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AnInstructor’sSolutionsManualtoAccompany

PRINCIPLESOFHEATTRANSFER,7THEDITION,SI FRANKKREITH RAJM.MANGLIK MARKS.BOHN SIEDITIONPREPAREDBY:SHALIGRAMTIWARI

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INSTRUCTOR'SSOLUTIONSMANUALTO ACCOMPANY

PRINCIPLESOF

HEATTRANSFER  

SEVENTHEDITION,SI    

FRANKKREITH RAJM.MANGLIK MARKS.BOHN SIEDITIONPREPAREDBY: SHALIGRAMTIWARI IndianInstituteofTechnologyMadras

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TABLEOFCONTENTS   

 

                  

CHAPTER

PAGE

1..............................................................................................................1 2............................................................................................................85 3..........................................................................................................231 4..........................................................................................................311 5..........................................................................................................421 6..........................................................................................................513 7..........................................................................................................607 8..........................................................................................................683 9..........................................................................................................781 10.........................................................................................................871

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CONTENTS Chapter 1 Basic Modes of Heat Transfer 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8

The Relation of Heat Transfer to Thermodynamics 3 Dimensions and Units 7 Heat Conduction 9 Convection 17 Radiation 21 Combined Heat Transfer Systems 23 Thermal Insulation 45 Heat Transfer and the Law of Energy Conservation 51 References 58 Problems 58 Design Problems 68

Chapter 2 Heat Conduction 2.1 2.2 2.3 2.4 2.5* 2.6 2.7* 2.8

2

70

Introduction 71 The Conduction Equation 71 Steady Heat Conduction in Simple Geometries Extended Surfaces 95 Multidimensional Steady Conduction 105 Unsteady or Transient Heat Conduction 116 Charts for Transient Heat Conduction 134 Closing Remarks 150 References 150 Problems 151 Design Problems 163

78

Chapter 3 Numerical Analysis of Heat Conduction 3.1 3.2 3.3

166

Introduction 167 One-Dimensional Steady Conduction 168 One-Dimensional Unsteady Conduction 180

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Two-Dimensional Steady and Unsteady Conduction 195 Cylindrical Coordinates 215 Irregular Boundaries 217 Closing Remarks 221 References 221 Problems 222 Design Problems 228

Chapter 4 Analysis of Convection Heat Transfer 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8* 4.9* 4.10* 4.11 4.12 4.13* 4.14

Introduction 231 Convection Heat Transfer 231 Boundary Layer Fundamentals 233 Conservation Equations of Mass, Momentum, and Energy for Laminar Flow Over a Flat Plate 235 Dimensionless Boundary Layer Equations and Similarity Parameters 239 Evaluation of Convection Heat Transfer Coefficients 243 Dimensional Analysis 245 Analytic Solution for Laminar Boundary Layer Flow Over a Flat Plate 252 Approximate Integral Boundary Layer Analysis 261 Analogy Between Momentum and Heat Transfer in Turbulent Flow Over a Flat Surface 267 Reynolds Analogy for Turbulent Flow Over Plane Surfaces 273 Mixed Boundary Layer 274 Special Boundary Conditions and High-Speed Flow 277 Closing Remarks 282 References 283 Problems 284 Design Problems 294

Chapter 5 Natural Convection 5.1 5.2 5.3 5.4* 5.5 5.6*

230

296

Introduction 297 Similarity Parameters for Natural Convection 299 Empirical Correlation for Various Shapes 308 Rotating Cylinders, Disks, and Spheres 322 Combined Forced and Natural Convection 325 Finned Surfaces 328

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Full file at https://buklibry.com/download/solutions-manual-principles-of-heat-transfer-7th-edition-by-kreith-manglikContents xi 5.7

Closing Remarks 333 References 338 Problems 340 Design Problems 348

Chapter 6 Forced Convection Inside Tubes and Ducts 6.1 6.2* 6.3 6.4* 6.5 6.6 6.7

Introduction 351 Analysis of Laminar Forced Convection in a Long Tube 360 Correlations for Laminar Forced Convection 370 Analogy Between Heat and Momentum Transfer in Turbulent Flow 382 Empirical Correlations for Turbulent Forced Convection 386 Heat Transfer Enhancement and Electronic-Device Cooling 395 Closing Remarks 406 References 408 Problems 411 Design Problems 418

