Analysis The characteristic length of the junction and the Biot number are

Similar documents
Chapter 3, Solution 1C.

Transient Conduction: Spatial Effects and the Role of Analytical Solutions

Conduction Heat Transfer

Department of Civil Engineering & Applied Mechanics McGill University, Montreal, Quebec Canada

CIRCLE YOUR DIVISION: Div. 1 (9:30 am) Div. 2 (11:30 am) Div. 3 (2:30 pm) Prof. Ruan Prof. Naik Mr. Singh

Module 7: Solved Problems

Natural Circulation Systems

3-42. Chapter 15 Steady Heat Conduction. Heat Conduction in Cylinders and Spheres

Chapter 6 : Gibbs Free Energy

Heat exchanger. Heat exchanger

Diodes Waveform shaping Circuits. Sedra & Smith (6 th Ed): Sec. 4.5 & 4.6 Sedra & Smith (5 th Ed): Sec. 3.5 & 3.6

Diodes Waveform shaping Circuits

Thermal-Fluids I. Chapter 18 Transient heat conduction. Dr. Primal Fernando Ph: (850)

Section 3: Detailed Solutions of Word Problems Unit 1: Solving Word Problems by Modeling with Formulas

Physic 231 Lecture 33

Chem 116 POGIL Worksheet - Week 8 Equilibrium Continued - Solutions

Lecture 12. Heat Exchangers. Heat Exchangers Chee 318 1

V. Electrostatics Lecture 27a: Diffuse charge at electrodes

PHY2053 Summer 2012 Exam 2 Solutions N F o f k

WYSE Academic Challenge 2014 Sectional Physics Exam SOLUTION SET. [ F][ d] [ t] [ E]

Module B3. VLoad = = V S V LN

Final Exam Spring 2014 SOLUTION

Lucas Imperfect Information Model

Heat is energy and is measured in joules (J) or kilojoules (kj). The symbol for heat is H.

_J _J J J J J J J J _. 7 particles in the blue state; 3 particles in the red state: 720 configurations _J J J _J J J J J J J J _

Physics 107 HOMEWORK ASSIGNMENT #20

Transfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system

element k Using FEM to Solve Truss Problems

9.5 Complex variables

Faculty of Engineering

Chapter 7. Systems 7.1 INTRODUCTION 7.2 MATHEMATICAL MODELING OF LIQUID LEVEL SYSTEMS. Steady State Flow. A. Bazoune

55:041 Electronic Circuits

Week 9 Chapter 10 Section 1-5

= 1.23 m/s 2 [W] Required: t. Solution:!t = = 17 m/s [W]! m/s [W] (two extra digits carried) = 2.1 m/s [W]

Numerical Transient Heat Conduction Experiment

Physics 2A Chapter 3 HW Solutions

Close!Reading!and!Text!Dependent!Questions!in!Science! Lunar!Rover!Making!Tracks!on!the!Moon!(Motion!and!Design!!Grade!4)!

PHYSICS 212 MIDTERM II 19 February 2003

Chem 204A, Fall 2004, Mid-term (II)

Chemical Engineering Department University of Washington

Analytical Modeling of Natural Convection in Horizontal Annuli

A/2 l,k. Problem 1 STRATEGY. KNOWN Resistance of a complete spherical shell: r rk. Inner and outer radii

Spring 2002 Lecture #13

PHYS 1101 Practice problem set 12, Chapter 32: 21, 22, 24, 57, 61, 83 Chapter 33: 7, 12, 32, 38, 44, 49, 76

IGEE 401 Power Electronic Systems. Solution to Midterm Examination Fall 2004

Relativistic Langevin and Fokker-Planck equations

SUPPLEMENTARY INFORMATION

MATH 5630: Discrete Time-Space Model Hung Phan, UMass Lowell March 1, 2018

Dynamic simulation of multi-effect falling-film evaporator: Milk powder production plant

Principles of Food and Bioprocess Engineering (FS 231) Solutions to Example Problems on Heat Transfer

Exercises H /OOA> f Wo AJoTHS l^»-l S. m^ttrt /A/ ?C,0&L6M5 INFERENCE FOR DISTRIBUTIONS OF CATEGORICAL DATA. tts^e&n tai-ns 5 2%-cas-hews^, 27%

Design of Analog Integrated Circuits

Homework for Diffraction-MSE 603: Solutions May 2002

Electric potential energy Electrostatic force does work on a particle : Potential energy (: i initial state f : final state):

