978-0123869449 Chapter 1 Solution Manual Part 1

Unlock access to all the studying documents.

View Full Document

PREFACE

This manual/web page contains the solutions to many (but not all) of the problems that are given at the end

of each chapter, in particular for problems on topics that are commonly covered in a first (or, at least, second)

graduate course on radiative heat transfer. Thus, solutions to problems of Chapters 1 through 6, 9 through

11, 13, 14 and 18 are almost complete; for other chapters (7, 15, 16, 19) only around half of solutions are

given, for problems on the more basic aspects covered in that chapter. Quite a few solutions, together with

Fortran90 codes, are also given for Chapter 20, not so much intended as homework solutions, but perhaps

useful for semester projects and/or to aid the researcher to write his/her first Monte Carlo code. At this date

no problem solutions are provided for the remaining chapters. However, it is the intent to periodically update

this web-based solution manual, at which time additional solutions may be posted.

Most solutions have been checked, and some have been rechecked. Still, only a major miracle could have

prevented me from making an occasional error or overlooking an occasional typo. I would appreciate it very

much if any such errors in the manual (or, for that matter, in the text) would be reported to me. In addition,

for the benefit of other instructors who will receive future editions of this manual, any reasonably written up

solutions to presently unsolved problems would also be appreciated.

This manual is posted as a pdf-file with hyperreferences enabled, including a Table of Contents and a

Bookmark column listing all chapters and problems. This enables the reader to immediately jump back and

forth within the document to locally referenced items (chapters, problems, figures, equations). References to

equations, figures, etc., in the book itself can, of course, not be reached in this way. Users of Adobe Acrobatrcan

easily assemble individual problem set solutions from this manual. To make this also possible for instructors

with access to only the shareware postscript/pdf viewer Ghostview c

, each individual problem is started at the

top of a new page.