Chapter 7 Forced Convection Over Exterior Surfaces 7.1 7.2 7.3* 7.4 7.5* 7.6* 7.7

Flow Over Bluff Bodies 421 Cylinders, Spheres, and Other Bluff Shapes Packed Beds 440 Tube Bundles in Cross-Flow 444 Finned Tube Bundles in Cross-Flow 458 Free Jets 461 Closing Remarks 471 References 473 Problems 475 Design Problems 482

Chapter 8 Heat Exchangers 8.1 8.2 8.3 8.4 8.5 8.6* 8.7*

350

420

422

484

Introduction 485 Basic Types of Heat Exchangers 485 Overall Heat Transfer Coefficient 494 Log Mean Temperature Difference 498 Heat Exchanger Effectiveness 506 Heat Transfer Enhancement 516 Microscale Heat Exchangers 524

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Closing Remarks 525 References 527 Problems 529 Design Problems 539

Chapter 9 Heat Transfer by Radiation 9.1 9.2 9.3 9.4 9.5 9.6 9.7* 9.8* 9.9 9.10

540

Thermal Radiation 541 Blackbody Radiation 543 Radiation Properties 555 The Radiation Shape Factor 571 Enclosures with Black Surfaces 581 Enclosures with Gray Surfaces 585 Matrix Inversion 591 Radiation Properties of Gases and Vapors 602 Radiation Combined with Convection and Conduction 610 Closing Remarks 614 References 615 Problems 616 Design Problems 623

Chapter 10 Heat Transfer with Phase Change 10.1 10.2 10.3 10.4 10.5* 10.6* 10.7*

624

Introduction to Boiling 625 Pool Boiling 625 Boiling in Forced Convection 647 Condensation 660 Condenser Design 670 Heat Pipes 672 Freezing and Melting 683 References 688 Problems 691 Design Problems 696

Appendix 1 The International System of Units Appendix 2 Data Tables

A3

A6

Properties of Solids A7 Thermodynamic Properties of Liquids A14 Heat Transfer Fluids A23

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Chapter 1 PROBLEM 1.1 The outer surface of a 0.2m-thick concrete wall is kept at a temperature of –5°C, while the inner surface is kept at 20°C. The thermal conductivity of the concrete is 1.2 W/(m K). Determine the heat loss through a wall 10 m long and 3 m high. GIVEN 10 m long, 3 m high, and 0.2 m thick concrete wall Thermal conductivity of the concrete (k) = 1.2 W/(m K) Temperature of the inner surface (Ti) = 20°C Temperature of the outer surface (To) = –5°C FIND The heat loss through the wall (qk) ASSUMPTIONS One dimensional heat flow The system has reached steady state SKETCH L = 0.2 m

L

=

10

m H=3m

qk Ti = 20°C To = – 5°C

SOLUTION The rate of heat loss through the wall is given by Equation (1.2) qk = qk =

AK L

(ΔT)

(10m)(3m) ( 1.2 W/(m K)) (20°C – (–5°C)) 0.2 m

qk = 4500 W COMMENTS Since the inside surface temperature is higher than the outside temperature heat is transferred from the inside of the wall to the outside of the wall.

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PROBLEM 2.5 A solution with a boiling point of 82°C boils on the outside of a 2.5 cm tube with a No. 14 BWG gauge wall. On the inside of the tube flows saturated steam at 4.2 bar (abs). The convective heat transfer coefficients are 8500 W/(m2 K) on the steam side and 6200 W/(m2 K) on the exterior surface. Calculate the increase in the rate of heat transfer for a copper over a steel tube. GIVEN • • • •

Tube with saturated steam on the inside and solution boiling at 82°C outside Tube specification: 2.5 cm No. 14 BWG gauge wall Saturated steam in the pipe is at 4.2 bar Convective heat transfer coefficients Steam side ( h ci ) : 8500 W/(m2 K) 

Exterior surface ( hco ) : 6200 W/(m2 K)

FIND •

The increase in the rate of heat transfer for a copper over a steel tube

ASSUMPTIONS • •

The system is in steady state Constant thermal conductivities

SKETCH

Twi Two

Steam Ts

T• = 82° C

PROPERTIES AND CONSTANTS From Appendix 2, Tables 10, 12, 13 and 42 • Temperature of saturated steam at 4.2 bar (Ts) = 144°C •

Thermal conductivities

•

 1% Carbon steel (ks) = 43 W/(m K) at 20°C Tube inside diameter (Di) = 0.834 in.



