	10.5 Wein’s Displacement Law
	10.6 Total Emissive Power: Stefan–Boltzmann Law
	10.7 Blackbody Radiation in a Wave Length Interval
	10.8 Real and Gray Bodies
	10.9 Kirchhoff’s Law
	10.10 Intensity of Radiation and Lambert’s Cosine Law
	10.11 Summary
	Review Questions
	Problems
	References
11 Exchange of Thermal Radiation Between Surfaces Separated by Transparent Medium
	11.1 Introduction
	11.2 Radiation Heat Exchange Between Two Black Surfaces and the Shape Factor
	11.3 Evaluation of the Shape Factor
		11.3.1 Salient Features of the Radiation Shape Factor
	11.4 Reciprocity Relation
	11.5 Radiation Exchange Between Infinite Parallel Planes
	11.6 Radiation Exchange Between Infinite Long Concentric Cylinders
	11.7 Radiation from a Gray Cavity
	11.8 Small Gray Bodies
	11.9 Electric Network Method for Solving Radiation Problems
		11.9.1 Electric Network for a System Consisting of Two Gray Surfaces
		11.9.2 System Consisting of Two Black Surfaces
		11.9.3 Closed System of N-Black Surfaces
		11.9.4 Systems Consisting of Two Black Surfaces Connected by a Single Refractory Surface
		11.9.5 System Consisting of Two Gray Surfaces Connected by a Single Refractory Surface
		11.9.6 System Consisting of Four Gray Surfaces Which See Each Other and Nothing Else
	11.10 Radiation Shields
	11.11 Radiation from a Gray Cavity (Alternative Method)
	11.12 Newton’s Law of Cooling and Overall Heat Transfer Coefficient
		11.12.1 Determination of Specific Heat Using Newton’s Law of Cooling
	11.13 Radiation Heat Transfer Coefficient
	11.14 Summary
	Review Questions
	Problems
	References
12 Heat Transfer in Absorbing and Emitting Media (Gaseous Radiation)
	12.1 Introduction
	12.2 Specific Features of Gaseous Radiation
		12.2.1 Selective Emitters
		12.2.2 Beer’s Law
		12.2.3 Transmissivity, Emissivity and Absorptivity
		12.2.4 Total Emissive Power
	12.3 Heat Exchange
		12.3.1 Radiation Emitted by a Gas
		12.3.2 Radiation Heat from Surface (Wall)
		12.3.3 Net Rate of Heat Transfer
		12.3.4 Mixture of CO2 and H2O Vapour
		12.3.5 Gray Enclosure
	12.4 Gray Gas Surrounded by Diffuse Gray Surfaces at Different Temperatures
	12.5 Flames
		12.5.1 Luminous Flames
		12.5.2 Non-luminous Flames
	12.6 Summary
	Review Questions
	Problems
	References
13 Heat Transfer in Condensing Vapours and Boiling Liquids
	13.1 Part A: Heat Transfer in Condensing Vapours
		13.1.1 Introduction
			13.1.1.1 Different Types of Condensation
				Dropwise Condensation
				Filmwise Condensation
		13.1.2 Nusselt’s Film Condensation Theory
			13.1.2.1 Laminar Film Condensation on a Vertical Surface
				Comparison of Horizontal and Vertical Orientation of Tubes
			13.1.2.2 Turbulent Film Flow
		13.1.3 Factors Affecting Film Condensation
	13.2 Part B: Heat Transfer in Boiling Liquids
		13.2.1 Introduction
		13.2.2 Boiling Heat Transfer
			13.2.2.1 Pool Boiling
			13.2.2.2 Forced-Flow Boiling
				Flow Pattern in a Vertical Heated Tube with Upward Flow
				Flow Pattern in Horizontal Evaporator Tube
	13.3 Relations for Boiling Heat Transfer in Pool Boiling
		13.3.1 Nucleate Boiling
			13.3.1.1 The Peak Heat Flux
		13.3.2 Simplified Relations for Boiling Heat Transfer with Water
	Review Questions
	Problems
	References
14 Heat Exchangers
	14.1 Part A: Heat Exchangers Fundamentals
		14.1.1 Introduction
		14.1.2 Heat Transfer Equation for Double Pipe (Concentric Tube) Heat Exchanger
		14.1.3 Log Mean Temperature Difference (LMTD)
			14.1.3.1 Parallel Flow Arrangement
			14.1.3.2 Counterflow Arrangement
		14.1.4 LMTD for Other Flow Arrangements
		14.1.5 Effectiveness-NTU Method
			14.1.5.1 Effectiveness-NTU Method for Counterflow Heat Exchanger
			14.1.5.2 Effectiveness-NTU Method for Parallel Flow Heat Exchanger
		14.1.6 Effectiveness-NTU Relations for Other Flow Arrangements
	14.2 Part B: Design of Heat Exchangers
		14.2.1 Introduction
		14.2.2 Double Pipe Exchangers
		14.2.3 Clean and Design Overall Heat Transfer Coefficients
	14.3 Summary
	Review Questions
	Problems
	References
15 Mass Transfer
	15.1 Introduction
	15.2 Fick’s Law of Diffusion
		15.2.1 Fick’s Law for Gases in Terms of Partial Pressures
		15.2.2 Fick’s Law on Mass Basis and Mole Basis
	15.3 Diffusion Coefficient
	15.4 Diffusion of Vapour Through a Stationary Gas: Stefan Law
	15.5 Convective Mass Transfer
		15.5.1 Convective Mass Transfer Equation in Terms of Partial Pressure Difference
	15.6 Dimensional Analysis Applied to Convective Mass Transfer
		15.6.1 Forced
		15.6.2 Free
	15.7 Mass Transfer Correlations
	15.8 Reynolds and Colburn (or Chilton-Colburn) Analogies
	15.9 Summary
	Review Questions
	Problems
16 Special Topic: Performance of Solar Air Heater
	16.1 Introduction
	16.2 Mathematical Model for Thermohydraulic Performance Prediction (Karwa et al. 2007; Karwa and Chauhan 2010)
		16.2.1 Top Loss
		16.2.2 Wind Heat Transfer Coefficient
		16.2.3 Sky Temperature
		16.2.4 Convective Heat Transfer Coefficient Between the Absorber Plate and Glass Cover
		16.2.5 Back and Edge Losses
		16.2.6 Heat Transfer and Friction Factor Correlations
	16.3 Enhanced Performance Solar Air Heaters
		16.3.1 Introduction
		16.3.2 Artificial Roughness for Heat Transfer Enhancement
			16.3.2.1 Effect of Rib Shape and Pitch
			16.3.2.2 Effect of Rib Arrangement
	16.4 Heat Transfer and Friction Factor Correlations for Roughened Rectangular Ducts
	16.5 Summary
	References
Appendix_1
Appendix_2
Bibliography for Further Reading
Index