Thermal Computations for Electronics: Conductive, Radiative, and Convective Air Cooling

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface to the Second Edition
Preface to the First Edition
About the Author
Chapter 1: Introduction
	1.1 Primary Mechanisms of Heat Flow
	1.2 Conduction
	1.3 Application Example: Silicon Chip Resistance Calculation
	1.4 Convection
	1.5 Application Example: Chassis Panel Cooled by Natural Convection
	1.6 Radiation
	1.7 Application Example: Chassis Panel Cooled only by Radiation
	1.8 Illustrative Example: Simple thermal Network Model for a Heat Sinked Power Transistor on a Circuit Board
	1.9 Illustrative Example: Thermal Network Circuit for a Printed Circuit Board
	1.10 Compact Component Models
	1.11 Illustrative Example: Pressure and Thermal Circuits for a Forced Air Cooled Enclosure
	1.12 Illustrative Example: A Single Chip Package on a Printed Circuit Board - the Problem
	1.13 Illustrative Example: A Single Chip Package on a Printed Circuit Board - Fourier Series Analytical Solution
	1.14 Illustrative Example: A Single Chip Package on a Printed Circuit Board - Thermal Network Solution
	1.15 Illustrative Example: A Single Chip Package on a Printed Circuit Board - Finite Element Method Solution
	1.16 Illustrative Example: A Single Chip Package on a Printed Circuit Board - Three Solution Methods Compared
	Exercises
Chapter 2: Thermodynamics of Airflow
	2.1 The First Law of Thermodynamics
	2.2 Heat Capacity at Constant Volume
	2.3 Heat Capacity at Constant Pressure
	2.4 Steady Gas Flow as an Open, Steady, Single Stream
	2.5 Air Temperature Rise: Temperature Dependence
	2.6 Air Temperature Rise: T Identified using Differential forms of ∆T, ∆Q
	2.7 Air Temperature Rise: T Identified as Average Bulk Temperature
	Exercises
Chapter 3: Airflow I: Forced Flow in Systems
	3.1 Preliminaries
	3.2 Bernoulli’s Equation
	3.3 Bernoulli’s Equation with Losses
	3.4 Fan Testing
	3.5 Estimate of Fan Test Error Accrued by Measurement of Downstream Static Pressure
	3.6 Derivation of the “One Velocity” Head Formula
	3.7 Fan and System Matching
	3.8 Adding Fans in Series and Parallel
	3.9 Airflow Resistance: Common Rlements
	3.10 Airflow Resistance: True Circuit Boards
	3.11 Modeled Circuit Board Elements
	3.12 Combining Airflow Resistances
	3.13 Application Example: Forced Air Cooled Enclosure
	Exercises
Chapter 4: Airflow II: Forced Flow in Ducts, Extrusions, and Pin Fin Arrays
	4.1 The Airflow Problem for Channels with a Rectangular Cross-Section
	4.2 Entrance and Exit Effects for Laminar and Turbulent Flow
	4.3 Friction Coefficient for Channel Flow
	4.4 Application Example: Two-Sided Extruded Heat Sink
	4.5 A pin Fin Correlation
	4.6 Application Example: Pin Fin Problem from Khan et al.
	4.7 Flow Bypass Effects According to Lee
	4.8 Application Example: Interfin Air Velocity Calculation for a Heat Sink in a Circuit Board Channel using the Flow Bypass Method of Lee with the Muzychka and Yovanovich Friction Factor Correlation
	4.9 Application Example: Interfin Air Velocity Calculation for a Heat Sink in a Circuit Board Channel Using the Flow Bypass Method of Lee with the Handbook of Heat Transfer Friction Factor Correlation
	4.10 Flow Bypass Effects According to Jonsson and Moshfegh
	4.11 Application Example: Pin Fin Problem from Khan et al., using the Jonsson and Moshfegh Correlation, Non-Bypass
	Exercises
Chapter 5: Airflow III: Buoyancy Driven Draft
	5.1 Derivation of Buoyancy Driven Head
	5.2 Matching Buoyancy Head to System
	5.3 Application Example: Buoyancy-Draft Cooled Enclosure
	5.4 System Models with Buoyant Airflow
	Exercises
Chapter 6: Forced Convective Heat Transfer I: Components
	6.1 Forced Convection from a Surface
	6.2 Dimensionless Numbers: Nusselt, Reynolds, and Prandtl
	6.3 More on the Reynolds Number
	6.4 Classical Flat Plate Forced Convection Correlation: Uniform Surface Temperature, Laminar Flow
	6.5 Empirical Correction to Classical Flat Plate Forced Convection Correlation, Laminar Flow
	6.6 Application Example: Winged Aluminum Heat Sink
	6.7 Classical Flat Plate Forced Convection Correlation: Uniform Heat Rate Per Unit Area, Laminar Flow
	6.8 Classical Flat Plate (Laminar) Forced Convection Correlation Extended to Small Reynolds Numbers: Uniform Surface Temperature