State College, PA

December 2002

Michael F. Modest

Department of Mechanical Engineering

The Pennsylvania State University

University Park, PA 16802

e-mail: mfm6@psu.edu

CONTENTS

Chapter 1 2

Problem 1.1 ……………………………………………. 2

Problem 1.2 ……………………………………………. 3

Problem 1.3 ……………………………………………. 4

Problem 1.4 ……………………………………………. 5

Problem 1.5 ……………………………………………. 6

Problem 1.6 ……………………………………………. 7

Problem 1.7 ……………………………………………. 8

Problem 1.8 ……………………………………………. 9

Problem 1.9 ……………………………………………. 10

Problem 1.10 …………………………………………… 11

Problem 1.11 …………………………………………… 12

Problem 1.12 …………………………………………… 13

Problem 1.13 …………………………………………… 15

Problem 1.14 …………………………………………… 16

Problem 1.15 …………………………………………… 17

Chapter 2 19

Problem 2.1 ……………………………………………. 19

Problem 2.2 ……………………………………………. 20

Problem 2.3 ……………………………………………. 22

Problem 2.4 ……………………………………………. 23

Problem 2.5 ……………………………………………. 24

Problem 2.6 ……………………………………………. 25

Chapter 3 27

Problem 3.1 ……………………………………………. 27

Problem 3.2 ……………………………………………. 28

Problem 3.3 ……………………………………………. 29

Problem 3.4 ……………………………………………. 30

Problem 3.5 ……………………………………………. 31

Problem 3.6 ……………………………………………. 33

Problem 3.7 ……………………………………………. 34

Problem 3.8 ……………………………………………. 35

Problem 3.9 ……………………………………………. 36

Problem 3.10 …………………………………………… 37

Problem 3.11 …………………………………………… 38

Problem 3.12 …………………………………………… 39

Problem 3.13 …………………………………………… 40

Problem 3.14 …………………………………………… 41

Problem 3.15 …………………………………………… 42

Problem 3.16 …………………………………………… 43

Problem 3.17 …………………………………………… 44

Problem 3.18 …………………………………………… 45

Problem 3.19 …………………………………………… 46

CONTENTS iii

Problem 3.20 …………………………………………… 47

Problem 3.21 …………………………………………… 48

Problem 3.22 …………………………………………… 49

Problem 3.23 …………………………………………… 50

Problem 3.24 …………………………………………… 52

Problem 3.25 …………………………………………… 53

Problem 3.26 …………………………………………… 54

Problem 3.27 …………………………………………… 55

Problem 3.28 …………………………………………… 56

Problem 3.29 …………………………………………… 57

Problem 3.30 …………………………………………… 58

Problem 3.31 …………………………………………… 59

Problem 3.32 …………………………………………… 60

Problem 3.33 …………………………………………… 61

Problem 3.34 …………………………………………… 62

Problem 3.35 …………………………………………… 63

Problem 3.36 …………………………………………… 65

Chapter 4 66

Problem 4.1 ……………………………………………. 66

Problem 4.2 ……………………………………………. 68

Problem 4.3 ……………………………………………. 69

Problem 4.4 ……………………………………………. 70

Problem 4.5 ……………………………………………. 72

Problem 4.6 ……………………………………………. 73

Problem 4.7 ……………………………………………. 74

Problem 4.8 ……………………………………………. 75

Problem 4.9 ……………………………………………. 76

Problem 4.10 …………………………………………… 77

Problem 4.11 …………………………………………… 78

Problem 4.12 …………………………………………… 79

Problem 4.13 …………………………………………… 80

Problem 4.14 …………………………………………… 81

Problem 4.15 …………………………………………… 82

Problem 4.16 …………………………………………… 83

Problem 4.17 …………………………………………… 84

Problem 4.18 …………………………………………… 85

Problem 4.19 …………………………………………… 87

Problem 4.20 …………………………………………… 88

Problem 4.21 …………………………………………… 89

Problem 4.22 …………………………………………… 90

Problem 4.23 …………………………………………… 92

Problem 4.24 …………………………………………… 93

Problem 4.25 …………………………………………… 94

Problem 4.26 …………………………………………… 96

Chapter 5 100

Problem 5.1 ……………………………………………. 100

Problem 5.2 ……………………………………………. 101

Problem 5.3 ……………………………………………. 103

Problem 5.4 ……………………………………………. 105

Problem 5.5 ……………………………………………. 106

Problem 5.6 ……………………………………………. 107

Problem 5.7 ……………………………………………. 108

Problem 5.9 ……………………………………………. 110

Problem 5.10 …………………………………………… 112

Problem 5.11 …………………………………………… 113

Problem 5.12 …………………………………………… 114

Problem 5.13 …………………………………………… 115

Problem 5.14 …………………………………………… 118

Problem 5.15 …………………………………………… 120

Problem 5.16 …………………………………………… 122

Problem 5.17 …………………………………………… 124

Problem 5.18 …………………………………………… 125

Problem 5.19 …………………………………………… 126

Problem 5.20 …………………………………………… 127

Problem 5.21 …………………………………………… 129

Problem 5.22 …………………………………………… 130

Problem 5.23 …………………………………………… 131

Problem 5.24 …………………………………………… 132

Problem 5.25 …………………………………………… 134

Problem 5.26 …………………………………………… 135

Problem 5.27 …………………………………………… 136

Problem 5.28 …………………………………………… 137

Problem 5.29 …………………………………………… 139

Problem 5.30 …………………………………………… 141

Problem 5.31 …………………………………………… 143

Problem 5.32 …………………………………………… 146

Problem 5.33 …………………………………………… 154

Problem 5.34 …………………………………………… 155

Problem 5.35 …………………………………………… 159

Problem 5.36 …………………………………………… 160

Problem 5.37 …………………………………………… 161

Problem 5.38 …………………………………………… 164

Problem 5.39 …………………………………………… 165

Problem 5.40 …………………………………………… 166

Chapter 6 168

Problem 6.1 ……………………………………………. 168

