Heat Transfer Engineering Applications Part 1 potx

Contents Preface IX Part 1 Laser-, Plasma- and Ion-Solid Interaction 1 Chapter 1 Mathematical Models of Heat Flow in Edge-Emitting Semiconductor Lasers 3 Michał Szymanski Chapter 2 Te

HEAT TRANSFER –

ENGINEERING APPLICATIONS Edited by Vyacheslav S Vikhrenko

Heat Transfer – Engineering Applications

Edited by Vyacheslav S Vikhrenko

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Contents

Preface IX Part 1 Laser-, Plasma- and Ion-Solid Interaction 1

Chapter 1 Mathematical Models of Heat Flow in

Edge-Emitting Semiconductor Lasers 3 Michał Szymanski

Chapter 2 Temperature Rise of Silicon Due to Absorption

of Permeable Pulse Laser 29

Etsuji Ohmura Chapter 3 Pulsed Laser Heating and Melting 47

David Sands Chapter 4 Energy Transfer in Ion– and Laser–Solid Interactions 71

Alejandro Crespo-Sosa

Chapter 5 Temperature Measurement of a Surface

Exposed to a Plasma Flux Generated Outside the Electrode Gap 87

Nikolay Kazanskiy and Vsevolod Kolpakov

Part 2 Heat Conduction – Engineering Applications 119

Chapter 6 Experimental and Numerical Evaluation of

Thermal Performance of Steered Fibre Composite Laminates 121

Z Gürdal, G Abdelal and K.C Wu Chapter 7 A Prediction Model for Rubber Curing Process 151

Shigeru Nozu, Hiroaki Tsuji and Kenji Onishi

Chapter 8 Thermal Transport in Metallic Porous Media 171

Z.G Qu, H.J Xu, T.S Wang, W.Q Tao and T.J Lu

VI Contents

Chapter 9 Coupled Electrical and Thermal Analysis of Power Cables

Using Finite Element Method 205 Murat Karahan and Özcan Kalenderli

Chapter 10 Heat Conduction for Helical and Periodical

Contact in a Mine Hoist 231 Yu-xing Peng, Zhen-cai Zhu and Guo-an Chen

Chapter 11 Mathematical Modelling of Dynamics of Boiler

Surfaces Heated Convectively 259 Wiesław Zima

Chapter 12 Unsteady Heat Conduction Phenomena in

Internal Combustion Engine Chamber and Exhaust Manifold Surfaces 283

G.C Mavropoulos

Chapter 13 Ultrahigh Strength Steel: Development of Mechanical

Properties Through Controlled Cooling 309

S K Maity and R Kawalla Part 3 Air Cooling of Electronic Devices 337

Chapter 14 Air Cooling Module Applications to

Masaru Ishizuka and Tomoyuki Hatakeyama

Chapter 16 Multi-Core CPU Air Cooling 377

M A Elsawaf, A L Elshafei and H A H Fahmy

Preface

Enormous number of books, reviews and original papers concerning engineering applications of heat transfer has already been published and numerous new publications appear every year due to exceptionally wide list of objects and processes that require to be considered with a view to thermal energy redistribution All the three mechanisms of heat transfer (conduction, convection and radiation) contribute to energy redistribution, however frequently the dominant mechanism can be singled out On the other hand, in many cases other phenomena accompany heat conduction and interdisciplinary knowledge has to be brought into use Although this book is mainly related to heat transfer, it consists of a considerable amount of interdisciplinary chapters

The book is comprised of 16 chapters divided in three sections The first section includes five chapters that discuss heat effects due to laser-, ion-, and plasma-solid interaction

In eight chapters of the second section engineering applications of heat conduction equations are considered In two first chapters of this section the curing reaction kinetics in manufacturing process for composite laminates (Chapter 6) and rubber articles (Chapter 7) is accounted for Heat conduction equations are combined with mass transport (Chapter 8) and ohmic and dielectric losses (Chapter 9) for studying heat effects in metallic porous media and power cables, respectively Chapter 10 is devoted to analysing the safety of mine hoist under influence of heat produced by mechanical friction Heat transfer in boilers and internal combustion engine chambers are considered in Chapters 11 and 12 In the last Chapter 13 of this section temperature management for ultrahigh strength steel manufacturing is described