	6.9 Circuit Boards: Adiabatic Heat Transfer Coefficients and Adiabatic Temperatures
	6.10 Adiabatic Heat Transfer Coefficient and Temperature According to Faghri et al.
	6.11 Adiabatic Heat Transfer Coefficient and Temperature for Low-Profile Components According to Wirtz
	6.12 Application Example: Circuit Board with 0.82 in.x0.24 In.x0.123 in. Convecting Modules
	Exercises
Chapter 7: Forced Convective Heat Transfer II: Ducts, Extrusions, and Pin Fin Arrays
	7.1 Boundary Layer Considerations
	7.2 A Convection/Conduction Model for Ducts and Heat Sinks
	7.3 Conversion of an Isothermal Heat Transfer Coefficient from Referenced-to-inlet Air to Referenced-to-local Air
	7.4 Nusselt Number for Fully Developed Laminar Duct Flow Corrected for Entry Length Effects
	7.5 A Newer Nusselt Number for Laminar Flow in Rectangular (Cross-Section) Ducts with Entry Length Effects
	7.6 Nusselt Number for Turbulent Duct Flow
	7.7 Application Example: Two-Sided Extruded Heat Sink
	7.8 Flow Bypass Effects According to Jonsson and Moshfegh
	7.9 Application Example: Heat Sink in a Circuit Board Channel using the Flow Bypass Method of Lee
	7.10 In-Line and Staggered Pin Fin Heat Sinks
	7.11 Application Example: Thermal Resistance of a Pin Fin Heat Sink using the
	7.12 Lee’s Flow Bypass Adapted to Non-Zero Bypass Resistance Problem, Compared Empirical Method of Jonsson & Moshfegh
	Exercises
Chapter 8: Natural Convection Heat Transfer I: Plates
	8.1 Dimensionless Numbers: Nusselt and Grashof
	8.2 Classical Flat Plate Correlations
	8.3 Small Device Flat Plate Correlations
	8.4 Application Example: Vertical Convecting Plate
	8.5 Application Example: Vertical Convecting and Radiating Plate
	8.6 Vertical Parallel Plate Correlations Applicable to Circuit Board Channels
	8.7 Application Example: Vertical Card Assembly
	8.8 Recommended Use of Vertical Channel Models in Sealed and Vented Enclosures
	8.9 Conversion of Isothermal Wall Channel Heat Transfer Coefficients from Referenced-to-inlet Air to Referenced-to-local Air
	8.10 Application Example: Enclosure with Circuit Boards - Enclosure Temperatures Inly
	8.11 Application Example: Enclosure with Circuit Boards - Circuit Board Temperatures Only
	8.12 Application Example: Enclosure with Circuit Boards, Comparison of Sections 8.10 and 8.11 Approximate Results with CFD
	8.13 Illustrative example: Metal-walled enclosure, ten PCBs
	8.14 Illustrative Example: Metal-Walled Enclosure with Heat Dissipation Provided by Several Wire-Wound Resistors
	Exercises
Chapter 9: Natural Convection Heat Transfer II: Heat Sinks
	9.1 Heat Sink Geometry and Some Nomenclature
	9.2 A rectangular U-channel Correlation from Van de Pol and Tierney
	9.3 Design Plots Representing the Van de Pol and Tierney Correlation
	9.4 A Few Useful Formulae
	9.5 Application Example: Natural Convection Cooled, Vertically Oriented Heat Sink
	9.6 Application Example: Natural Convection Cooled, Nine-fin Heat Sink with Calculations Compared to Test Data
	Exercises
Chapter 10: Thermal Radiation Heat Transfer
	10.1 Blackbody Radiation
	10.2 Spacial Effects and the View Factor
	10.3 Application Example: View Factors for Finite Parallel Plates
	10.4 Nonblack Surfaces
	10.5 The Radiation Heat Transfer Coefficient
	10.6 Application Example: Radiation and Natural Convection Cooled Enclosure with Circuit Boards - Enclosure Temperatures Only
	10.7 Radiation for Multiple Gray-body Surfaces
	10.8 Hottel Script F ( F ) Method for Gray-body Radiation Exchange
	10.9 Application Example: Gray-body Circuit Boards Analyzed as Infinite Parallel Plates
	10.10 Application Example: Gray-body Circuit Boards Analyzed as Finite Parallel Plates
	10.11 Thermal Radiation Networks
	10.12 Thermal Radiation Shielding for Rectangular U-channels (Fins)
	10.13 Application Example: Natural Convection and Radiation Cooled, Vertically Oriented Heat Sink (see Section 9.4)
	10.14 Application Example: Natural Convection and Radiation Cooled Nine-fin Heat Sink - Calculations Compared to Test Data
	10.15 Application Example: Natural Convection and Radiation Cooled Nine-fin Heat Sink Analyzed for a Temperature Rise not Included in Figure 9.2
	10.16 Illustrative Example: Natural Convection and Radiation Cooled Nine-fin Heat Sink Analyzed for Optimum Number of Fins
