Introduction to Convective Heat Transfer: A Software-Based Approach Using Maple and MATLAB

ISBN-13: 9781119766766 / Angielski / Twarda / 2023 / 832 str.

Nevzat Onur

Spis treści

Preface xvAbout the Author xviiAbout the Companion Website xviii1 Foundations of Convective Heat Transfer 11.1 Fundamental Concepts 11.2 Coordinate Systems 11.3 The Continuum and Thermodynamic Equilibrium Concepts 21.4 Velocity and Acceleration 31.5 Description of a Fluid Motion: Eulerian and Lagrangian Coordinates and Substantial Derivative 41.5.1 Lagrangian Approach 41.5.2 Eulerian Approach 51.6 Substantial Derivative 71.7 Conduction Heat Transfer 101.8 Fluid Flow and Heat Transfer 111.9 External Flow 111.9.1 Velocity Boundary Layer and Newton's Viscosity Relation 111.9.2 Thermal Boundary Layer 121.10 Internal Flow 191.10.1 Mean Velocity 191.10.2 Mean Temperature 201.11 Thermal Radiation Heat Transfer 221.12 The Reynolds Transport Theorem: Time Rate of Change of an Extensive Property of a System Expressed in Terms of a Fixed Finite Control Volume 22Problems 28References 312 Fundamental Equations of Laminar Convective Heat Transfer 332.1 Introduction 332.2 Integral Formulation 332.2.1 Conservation of Mass in Integral Form 332.2.2 Conservation of Linear Momentum in Integral Form 342.2.3 Conservation of Energy in Integral Form 362.3 Differential Formulation of Conservation Equations 382.3.1 Conservation of Mass in Differential Form 382.3.1.1 Cylindrical Coordinates 412.3.1.2 Spherical Coordinates 412.3.2 Conservation of Linear Momentum in Differential Form 422.3.2.1 Equation of Motion for a Newtonian Fluid with Constant Dynamic Viscosity mu and Density rho 452.3.2.2 Cartesian Coordinates (x, y, z) 452.3.2.3 Cylindrical Coordinates (r, theta,z) 462.3.2.4 Spherical Coordinates (r, theta, Õ) 462.3.3 Conservation of Energy in Differential Form 472.3.3.1 Mechanical Energy Equation 532.3.3.2 Thermal Energy Equation 532.3.3.3 Thermal Energy Equation in Terms of Internal Energy 542.3.3.4 Thermal Energy Equation in Terms of Enthalpy 552.3.3.5 Temperature T and Constant Volume Specific Heat CV 552.3.3.6 Temperature and Constant Pressure Specific Heat cp 562.3.3.7 Special Cases of the Differential Energy Equation 582.3.3.8 Perfect Gas and the Thermal Energy Equation Involving T and cp 582.3.3.9 Perfect Gas and the Thermal Energy Equation Involving T and CV 582.3.3.10 An Incompressible Pure Substance 582.3.3.11 Rectangular Coordinates 592.3.3.12 Cylindrical Coordinates (r, theta, z) 592.3.3.13 Spherical Coordinates (r, theta, Õ) 59Problems 64References 673 Equations of Incompressible External Laminar Boundary Layers 693.1 Introduction 693.2 Laminar Momentum Transfer 693.3 The Momentum Boundary Layer Concept 703.3.1 Scaling of Momentum Equation 713.4 The Thermal Boundary Layer Concept 763.4.1 Scaling of Energy Equation 773.5 Summary of Boundary Layer Equations of Steady Laminar Flow 82Problems 82References 834 Integral Methods in Convective Heat Transfer 854.1 Introduction 854.2 Conservation of Mass 854.3 The Momentum Integral Equation 874.3.1 The Displacement Thickness delta1 884.3.2 Momentum Thickness delta2 894.4 Alternative Form of the Momentum Integral