Three chapters of the last section are devoted to air cooling of electronic devices In the first chapter of this section it is shown how an air-cooling thermal module is comprised with single heat sink, two-phase flow heat transfer modules with high heat transfer efficiency, to effectively reduce the temperature of consumer-electronic products such as personal computers, note books, servers and LED lighting lamps of small area and high power Effects of the size and the location of outlet vent as well as the relative distance from the outlet vent location to the power heater position of electronic equipment on the cooling efficiency is investigated experimentally in

X Preface

Chapter 15 The last chapter objective is to minimize air cooling limitation effect and ensure stable CPU utilization using dynamic thermal management controller based on fuzzy logic control

Dr Prof Vyacheslav S Vikhrenko

Belarusian State Technological University,

Belarus

Part 1 Laser-, Plasma- and Ion-Solid Interaction

Mathematical Models of Heat Flow

in Edge-Emitting Semiconductor

Lasers

Michał Szyma ´nski

Institute of Electron Technology

Poland

1 Introduction

Edge-emitting lasers started the era of semiconductor lasers and have existed up tonowadays, appearing as devices fabricated out of various materials, formed sometimes invery tricky ways to enhance light generation However, in all cases radiative processesare accompanied by undesired heat-generating processes, like non-radiative recombination,Auger recombination, Joule effect or surface recombination Even for highly efficient lasersources, great amount of energy supplied by pumping current is converted into heat.High temperature leads to deterioration of the main laser parameters, like threshold current,output power, spectral characteristics or lifetime In some cases, it may result in irreversibledestruction of the device via catastrophic optical damage (COD) of the mirrors Therefore,deep insight into thermal effects is required while designing the improved devices

From the thermal point of view, the laser chip (of dimensions of 1-2 mm or less) is a rectangularstack of layers of different thickness and thermal properties This stack is fixed to a slightlylarger heat spreader, which, in turn, is fixed to the huge heat-sink (of dimensions of severalcm), transferring heat to air by convection or cooled by liquid or Peltier cooler Schematic view

of the assembly is shown in Fig 1 Complexity and large size differences between the elementsoften induce such simplifications like reduction of the dimensionality of equations, thermalscheme geometry modifications or using non-uniform mesh in numerical calculations.Mathematical models of heat flow in edge-emitting lasers are based on the heat conductionequation In most cases, solving this equation provides a satisfactory picture of thermalbehaviour of the device More precise approaches use in addition the carrier diffusionequation The most sophisticated thermal models take into consideration variable photondensity found by solving photon rate equations

The heat generated inside the chip is mainly removed by conduction and, in a minor degree,

by convection Radiation can be neglected Typical boundary conditions for heat conductionequation are the following: isothermal condition at the bottom of the device, thermallyinsulated side walls, convectively cooled upper surface It must be said that obtaining reliabletemperature profiles is often impossible due to individual features of particular devices,which are difficult to evaluate within the quantitative analysis Mounting imperfections

1

Since quantum cascade lasers (QCL’s) exploit superlattices (SL’s) as active layers, they havebrought new challenges in the field of thermal modelling Numerous experiments show thatthe thermal conductivity of a superlattice is significantly reduced The phenomenon can

be explained in terms of phonon transport across a stratified medium As a consequence,mathematical models of heat flow in quantum cascade lasers resemble those created forstandard edge-emitting lasers, but the stratified active region is replaced by an equivalentlayer described by anisotropic thermal conductivity In earlier works, the cross-plane andin-plane values of this parameter were obtained by arbitrary reduction of bulk values ortreated as fitting parameters Recently, some theoretical methods of assessing the thermalconductivity of superlattices have been developed

The present chapter is organised as follows In sections 2, 3 and 4, one can find the description

of static thermal models from the simplest to the most complicated ones Section 5 provides adiscussion of the non-standard boundary condition assumed at the upper surface Dynamicalissues of thermal modelling are addressed in section 6, while section 7 is devoted to quantumcascade lasers In greater part, the chapter is a review based on the author’s researchsupported by many other works However, Fig 7, 8, 12 and 13 present the unpublishedresults dealing with facet temperature reduction techniques and dynamical thermal behaviour

of laser arrays Note that section 8 is not only a short revision of the text, but containssome additional information or considerations, which may be useful for thermal modelling

of edge-emitting lasers The most important mathematical symbols are presented in Table 1.Symbols of minor importance are described in the text just below the equations, in which theyappear

