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

A total revision of the author’s previous work, Thermal Computations for Electronics: Conductive, Radiative, and Convective Air Cooling is a versatile reference that was carefully designed to help readers master mathematical calculation, prediction, and application methods for conductive, radiative, and convective heat transfer in electronic equipment. Presenting material in a way that is practical and useful to engineers and scientists, as well as engineering students, this book provides very detailed text examples and their solutions. This approach helps users at all levels of comprehension to strengthen their grasp of the subject and detect their own calculation errors. The beginning of this book is largely devoted to prediction of airflow and well-mixed air temperatures in systems and heat sinks, after which it explores convective heat transfer from heat sinks, circuit boards, and components. Applying a systematic presentation of information to enhance understanding and computational practice, this book: Provides complete mathematical derivations and supplements formulae with design plots Offers complete exercise solutions (Mathcad™ worksheets and PDF images of Mathcad worksheets), lecture aids (landscape-formatted PDF files), and text-example Mathcad worksheets for professors adopting this book Addresses topics such as methods for multi-surface radiation exchange, conductive heat transfer in electronics, and finite element theory with a variational calculus method explained for heat conduction Presents mathematical descriptions of large thermal network problem formulation Discusses comprehensive thermal spreading resistance theory, and includes steady-state and time-dependent problems This reference is useful as a professional resource and also ideal for use in a complete course on the subject of electronics cooling, with its suggested course schedule and other helpful advice for instructors. Selected sections may be used as application examples in a traditional heat transfer course or to help professionals improve practical computational applications.

Table of Contents:
Introduction Primary mechanisms of heat flow Conduction Application example: Silicon chip resistance calculation Convection Application example: Chassis panel cooled by natural convection Radiation Application example: Chassis panel cooled only by radiation 7 Illustrative example: Simple thermal network model for a heat sinked power transistor Illustrative example: Thermal network circuit for a printed circuit board Compact component models Illustrative example: Pressure and thermal circuits for a forced air cooled enclosure Illustrative example: A single chip package on a printed circuit board—the problem Illustrative example: A single chip package on a printed circuit board—Fourier series solution Illustrative example: A single chip package on a printed circuit board—thermal network solution Illustrative example: A single chip package on a printed circuit board—finite element solution Illustrative example: A single chip package on a printed circuit board—methods compared Thermodynamics of airflow The first law of thermodynamics Heat capacity at constant volume Heat capacity at constant pressure Steady gas flow as an open, steady, single stream Air temperature rise: Temperature dependence Air temperature rise: T identified using differential forms of ΔT,ΔQ Air temperature rise: T identified as average bulk temperature Airflow I: Forced flow in systems Preliminaries Bernoulli’s equation Bernoulli’s equation with losses Fan testing Estimate of fan test error accrued by measurement of downstream static pressure Derivation of the "one velocity" head formula Fan and system matching Adding fans in series and parallel Airflow resistance: Common elements Airflow resistance: True circuit boards Modeled circuit board elements Combining airflow resistances Application example: Forced air cooled enclosure Airflow II: Forced flow in ducts, extrusions, and pin fin arrays The airflow problem for channels with a rectangular cross-section Entrance and exit effects for laminar and turbulent flow Friction coefficient for channel flow Application example: Two-sided extruded heat sink A pin fin correlation Application example: Pin fin problem from Khan, et al. Flow bypass effects according to Lee Application example: Flow bypass method using Muzychka and Yovanovich correlation Application example: Flow bypass method using HBT friction factor correlation Flow bypass effects according to Jonsson and Moshfegh Application example: Pin fin problem using Jonsson and Moshfegh correlation Airflow III: Buoyancy driven draft Derivation of buoyancy driven head Matching buoyancy head to system Application example: Buoyancy-draft cooled enclosure System models with buoyant airflow Forced convective heat transfer I: Components Forced convection from a surface The Nusselt and Prandtl numbers The Reynold’s number Classical flat plate forced convection correlation: Uniform surface temperature, laminar flow Empirical correction to classical flat plate forced convection correlation, laminar flow Application example: Winged aluminum heat sink Classical flat plate forced convection correlation: Uniform heat rate per unit area, laminar flow Classical flat plate (laminar) forced convection correlation extended to small Reynold’s number Circuit boards: Adiabatic heat transfer coefficients and adiabatic temperatures Adiabatic heat transfer coefficient and temperature according to M. Faghri, et al. Adiabatic heat transfer coefficient and temperature according to R. Wirtz Application example: Circuit board with 1.5 in. / 1.5 in. / 0.6 in. convecting modules Application example: Circuit board with 0.82 in./ 0.24 in. /0.123 in. convecting