	Exercises
Chapter 11: Conduction I: Basics
	11.1 Fourier’s Law of Heat Conduction
	11.2 Application Example: Mica Insulator with Thermal Paste
	11.3 Thermal Conduction Resistance of Some Simple Structures
	11.4 The One-dimensional Differential Equation for Heat Conduction
	11.5 Application Example: Aluminum Core Board with Negligible Air Cooling
	11.6 Application Example: Aluminum Core Board with Forced Air Cooling
	11.7 Application Example: Simple Heat Sink
	11.8 Fin Efficiency
	11.9 Differential Equations for More than One Dimension
	11.10 Physics of Thermal Conductivity of Solids
	11.11 Thermal Conductivity of Circuit Boards (Epoxy-glass Laminates)
	11.12 Application Example: Epoxy-glass Circuit Board with Copper
	11.13 Thermal Interface Resistance
	11.14 Application Example: Interface Resistance for an Aluminum Joint
	Exercises
Chapter 12: Conduction II: Spreading Resistance
	12.1 The Spreading Problem
	12.2 Fixed Spreading Angle Theories
	12.3 Circular-source, Semi-infinite Media Solution, Uniform Flux, Average Source Temperature, by Carslaw and Jaeger (1986)
	12.4 Rectangular-source, Time-dependent, Semi-infinite Media Solution, Uniform Flux, Peak Source Temperature by Joy and Schlig (1970)
	12.5 Other Circular Source Solutions
	12.6 Rectangular Source on Rectangular, Finite-media with One Convecting Surface: Theory
	12.7 Rectangular Source on Rectangular, Finite-media: Design Curves
	12.8 Application Example: Heat Source Centered on a Heat Sink (Ellison, 2003)
	12.9 Illustration Example: Spreading Contribution to Forced Air Cooled Heat Sink
	Exercises
Chapter 13: Additional Mathematical Methods
	13.1 Thermal Networks: Steady-state Theory
	13.2 Illustrative Example: A Simple Steady-state, Thermal Network Problem, Gauss-Seidel and Simultaneous Equation Solutions Compared
	13.3 Thermal Networks: Time-dependent Theory
	13.4 Illustrative Example: A Simple Time-dependent, Thermal Network Problem
	13.5 Finite Difference Theory for Conduction with Newtonian Cooling
	13.6 Programming the Pressure/Airflow Network Problem
	13.7 Finite Element Theory - the Concept of the Calculus of Variations
	13.8 Finite Element Theory - Derivation of the One-dimensional Euler-Lagrange Equation
	13.9 Finite Element Theory - Application of the One-dimensional Euler-Lagrange Equation to a Heat Conduction Problem
Appendix i: Physical Properties of Dry Air at Atmospheric Pressure
Appendix ii: Radiation Emissivity at Room Temperature
Appendix iii: Thermal Conductivity of Some Common Electronic Packaging Materials
Appendix iv: Some Properties of Bessel Functions
Appendix v: Some Properties of the Dirac Delta Function
Appendix vi: Fourier Coefficients for a Rectangular Source
Appendix vii: Derivation of the Green’s Function Properties for the Spreading Problem of a Rectangular Source and Substrate - Method A
Appendix viii: Derivation of the Green’s Function Properties for the Spreading Problem of a Rectangular Source and Substrate - Method B
Appendix ix: Proof of Reciprocity for the Steady-state Green’s Function;
	Proof of Reciprocity for the Three-dimensional, Time-dependent Green’s Function
Appendix x: Finned Surface to Flat Plate h Conversion
Appendix xi: Some Conversion Factors
Appendix xii: Altitude Effects for Fan Driven Airflow and Forced Convection Cooled Enclosures
	xii.1: Derivation of the Fan Laws
	xii.2: Air Presssure at an Elevated Altitude
	xii.3: The Ideal Gas Law and an Air Density Model at Altitude
	xii.4: Fan and System Interaction at Altitude
	xii.5: Appication Example - Fan Cooled Heat Sink
Appendix xiii: Altitude Effects for Buoyancy Driven Airflow and Natural Convection Cooled Enclosures
	xiii.1: Derivation of Air Temperature Rise Formula
	xiii.2: Derivation of Air Temperature Rise using Average Bulk Temperature for Properties
	xiii.3: Head Loss Due to Buoyancy Pressure
	xiii.4: Matching System Loss to Buoyancy Pressure Head
	xiii.5: Application Example - Buoyancy Draft Cooled Enclosure from Section 5.3
	xiii.6: Application Example - Vertical Convecting Plte from Section 8.4
	xiii.7: Comments Concerning Other Heat Transfer Coefficients at an Elevated Altitude
Bibliography
Index