Mathematical Models of Heat Flow in Edge-Emitting Semiconductor Lasers 3

Symbol Description

A nr non-radiative recombination coefficient

B bi-molecular recombination coefficient

b chip width (see Fig 2)

C A Auger recombination coefficient

c h specific heat

D diffusion coefficient

d n total thickness of the n-th medium

g heat source function

I driving current

L resonator length

n e f f effective refractive index

n i number of interfaces

N, N tr carrier concentration, transparency carrier concentration

R f , R b power reflectivity of the front and back mirror

rBd(1→2) TBR for the heat flow from medium 1 to 2

S total photon density

S f , S b photon density of the forward and backward travelling wave

S av averaged photon density

T temperature

T up temperature of the upper surface

V voltage

v sur surface recombination velocity

w contact width (see Fig 2)

y t top of the structure (see Fig 2)

x, y, z spatial coordinates (see Fig 1)

α convection coefficient

α gain linear gain coefficient

α int internal loss within the active region

β spontaneous emission coupling coefficient

Γ confinement factor

λ thermal conductivity

λ ⊥,λ  thermal conductivity of QCL’s active layer in the directionperpendicular and parallel to epitaxial layers, respectively

ν frequency

ρ n density, subscript n (if added) denotes the medium number

τ, τ av carrier lifetime, averaged carrier lifetime

c, e, h, k B physical constants: light velocity, elementary charge, Planck

and Boltzmann constants, respectively

Table 1 List of symbols

5

Mathematical Models of Heat Flow in Edge-Emitting Semiconductor Lasers

4 Will-be-set-by-IN-TECH

Fig 2 Schematic view of a laser chip cross-section (A) Function describing the heat source(B)

2 Models based on the heat conduction equation only

Basic thermal behaviour of an edge-emitting laser can be described by the stationary heatconduction equation:

∇( λ(y )∇ T(x, y )) = − g(x, y) (1)accepting the following assumptions (see Fig 2):

— the laser is a rectangular stack of layers of different thickness and thermal conductivities;1

— there is no heat escape from the top and side walls, while the temperature of the bottom

of the structure is constant;

— the active layer is the only heat source in the structure and it is represented by infinitelythin stripe placed between the waveguide layers

The heat power density is determined according to the crude approximation:

g(x, y) = V I − P out

which physically means that the difference between the total power supplied to the deviceand the output power is uniformly distributed over the surface of the selected region.2 Theproblem was solved analytically by Joyce & Dixon (1975) Further works using this modelintroduced convective cooling at the top of the laser, considered extension and diversity ofheat sources or changed the thermal scheme in order to take into account the non-ideal heatsink (Bärwolff et al (1995); Puchert et al (1997); Szyma ´nski et al (2007; 2004)) Such approachallows to calculate temperature inside the resonator, while the temperature in the vicinity of

1 Note that the thermal scheme can be easily generalised to laser array by periodic duplication of stack

along the x axis.

2 In a three-dimensional case the surface is replaced by the volume.

Mathematical Models of Heat Flow in Edge-Emitting Semiconductor Lasers 5

mirrors is reliable only in the near-threshold regime The work by Szyma ´nski et al (2007) can

be regarded as a recent version of this model and will be briefly described below

Assuming no heat escape from the side walls:

∂

∂x T (± b

and using the separation of variables approach (Bärwolff et al (1995); Joyce & Dixon (1975)),

one obtains the solution for T in two-fold form In the layers above the active layer (n - even)

A (k) 2K[w (k) A,n exp(μ k y) +w (k) B,n exp (− μ k y)]cos(μ k x), (4)

while under the active layer (n - odd) it takes the form:

In (4) and (5)μ k=2k π/b is the separation constant and thus it appears in both directions (x

and y) Integer number k numerates the heat modes Coefficients w (k) A,n and w (k) B,nand relation

between A (k) 2K and A (k) 2M −1can be found in Szyma ´nski (2007) They are determined by thebottom boundary condition, continuity conditions for the temperature and heat flux at thelayer interfaces and the top boundary condition

Fig 3 Thermal scheme modification Assuming larger b allows to keep the rectangular

cross-section of the whole assembly and hence equations (4) and (5) can be used

The results obtained according to the model described above are presented in Table 2 Thecalculated values are slightly underestimated due to bonding imperfections, which elude

7

Mathematical Models of Heat Flow in Edge-Emitting Semiconductor Lasers