Equation 904.5 Momentum Integral Equation for Two-Dimensional Flow 904.6 Energy Integral Equation 914.6.1 Enthalpy Thickness 934.6.2 Conduction Thickness 934.6.3 Convection Conductance or Heat Transfer Coefficient 934.7 Alternative Form of the Energy Integral Equation 944.8 Energy Integral Equation for Two-Dimensional Flow 94Problems 94References 965 Dimensional Analysis 975.1 Introduction 975.2 Dimensional Analysis 1015.2.1 Dimensional Homogeneity 1025.2.2 Buckingham pi Theorem 1025.2.3 Determination of pi Terms 1035.3 Nondimensionalization of Basic Differential Equations 1165.4 Discussion 1255.5 Dimensionless Numbers 1255.5.1 Reynolds Number 1255.5.2 Peclet Number 1265.5.3 Prandtl Number 1265.5.4 Nusselt Number 1265.5.5 Stanton Number 1265.5.6 Skin Friction Coefficient 1265.5.7 Graetz Number 1275.5.8 Eckert Number 1275.5.9 Grashof Number 1275.5.10 Rayleigh Number 1275.5.11 Brinkman Number 1275.6 Correlations of Experimental Data 128Problems 136References 1476 One-Dimensional Solutions in Convective Heat Transfer 1496.1 Introduction 1496.2 Couette Flow 1516.3 Poiseuille Flow 1566.4 Rotating Flows 171Problems 175References 1807 Laminar External Boundary Layers: Momentum and Heat Transfer 1837.1 Introduction 1837.2 Velocity Boundary Layer over a Semi-Infinite Flat Plate: Similarity Solution 1837.2.0.1 x-Component of Velocity - u/ U infinity 1907.2.0.2 Boundary Layer Thickness delta(x) 1907.2.0.3 Wall Shear Stress tauw 1917.2.0.4 Local Skin Friction Coefficient cf (x) 1917.2.0.5 drag Force d 1927.2.0.6 Average Skin Friction Coefficient cf 1927.2.0.7 Displacement Thickness delta1(x) 1927.2.0.8 Momentum Thickness delta2(x) 1927.3 Momentum Transfer over a Wedge (Falkner-Skan Wedge Flow): Similarity Solution 1957.4 Application of Integral Methods to Momentum Transfer Problems 2017.4.1 Laminar Forced Flow over a Flat Plate with Uniform Velocity 2037.4.2 Two-Dimensional Laminar Flow over a Surface with Pressure Gradient (Variable Free Stream Velocity) 2047.4.2.1 The Correlation Method of Thwaites 2077.4.2.2 A Thwaites Type Correlation for Axisymmetric Body 2127.5 Viscous Incompressible Constant Property Parallel Flow over a Semi-Infinite Flat Plate: Similarity Solution for Uniform Wall Temperature Boundary Condition 2127.6 Low-Prandtl-Number Viscous Incompressible Constant Property Parallel Flow over a Semi-Infinite Flat Plate: Similarity Solutions for Uniform Wall Temperature Boundary Condition 2257.7 High-Prandtl-Number Viscous Incompressible Constant Property Parallel Flow over a Semi-Infinite Flat Plate: Similarity Solutions for Uniform Wall Temperature Boundary Condition 2287.8 Viscous Incompressible Constant Property Parallel Flow over a Semi-Infinite Flat Plate: Similarity Solution for Uniform Heat Flux Boundary Condition 2307.9 Viscous Incompressible Constant Property Parallel Flow over a Semi-Infinite Flat Plate: Similarity Solutions for Variable Wall Temperature Boundary Condition 2377.9.1 Superposition Principle 2457.10 Viscous Incompressible Constant Property Flow over a Wedge (Falkner-Skan Wedge Flow): Similarity Solution for Uniform Wall Temperature Boundary Condition 2497.11 Effect of Property Variation 2527.12 