Example

Section 8.3 Polar Form of Complex Numbers

Section 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law

EE 204 Lecture 25 More Examples on Power Factor and the Reactive Power

Lecture 2. Basic Semiconductor Physics

CHAPTER 14 GENERAL PERTURBATION THEORY

GEL 446: Applied Environmental Geology

Chapter 3. r r. Position, Velocity, and Acceleration Revisited

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1

Differentiation Applications 1: Related Rates

Problem 1 Known: Dimensions and materials of the composition wall, 10 studs each with 2.5m high

ENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15

( ) = ( ) + ( 0) ) ( )

Exercise 10: Theory of mass transfer coefficient at boundary

GAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME PHYSICAL SCIENCES GRADE 12 SESSION 1 (LEARNER NOTES)

Spring 2002 Lecture #17

Week3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity

Section 8.1 Exercises

Four Bar Linkages in Two Dimensions. A link has fixed length and is joined to other links and also possibly to a fixed point.

e a = 12.4 i a = 13.5i h a = xi + yj 3 a Let r a = 25cos(20) i + 25sin(20) j b = 15cos(55) i + 15sin(55) j

Approach: (Equilibrium) TD analysis, i.e., conservation eqns., state equations Issues: how to deal with

Chapter 4: Transient Heat Conduction. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University

Multicommodity Distribution System Design

Part 3 Introduction to statistical classification techniques

Q x = cos 1 30 = 53.1 South

6.3.7 Example with Runga Kutta 4 th order method

University of Southern California School Of Engineering Department Of Electrical Engineering

1 Derivation of Point-to-Plane Minimization

1. Adsorption Separation of Immunoglobulin G using Modified Dextran (adapted from Belter, Cussler, & Hu, pg 153).

Materials o o o o o o o o o

t } = Number of calls in progress at time t. Engsett Model (Erlang-B)

ANALOG ELECTRONICS 1 DR NORLAILI MOHD NOH

Math1110 (Spring 2009) Prelim 3 - Solutions

Wp/Lmin. Wn/Lmin 2.5V

A New Method for Solving Integer Linear. Programming Problems with Fuzzy Variables

n α j x j = 0 j=1 has a nontrivial solution. Here A is the n k matrix whose jth column is the vector for all t j=0

The University of Iowa Dept. of Civil & Environmental Engineering 53:030 SOIL MECHANICS Midterm Exam #2, Fall Semester 2005

MAGNETISM MAGNETIC DIPOLES

Effects of high RH on α-pinene SOA phase partitioning

Exploiting vector space properties for the global optimization of process networks

Solution to HW14 Fall-2002

Use a lens holder fabricated from SiC. SiC has a larger CTE than C-C, i.e. it is better matched to the SFL6.

Managing Capacity Through Reward Programs. on-line companion page. Byung-Do Kim Seoul National University College of Business Administration

MECHANICS OF SOLIDS TORSION TUTORIAL 2 TORSION OF THIN WALLED SECTIONS AND THIN STRIPS

PHYS 1441 Section 001 Lecture #15 Wednesday, July 8, 2015

ECE 6340 Intermediate EM Waves. Fall Prof. David R. Jackson Dept. of ECE. Notes 3

Transcription:

-4 4 The temerature f a gas stream s t be measured by a thermule. The tme t taes t regster 99 erent f the ntal ΔT s t be determned. Assumtns The juntn s sheral n shae wth a dameter f D 0.00 m. The thermal rertes f the juntn are nstant. The heat transfer effent s nstant and unfrm ver the entre surfae. 4 Radatn effets are neglgble. 5 The Bt number s B < 0. s that the lumed system analyss s alable (ths assumtn wll be verfed. Prertes The rertes f the juntn are gven t be 5 W/m. C, ρ 8500 g/m, and 0 J/g. C. Analyss The haraterst length f the juntn and the Bt number are V πd / 6 D 0.00 m 0.000 m A surfae πd 6 6 h (90 W/m. C(0.000 m B 0.0005< 0. (5 W/m. C Sne B < 0., the lumed system analyss s alable. Then the tme erd fr the thermule t read 99% f the ntal temerature dfferene s determned frm T 0.0 ha h b ρ V ρ (8500 g/m Gas 90 W/m. C 0.654 s (0 J/g. C(0.000 m h, T Juntn D T(t T e 0.0 e (0.654 s t t 7.8 s PROPRIETARY MATERIA. 008 The MGraw-Hll Cmanes, In. mted dstrbutn ermtted nly t teahers and eduatrs fr urse rearatn. If yu are a student usng ths Manual, yu are usng t wthut ermssn.