modules Forced convective heat transfer II: Ducts, extrusions, and pin fin arrays Boundary layer considerations A convection/conduction model for ducts and heat sinks Conversion of an isothermal heat transfer coefficient referenced to inlet to referenced to local air Nusselt number for fully developed laminar duct flow corrected for entry length effects A newer Nusselt number for laminar flow in rectangular (cross-section) ducts Nusselt number for turbulent duct flow Application example: Two-sided extruded heat sink Flow bypass effects according to Jonsson and Moshfegh Application example: Heat sink in a circuit board channel using the flow bypass method of Lee In-line and staggered pin fin heat sinks Application example: Thermal resistance of a pin fin heat sink Natural convection heat transfer I: Plates Nusselt and Grashof numbers Classical flat plate correlations Small device flat plate correlations Application example: Vertical convecting plate Application example: Vertical convecting and radiating plate Vertical parallel plate correlations applicable to circuit board channels Application example: Vertical card assembly Recommended use of vertical channel models in sealed and vented enclosures Conversion of heat transfer coefficients referenced-to-inlet air to referenced-to-local air Application example: Enclosure with circuit boards - enclosure temperatures only Application example: Enclosure with circuit boards - circuit board temperatures only Application example: Enclosure with circuit boards, comparison with CFD Application example: Single circuit board enclosure with negligible circuit board radiation Illustrative example: Single circuit board enclosure with radiation exchange between interior enclosure walls and circuit board, results compared with experiment Illustrative example: Metal walled enclosure with ten circuit boards Illustrative example: Metal walled enclosure with heat dissipation provided Natural convection heat transfer II: Heat sinks Heat sink geometry and some nomenclature A rectangular U-channel correlation from Van de Pol and Tierney Design plots representing the Van de Pol & Tierney correlation A few useful formulae Application example: Natural convection cooled, vertically oriented heat sink Application example: Natural convection cooled, nine fin heat sink compared to test data Thermal radiation heat transfer Blackbody radiation Spacial effects and the view factor Application example: View factors for finite parallel plates Non-black surfaces The radiation heat transfer coefficient Application example: Radiation and natural convection cooled enclosure with circuit boards Radiation for multiple gray-body surfaces Hottel script F (F) method for gray-body radiation exchange Application example: Gray-body circuit boards analyzed as infinite parallel plates Application example: Gray-body circuit boards analyzed as finite parallel plates Thermal radiation networks Thermal radiation shielding for rectangular U-channels (fins) Application example: Natural convection and radiation cooled heat sink Application example: Nine fin heat sink, compared with test data Application example: Natural convection and radiation cooled nine fin heat sink Illustrative example: Natural convection and radiation cooled heat sink Conduction I: Some basics Fourier’s law of heat conduction Application example: Mica insulator with thermal paste Thermal conduction resistance of some simple structures The one-dimensional differential equation for heat conduction Application example: Aluminum core board with negligible air cooling Application example: Aluminum core board with forced air cooling Application example: Simple heat sink Fin efficiency Differential equations for more than one dimension Physics of thermal conductivity of solids Thermal conductivity of circuit boards (epoxy-glass laminates) Application example: Epoxy-glass circuit board with copper Thermal interface resistance Application example: Contact resistance for an aluminum joint Conduction II: Spreading resistance The spreading problem Fixed spreading angle theories Circular-source, semi-infinite media solution by Carslaw and Jaeger (1986) Rectangular-source, time dependent, semi-infinite media solution by Joy & Schlig (1970) Other circular source solutions Rectangular source on rectangular, finite-media with one convecting surface: Theory Rectangular source on rectangular, finite-media: Design curves Application example: Heat source centered on a heat sink (Ellison, 2003) Application example: IC chip on an alumina substrate Rectangular source on rectangular, finite-media with two convecting surfaces: Theory Exploring the difference between one-sided and two-sided Newtonian cooling Including the effect of two different ambients to the two-sided spreading theory Application example: Heat sink with two convecting sides, one finned and one flat Square source on square, finite-media with one convecting surface - time dependent (Rhee and Bhatt, 2007) Additional mathematical methods Thermal networks: Steady-state theory Illustrative example: A simple steady-state, thermal network problem, solutions compared Thermal networks: Time-dependent theory Illustrative example: A simple time-dependent, thermal network problem Finite difference theory for conduction with Newtonian cooling Programming the pressure/airflow network problem Finite element theory - the concept of the calculus of variations Finite element theory - derivation of the one-dimensional Euler-Lagrange equation Finite element theory - application of the one-dimensional Euler-Lagrange equation Finite element theory - derivation of the two-dimensional Euler-Lagrange equation Finite element theory - application of the Euler-Lagrange equation to two dimensions Appendices Bibliography Index