Application of Integral Methods to Heat Transfer Problems 2537.12.1 Viscous Flow with Constant Free Stream Velocity Along a Semi-Infinite Plate Under Uniform Wall Temperature: With Unheated Starting Length or Adiabatic Segment 2567.12.1.1 The Plate Without Unheated Starting Length 2627.12.2 Viscous Flow with Constant Free Stream Velocity Along a Semi-Infinite Plate with Uniform Wall Heat Flux: With Unheated Starting Length (Adiabatic Segment) 2627.12.2.1 The Plate with No Unheated Starting Length 2657.13 Superposition Principle 2657.13.1 Superposition Principle Applied to Slug Flow over a Flat Plate: Arbitrary Variation in Wall Temperature 2667.13.1.1 Boundary Condition: Single Step at X = 0 2667.13.1.2 Boundary Condition: Two Steps at X = 0 and X =xi1 2687.13.1.3 Boundary Condition: Three Steps at X = 0, X =xi1 , and X =xi2 2687.13.2 Superposition Principle Applied to Slug Flow over a Flat Plate: Arbitrary Variation in Wall Heat Flux 2727.13.2.1 Boundary Condition: Single Step at X = 0 2737.13.2.2 Boundary Condition: Two Steps at X = 0 and X =xi1 2747.13.2.3 Boundary Condition: Triple Steps at X = 0, X =xi1 , and X =xi2 2757.13.3 Superposition Principle Applied to Viscous Flow over a Flat Plate: Stepwise Variation in Wall Temperature 2787.13.3.1 First Problem 2787.13.3.2 Second Problem 2797.13.3.3 Heat Flux for 07.13.3.4 The Heat Flux for X > xi 1 2807.13.4 Superposition Principle Applied to Viscus Flow over a Flat Plate: Stepwise Variation in Surface Heat Flux 2827.13.4.1 First Problem 2827.13.4.2 Second Problem 2837.14 Viscous Flow over a Flat Plate with Arbitrary Surface Temperature Distribution 2847.15 Viscous Flow over a Flat Plate with Arbitrarily Specified Heat Flux 2897.16 One-Parameter Integral Method for Incompressible Two-Dimensional Laminar Flow Heat Transfer: Variable U infinity (x) and Constant Tw . T infinity = const 2937.17 One-Parameter Integral Method for Incompressible Laminar Flow Heat Transfer over a Constant Temperature of a Body of Revolution 295Problems 299References 3108 Laminar Momentum and Heat Transfer in Channels 3138.1 Introduction 3138.2 Momentum Transfer 3138.2.1 Hydrodynamic Considerations in Ducts 3138.2.2 Fully Developed Laminar Flow in Circular Tube 3188.2.3 Fully Developed Flow Between Two Infinite Parallel Plates 3238.3 Thermal Considerations in Ducts 3268.4 Heat Transfer in the Entrance Region of Ducts 3358.4.1 Circular Pipe: Slug Flow Heat Transfer in the Entrance Region 3378.4.1.1 Heat Transfer for Low-Prandtl-Number Fluid Flow (Slug Flow) in the Entrance Region of Circular Tube Subjected to Constant Wall Temperature 3378.4.1.2 Heat Transfer to Low-Prandtl-Number Fluid Flow (Slug Flow) in the Entrance Region of the Circular Tube Subjected to Constant Heat Flux 3458.4.1.3 Empirical and Theoretical Correlations for Viscous Flow Heat Transfer in the Entrance Region of the Circular Tube 3508.4.2 Parallel Plates: Slug Flow Heat Transfer in the Entrance Region 3558.4.2.1 Heat Transfer to a Low-Prandtl-Number Fluid (Slug Flow) in the Entrance Region of Parallel Plates: Both Plates Are Subjected to Constant Wall Temperatures 3558.4.2.2 Heat Transfer for Low-Prandtl-Number Fluid Flow (Slug Flow) in the Entrance Region of Parallel Plates: Both Plates Are Subjected to UHF 3588.4.2.3 Heat Transfer for Low-Prandtl-Number Fluid Flow (Slug Flow) in the Entrance Region of Parallel Plates: Upper Plate Is Insulated While the Lower Plate Is Subjected to Constant Wall Temperature 3638.4.2.4 Heat Transfer for Low-Prandtl-Number Fluid Flow (Slug Flow) in the Entrance Region of Parallel Plates: Upper Plate Is Insulated While the Lower Plate Is Subjected to Constant Heat Flux 3678.4.2.5 Empirical and Theoretical Correlations for Viscous Flow Heat Transfer in the Entrance Region of Parallel Plates 3708.5 Fully Developed Heat Transfer 3728.5.1 Circular Tube 3728.5.1.1 HFD and TFD Laminar Forced Convection Heat Transfer for Slug Flow in a Circular Pipe Subjected to Constant Wall Heat Flux 3728.5.1.2 HFD and TFD Laminar Forced Convection Heat Transfer for Viscous Flow in a Circular Tube Subjected to Constant Wall Heat Flux 3758.5.1.3 HFD and TFD Laminar Forced Convection Heat Transfer for Viscous Flow in a Circular Tube Subjected to Constant Wall Temperature 3788.5.2 Infinite Parallel Plates 3828.5.2.1 HFD and TFD Laminar Forced Convection Heat Transfer for Viscous Flow Between a Parallel Plate Channel. Both Plates Are Subjected to Constant Wall Heat Flux Boundary Condition 3838.6 Heat Transfer in the Thermal Entrance Region 3878.6.1 Circular Tube 3888.6.1.1 Graetz Problem: HFD and Thermally Developing Flow in a Circular Tube under Constant Wall Temperature Boundary Condition 3888.6.1.2 The Leveque Solution: UWT Boundary Condition 4018.6.1.3 Graetz Problem: HFD and Thermally Developing Flow for Viscous Flow in Circular Tube Under Uniform Wall Heat Flux Boundary Condition 4068.6.1.4 Empirical and Theoretical Correlations for Viscous Flow in the Thermal Entrance Region of the Pipe 4158.6.2 Two Infinite Parallel Plates 4198.6.2.1 Graetz Problem: HFD and Thermally Developing Flow Between Parallel Plates Subjected to Constant Wall Temperature 4198.6.2.2 Graetz Problem: HFD and Thermally Developing Flow Between Parallel Plates Subjected to Constant Wall Heat Flux 4288.6.2.3 Empirical and Theoretical Correlations for Viscous Flow in Thermal Entrance Region of Parallel Plates 4368.7 Circular Pipe with Variable Surface Temperature Distribution in the Axial Direction 4388.8 Circular Pipe with Variable Surface Heat Flux Distribution in the Axial Direction 4438.9 Short Tubes 4468.10 Effect of Property Variation 4488.11 Regular Sturm-Liouville Systems 449Problems 450References 4639 Foundations of Turbulent Flow 4659.1 Introduction 4659.2 The Reynolds Experiment 4659.3 Nature of Turbulence 4669.4 Time Averaging and Fluctuations 4679.5 Isotropic Homogeneous Turbulence 4709.6 Reynolds Averaging 4709.7 Governing Equations of Incompressible Steady Mean Turbulent Flow 4749.8 Turbulent Momentum Boundary Layer Equation 4779.9 Turbulent Energy Equation 4789.10 Turbulent Boundary Layer Energy Equation 4799.11 Closure Problem of Turbulence 4809.12 Eddy Diffusivity of Momentum 4819.13 Eddy Diffusivity of Heat 4829.14 Transport Equations in the Cylindrical Coordinate System 4839.15 Experimental Work on the Turbulent Mean Flow 4849.15.1 Turbulent