Problem 6.2 ……………………………………………. 169

Problem 6.3 ……………………………………………. 170

Problem 6.4 ……………………………………………. 172

Problem 6.5 ……………………………………………. 174

Problem 6.6 ……………………………………………. 176

Problem 6.7 ……………………………………………. 178

Problem 6.8 ……………………………………………. 179

Problem 6.9 ……………………………………………. 180

Problem 6.10 …………………………………………… 182

Problem 6.11 …………………………………………… 183

Problem 6.12 …………………………………………… 184

Problem 6.13 …………………………………………… 185

Problem 6.14 …………………………………………… 187

Problem 6.15 …………………………………………… 188

Problem 6.16 …………………………………………… 189

Problem 6.17 …………………………………………… 191

Problem 6.18 …………………………………………… 192

Problem 6.19 …………………………………………… 193

Problem 6.21 …………………………………………… 195

Problem 6.22 …………………………………………… 198

CONTENTS v

Problem 6.24 …………………………………………… 200

Problem 6.26 …………………………………………… 202

Problem 6.27 …………………………………………… 203

Problem 6.29 …………………………………………… 205

Problem 6.30 …………………………………………… 208

Problem 6.31 …………………………………………… 210

Problem 6.34 …………………………………………… 212

Problem 6.35 …………………………………………… 213

Chapter 7 214

Problem 7.1 ……………………………………………. 214

Problem 7.2 ……………………………………………. 216

Problem 7.5 ……………………………………………. 218

Problem 7.6 ……………………………………………. 219

Problem 7.8 ……………………………………………. 221

Problem 7.10 …………………………………………… 224

Problem 7.11 …………………………………………… 225

Problem 7.13 …………………………………………… 227

Problem 7.14 …………………………………………… 232

Problem 7.15 …………………………………………… 234

Problem 7.16 …………………………………………… 237

Chapter 8 241

Problem 8.1 ……………………………………………. 241

Problem 8.2 ……………………………………………. 242

Problem 8.3 ……………………………………………. 243

Problem 8.4 ……………………………………………. 245

Problem 8.5 ……………………………………………. 246

Problem 8.6 ……………………………………………. 247

Problem 8.7 ……………………………………………. 248

Problem 8.8 ……………………………………………. 249

Problem 8.9 ……………………………………………. 251

Problem 8.10 …………………………………………… 254

Problem 8.14 …………………………………………… 255

Problem 8.15 …………………………………………… 260

Chapter 9 265

Problem 9.1 ……………………………………………. 265

Chapter 10 267

Problem 10.1 …………………………………………… 267

Problem 10.2 …………………………………………… 269

Problem 10.3 …………………………………………… 270

Problem 10.4 …………………………………………… 272

Problem 10.5 …………………………………………… 273

Problem 10.6 …………………………………………… 275

Problem 10.7 …………………………………………… 276

Problem 10.8 …………………………………………… 278

Problem 10.9 …………………………………………… 279

Problem 10.10 …………………………………………… 280

Problem 10.11 …………………………………………… 281

Problem 10.12 …………………………………………… 283

Problem 10.13 …………………………………………… 285

Problem 10.14 …………………………………………… 287

Problem 10.15 …………………………………………… 288

vi CONTENTS

Chapter 11 289

Problem 11.1 …………………………………………… 289

Problem 11.2 …………………………………………… 290

Problem 11.3 …………………………………………… 291

Problem 11.4 …………………………………………… 292

Problem 11.5 …………………………………………… 293

Problem 11.6 …………………………………………… 294

Problem 11.7 …………………………………………… 295

Problem 11.8 …………………………………………… 296

Problem 11.9 …………………………………………… 297

Problem 11.10 …………………………………………… 298

Problem 11.11 …………………………………………… 299

Problem 11.12 …………………………………………… 300

Problem 11.13 …………………………………………… 301

Problem 11.14 …………………………………………… 302

Problem 11.15 …………………………………………… 303

Problem 11.16 …………………………………………… 304

Problem 11.17 …………………………………………… 305

Problem 11.18 …………………………………………… 306

Problem 11.19 …………………………………………… 307

Problem 11.20 …………………………………………… 309

Problem 11.21 …………………………………………… 310

Problem 11.22 …………………………………………… 311

Problem 11.23 …………………………………………… 313

Problem 11.24 …………………………………………… 314

Problem 11.25 …………………………………………… 316

Problem 11.26 …………………………………………… 317

Problem 11.27 …………………………………………… 318

Problem 11.28 …………………………………………… 319

Problem 11.29 …………………………………………… 320

Problem 11.30 …………………………………………… 321

Problem 11.31 …………………………………………… 323

Problem 11.32 …………………………………………… 324

Problem 11.33 …………………………………………… 325

Problem 11.34 …………………………………………… 327

Problem 11.35 …………………………………………… 328

Problem 11.37 …………………………………………… 329

Problem 11.38 …………………………………………… 330

Problem 11.39 …………………………………………… 331

Problem 11.40 …………………………………………… 332

Problem 11.41 …………………………………………… 334

Problem 11.42 …………………………………………… 337

Chapter 12 339

Problem 12.1 …………………………………………… 339

Problem 12.2 …………………………………………… 340

Problem 12.3 …………………………………………… 341

Problem 12.4 …………………………………………… 342

Problem 12.5 …………………………………………… 343

Problem 12.6 …………………………………………… 344

Problem 12.7 …………………………………………… 345

Problem 12.8 …………………………………………… 346

Problem 12.9 …………………………………………… 347

Problem 12.10 …………………………………………… 348

Problem 12.11 …………………………………………… 349

CONTENTS vii

Problem 12.13 …………………………………………… 350

Problem 12.14 …………………………………………… 351

Problem 12.15 …………………………………………… 352

Problem 12.16 …………………………………………… 353

Problem 12.17 …………………………………………… 354