Copper (kc) = 390 W/(m K) at 127°C

SOLUTION The thermal circuit for the tube is shown below Ts

Twi Rci

T•

Two RK

Rco

The individual resistances are Rci =

0.0018 1 1 1 1 K/W = = = 2 –2 L hci Ai hci π Di L L (8500 W/(m K))π (2.08 × 10 m)

Rco =

0.00205 1 1 1 1 = K/W = = 2 –2 L hco Ao hco π Di L L (6200 W/(m K)) π (2.5 × 10 m) 92

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The temperature-time history of the water is

(

1

− 4.71 × 10 −4 − 3.28 × 10 −5 s Tw − T∞ = e To − T∞ − 4.38 ×10 −4

)

t

−

− 3.28 × 10 −5 − 4.38 × 10

−4

(

e

− 4.71 × 10 −4

1

s

)

t

For the water to cool to 16°C 16° C − 0° C = 0.1720 = 1.075 E 93 °C − 0 °C

(

− 3.28 × 10 −5

)

1 t s

(

− 4.71 × 10 −4

– 0.075 E

)

1 t s

By trial and error: t = 55,870 s = 15.5 hours (b) The energy balance for the fluid is given by Equation (2.86a) dTw = h i Ai (Tw – Ts) dt Differentiating the temperature-time history

– (c ρ V)w

m − m 2 m 1t m m m m dTw = (T0 – T∞)  1 2 e m 1t − 1 2 em 1t  = (T0 – T∞) 1 ( e − em 2t ) − − dt m m m m m m −  2  2 1 1 2 1

Substituting this into the energy balance for the fluid – (c ρ V)w (T0 – T∞)

T0 = Tw +

T s = 16°C +

m1 m2 ( em1 t − em 2 t ) = hci Ai (Tw – Ts) m 2 − m1

m1 m2 (cm) w ( em1 t − em 2 t ) (T0 – T∞) m 2 − m1 h ci Ai

− 3.28 × 10 −5(1/s) (− 4.71 × 10 −4 (1/s) ) [4187J/(kg K)](45 kg) (93°C – 0°C) 2 2 − 4.38 × 10−4 (1/s) [17 W/(m K)] π (0.44 m)

× ( e −3.28 × 10

−5

(1/s) (55870a)

−e

−4.71 × 10−4 (1/s) (55870a)

)

Ts = 6.4 s PROBLEM 2.64 A copper wire, 0.8 – mm – OD, 5 cm long, is placed in an air stream whose temperature rises at Tair = (10 + 14 t )°C where t is the time in seconds. If the initial temperature of the wire is 10°C, determine its temperature after 2 s, 10 s and 1 min. The heat transfer coefficient between the air and the wire is 40 W(m2 K). GIVEN • • • • •

A copper wire is placed in an air stream Wire diameter (D) = 0.8 mm = 8 × 10–3 m Wire length (L) = 5 cm = 5 × 10–2 m Air stream temperature is: Tair = (10 + 14 t)°C The initial temperature of the wire (To) = 10°C

•

The heat transfer coefficient (h c ) = 40 W/(m2 K)

FIND •

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The equations were solved using Δt = 10 seconds. A check was performed by hand on each of the seven unique control volume energy balances. The maximum temperature occurs at i = 6, j = 1, and the minimum temperature occurs at i = 1, j = 3. The resulting temperature as a function of time is given below. 400 350

Temperature (°C)

300 250 200 150 100 50 0

0

500

1000

1500

2000

2500

3000

3500

4000

Time (s)

PROBLEM 3.46 A steel billet is to be heat treated by immersion in a molten salt bath. The billet is 5 cm square and 1 m long. Prior to immersion in the bath, the billet is at a uniform temperature of 20°C. The bath is at 600°C and the heat transfer coefficient at the billet surface is 20 W/(m2K). Plot the temperature at the center of the billet as a function of time. How much time is nee...