Flow in Pipe: Velocity Profiles 4859.15.2 Turbulent Flow over a Flat Plate: Velocity Profiles 4919.16 Transition to Turbulent Flow 496Problems 498References 50410 Turbulent External Boundary Layers: Momentum and Heat Transfer 50710.1 Introduction 50710.2 Turbulent Momentum Boundary Layer 50710.3 Turbulence Models 50810.3.1 Zero-Equation Models 50810.3.1.1 Boussinesq Model 50810.3.1.2 Prandtl's Mixing-Length Model 50810.3.1.3 Van Driest Model 50910.4 Turbulent Flow over a Flat Plate with Constant Free-Stream Velocity: Couette Flow Approximation 51010.4.1 Inner Region 51010.5 The Universal Velocity Profile 51110.5.1 Three-Layer (von Karman) Model for the Velocity Profile 51110.5.2 Other Velocity Models 51410.6 Approximate Solution by the Integral Method for the Turbulent Momentum Boundary Layer over a Flat Plate 51410.7 Laminar and Turbulent Boundary Layer 51910.8 Other Eddy Diffusivity Momentum Models 52110.9 Turbulent Heat Transfer 52210.10 Analogy Between Momentum and Heat Transfer 52910.10.1 Reynold's Analogy 52910.10.2 Chilton-Colburn Analogy 53110.10.3 Prandtl-Taylor Analogy 53210.10.4 Von Karman Analogy 53510.11 Some Other Correlations for Turbulent Flow over a Flat Plate 53910.12 Turbulent Flow Along a Semi-infinite Plate with Unheated Starting Length: Constant Temperature Solution 54210.13 Flat Plate with Arbitrarily Specified Surface Temperature 55010.14 Constant Free-Stream Velocity Flow Along a Flat Plate with Uniform Heat Flux 55310.15 Turbulent Flow Along a Semi-Infinite Plate with Arbitrary Heat Flux Distribution 55410.16 Turbulent Transition and Overall Heat Transfer 55810.17 Property Variation 564Problems 564References 56911 Turbulent Internal Flow: Momentum and Heat Transfer 57311.1 Introduction 57311.2 Momentum Transfer 57311.2.1 Momentum Transfer in Infinite Two Parallel Plates 57311.2.1.1 The Entrance Region 57411.2.1.2 The HFD Region 57511.2.1.3 Prandtl's Mixing-Length Model 57811.2.1.4 Buffer Region 57911.2.1.5 The Mean Velocity 58211.2.1.6 Skin Friction Coefficient or Fanning Friction Factor cf 58211.2.2 Momentum Transfer in Circular Pipe Flow 58511.2.2.1 Entrance Region 58511.2.2.2 The HFD Region 58611.2.2.3 Average Velocity V 58911.2.2.4 Skin Friction Factor cf 58911.2.2.5 Moody Friction Factor f 58911.2.2.6 Prandtl Mixing-Length Model 59011.2.2.7 Laminar Sublayer 59111.2.2.8 Buffer Region 59111.2.2.9 Turbulent Region 59111.2.2.10 Moody Friction Factor 59211.2.2.11 Fanning Friction Factor 59311.2.2.12 The Power Law Velocity Distribution 59611.3 Fully Developed Turbulent Heat Transfer 59711.3.1 TFD and HFD Turbulent Flow Between Parallel Plates Subjected to UHF 59811.3.1.1 Mean Stream Temperature 60211.3.2 TFD and HFD Turbulent Flow in a Pipe Subjected to UHF 60511.3.2.1 Laminar Viscous Sublayer: 0 +11.3.2.2 Buffer Layer: 5 +11.3.2.3 Turbulent Region: y+ > 30 61011.4 HFD Thermally Developing Turbulent Heat Transfer 61811.4.1 Circular Duct with UWT 61811.4.2 Circular Duct with Uniform Wall Heat Flux 62511.4.2.1 Solution for Fully Developed Temperature Distribution theta1 62611.4.2.2 Solution for the Entry Region Temperature Distribution theta2 62711.5 Analogies for Internal Flow 62911.5.1 Reynolds