Problem 12.18 …………………………………………… 355

Problem 12.19 …………………………………………… 356

Problem 12.20 …………………………………………… 358

Problem 12.21 …………………………………………… 359

Chapter 14 360

Problem 14.1 …………………………………………… 360

Problem 14.2 …………………………………………… 361

Problem 14.3 …………………………………………… 362

Problem 14.4 …………………………………………… 364

Problem 14.5 …………………………………………… 366

Problem 14.6 …………………………………………… 367

Problem 14.7 …………………………………………… 368

Problem 14.8 …………………………………………… 369

Problem 14.9 …………………………………………… 370

Problem 14.10 …………………………………………… 371

Problem 14.11 …………………………………………… 372

Problem 14.12 …………………………………………… 373

Problem 14.13 …………………………………………… 374

Problem 14.14 …………………………………………… 376

Chapter 15 377

Problem 15.1 …………………………………………… 377

Problem 15.2 …………………………………………… 378

Problem 15.3 …………………………………………… 379

Problem 15.4 …………………………………………… 380

Problem 15.5 …………………………………………… 382

Problem 15.6 …………………………………………… 383

Problem 15.7 …………………………………………… 384

Problem 15.8 …………………………………………… 386

Problem 15.9 …………………………………………… 387

Problem 15.10 …………………………………………… 388

Problem 15.11 …………………………………………… 390

Problem 15.12 …………………………………………… 392

Problem 15.13 …………………………………………… 394

Problem 15.14 …………………………………………… 396

Problem 15.15 …………………………………………… 397

Problem 15.16 …………………………………………… 399

Problem 15.18 …………………………………………… 401

Problem 15.19 …………………………………………… 403

Chapter 16 405

Problem 16.1 …………………………………………… 405

Problem 16.2 …………………………………………… 406

Problem 16.3 …………………………………………… 407

Problem 16.4 …………………………………………… 408

Problem 16.5 …………………………………………… 410

Problem 16.6 …………………………………………… 412

Problem 16.7 …………………………………………… 413

Problem 16.9 …………………………………………… 417

Problem 16.10 …………………………………………… 419

Problem 16.11 …………………………………………… 420

Problem 16.12 …………………………………………… 421

Problem 16.13 …………………………………………… 423

Problem 16.14 …………………………………………… 424

Problem 16.15 …………………………………………… 426

Problem 16.18 …………………………………………… 428

Chapter 17 429

Problem 17.1 …………………………………………… 429

Problem 17.2 …………………………………………… 430

Problem 17.3 …………………………………………… 431

Problem 17.4 …………………………………………… 432

Problem 17.5 …………………………………………… 434

Problem 17.6 …………………………………………… 436

Problem 17.7 …………………………………………… 438

Problem 17.8 …………………………………………… 439

Problem 17.9 …………………………………………… 441

Problem 17.10 …………………………………………… 443

Chapter 19 445

Problem 19.1 …………………………………………… 445

Problem 19.2 …………………………………………… 447

Problem 19.3 …………………………………………… 448

Problem 19.4 …………………………………………… 449

Problem 19.5 …………………………………………… 450

Problem 19.6 …………………………………………… 451

Problem 19.7 …………………………………………… 452

Chapter 20 454

Problem 20.1 …………………………………………… 454

Problem 20.2 …………………………………………… 455

Problem 20.3 …………………………………………… 456

Problem 20.4 …………………………………………… 457

Problem 20.5 …………………………………………… 459

Problem 20.7 …………………………………………… 464

Problem 20.8 …………………………………………… 466

Problem 20.9 …………………………………………… 468

Problem 20.10 …………………………………………… 469

Problem 20.11 …………………………………………… 470

Problem 20.15 …………………………………………… 472

Problem 20.20 …………………………………………… 474

Chapter 21 477

Problem 21.1 …………………………………………… 477

Problem 21.8 …………………………………………… 479

CHAPTER 1

1.1 Solar energy impinging on the outer layer of earth’s atmosphere (usually called “solar constant”) has been

measured as 1367 W/m2. What is the solar constant on Mars? (Distance earth to sun =1.496 ×1011 m, Mars

to sun =2.28 ×1011 m).

Solution

The total energy emitted from the sun Q=4πR2

SσT4

sun goes equally into all directions, so that

1.2 Assuming earth to be a blackbody, what would be its average temperature if there was no internal heating

from the core of earth?

1.3 Assuming earth to be a black sphere with a surface temperature of 300 K, what must earth’s internal heat

generation be in order to maintain that temperature (neglect radiation from the stars, but not the sun) (radius

of the earth RE=6.37 ×106m).

1.4 To estimate the diameter of the sun, one may use solar radiation data. The solar energy impinging onto the

earth’s atmosphere (called the “solar constant”) has been measured as 1367 W/m2. Assuming that the sun

may be approximated to have a black surface with an eﬀective temperature of 5777 K, estimate the diameter

of the sun (distance sun to earth SES ≃1.496 ×1011 m).

=1.496 ×1011 m 1367 W/m2

RS=6.96 ×108m

6RADIATIVE HEAT TRANSFER

1.5 Solar energy impinging on the outer layer of earth’s atmosphere (usually called “solar constant”) has been

measured as 1367 W/m2. Assuming the sun may be approximated as having a surface that behaves like a

blackbody, estimate its eﬀective surface temperature. (Distance sun to earth SES ≃1.496 ×1011 m, radius of

sun RS≃6.96 ×108m).

Tsun =5777 K