Analogy 62911.5.2 Colburn Analogy 63111.5.3 Prandtl-Taylor Analogy 63111.5.3.1 Laminar Sublayer 63211.5.3.2 Turbulent Core 63211.5.4 von Karman Analogy 63311.5.4.1 Laminar Sublayer: 0 <= y+ << 5 63411.5.4.2 Buffer Layer: 5 <= y+ << 30 63511.5.4.3 Turbulent Core: y+ >= 30 63511.5.5 The Analogy of Kadar and Yaglom 63611.5.6 The Analogy of Yu et al. 63711.5.7 Martinelli Analogy 63911.6 Combined Entrance Region 64111.7 Empirical and Theoretical Correlations for Turbulent Flow in Channels 64211.7.1.1 Colburn Correlation 64511.7.1.2 Dittus and Boelter Correlation 64611.7.1.3 Sieder-Tate Correlation 64611.7.1.4 Hausen Correlations 64711.7.1.5 Petukhov Correlation 64711.7.1.6 Gnielinski Correlation 64911.7.1.7 Gnielinski Correlation with Modification 65011.7.1.8 Sleicher and Rouse Correlation 65011.7.1.9 Nusselt Correlation 65111.8 Heat Transfer in Transitional Flow 65211.8.1 Friction Factor in the Transitional Flow 65311.8.2 Heat Transfer in the Transition Region 65411.8.2.1 Tam and Ghajar Approach 65411.8.2.2 Churchill Approach 65511.8.2.3 Gnielinski Approach 65611.8.2.4 Abraham et al. Approach 65711.9 Effect of Property Variation 660Problems 660References 67012 Free Convection Heat Transfer 67512.1 Introduction 67512.2 Fundamental Equations and Dimensionless Parameters of Free Convection 67512.3 Scaling in Natural Convection 67912.4 Similarity Solution for Laminar Boundary Layer over a Semi-Infinite Vertical Flat Plate 68112.4.1 Constant Wall Temperature 68112.4.2 Uniform Heat Flux 68812.5 Integral Method (von Karman-Pohlhausen Method): An Approximate Analysis of Laminar Free Convection on a Vertical Plate 69512.5.1 Constant Wall Temperature 69712.5.2 Uniform Heat Flux 70012.6 Turbulent Free Convection Heat Transfer on a Vertical Plate 70212.7 Empirical Correlations for Free Convection 70412.7.1 Vertical Plate 70412.7.2 Horizontal Plate 71212.7.3 Inclined Plates 71512.7.4 Vertical Cylinders 71912.7.5 Horizontal Cylinder 72212.7.6 Inclined Cylinder 72312.7.7 Free Convection from Vertical Cylinders of Small Diameter 72412.8 Free Convection Within Parallel Plate Channels 72512.8.1 Vertical Parallel Plate Channel 72512.8.2 Horizontal Parallel Plate Channel 73112.8.3 Inclined Parallel Plate Channel 73212.9 Rectangular Enclosures 73512.9.1 Horizontal Rectangular Enclosure (theta=0) 73512.9.2 Vertical Rectangular Enclosure 73712.9.3 Inclined Rectangular Enclosure 74012.10 Horizontal Concentric Cylinders 74312.11 Concentric Spheres 74412.12 Spheres 744Problems 745References 752Index 755

O autorze

Nevzat Onur is Emeritus Professor of Mechanical Engineering at Gazi University. He pursued his undergraduate studies in mechanical engineering at the University of California, Davis, USA where he received his B.S. degree in 1974. He then attended the Tennessee Technological University, Cookeville, USA completing his M.S. and Ph.D. degree in 1976 and 1980. He taught at different universities in Turkey and he retired from Gazi University in 2011. He has over thirty years' experience in heat transfer research and development. His research interests have mainly been in viscous flow and convection heat transfer. He lives in Ankara, Turkey.