-9-0 The heatng tmes f a shere, a ube, and a retangular rsm wth smlar dmensns are t be determned. Assumtns The thermal rertes f the gemetres are nstant. The heat transfer effent s nstant and unfrm ver the entre surfae. Prertes The rertes f slver are gven t be 49 W/m ºC, ρ 0,500 g/m, and 0.5 J/g ºC. Analyss Fr shere, the haraterst length and the Bt number are V πd / 6 D 0.05 m 0.008 m 5 m Ar Asurfae πd 6 6 h, T h ( W/m. C(0.008 m B 0.000 < 0. (49 W/m. C Sne B < 0., the lumed system analyss s alable. Then the tme erd fr the shere temerature t reah t 5ºC s determned frm b ha ρ V ρ h (0,500 g/m W/m. C 0.000586 s (5 J/g. C(0.008 m Cube: V A h B b T surfae ha ρ 6 e 5 e 0 (0.000586 s t 0.05 m 0.008 m 6 6 ( W/m. C(0.008 m 0.000 < 0. (49 W/m. C V ρ h (0,500 g/m t 48 s 40.5 mn 5 m 5 m 5 m W/m. C 0.000586 s (5 J/g. C(0.008 m Ar h, T T e Retangular rsm: V A h B b surfae (0,500 g/m ha ρ 5 e 0 (0.000586 s t ( W/m. C(0.00808 m 0.000 < 0. (49 W/m. C V ρ t 48 s 40.5 mn (0.04 m(0.05 m(0.06 m 0.00808 (0.04 m(0.05 m + (0.04 m(0.06 m + (0.05 m(0.06 m h W/m. C 0.0005998 s (5 J/g. C(0.00808 m 4 m 5 m 6 m m Ar h, T T e 5 e 0 (0.0005998 s t t 6s 9.4 mn The heatng tmes are same fr the shere and ube whle t s smaller n retangular rsm. PROPRIETARY MATERIA. 008 The MGraw-Hll Cmanes, In. mted dstrbutn ermtted nly t teahers and eduatrs fr urse rearatn. If yu are a student usng ths Manual, yu are usng t wthut ermssn.

9-6 Tmates are laed nt ld water t l them. The heat transfer effent and the amunt f heat transfer are t be determned. Assumtns The tmates are sheral n shae. Heat ndutn n the tmates s ne-dmensnal beause f symmetry abut the mdnt. The thermal rertes f the tmates are nstant. 4 The heat transfer effent s nstant and unfrm ver the entre surfae. 5 The Furer number s τ > 0. s that the ne-term arxmate slutns (r the transent temerature harts are alable (ths assumtn wll be verfed. Prertes The rertes f the tmates are gven t be 0.59 W/m. C, α 0.4 0-6 m /s, ρ 999 g/m and.99 J/g. C. Analyss The Furer number s αt τ r 6 (0.4 0 m /s( 600 s 0.65 (0.04 m whh s greater than 0.. Therefre ne-term slutn s alable. The rat f the dmensnless temeratures at the surfae and enter f the tmates are θ θ T sn( s τ Ae s, sh T Ts sn( 0,sh T 0 τ A e T Substtutng, 7. 7 sn(.040 0 7 Frm Table -, the rresndng Bt number and the heat transfer effent are B. hr B h B r (0.59 W/m. C(. 459 W/m. C (0.04 m The mum amunt f heat transfer s m 8ρV 8ρπD / 6 8(999 g/m [ π (0.08 m / 6].4 g m [ T ] (.4 g(.99 J/g. C(0 7 C 96.6 J Then the atual amunt f heat transfer bemes yl T 0.9565 0.9565(96.6 J 88 J sn s 0 7 sn(.040 (.040 s(.040 0.9565 0 7 (.040 Water 7 C Tmat T 0 C PROPRIETARY MATERIA. 008 The MGraw-Hll Cmanes, In. mted dstrbutn ermtted nly t teahers and eduatrs fr urse rearatn. If yu are a student usng ths Manual, yu are usng t wthut ermssn.

-5-4 A lng ylndral shaft at 400 C s allwed t l slwly. The enter temerature and the heat transfer er unt length f the ylnder are t be determned. Assumtns Heat ndutn n the shaft s ne-dmensnal sne t s lng and t has thermal symmetry abut the enter lne. The thermal rertes f the shaft are nstant. The heat transfer effent s nstant and unfrm ver the entre surfae. 4 The Furer number s τ > 0. s that the ne-term arxmate slutns (r the transent temerature harts are alable (ths assumtn wll be verfed. Prertes The rertes f stanless steel 04 at rm temerature are gven t be 4.9 W/m. C, ρ 7900 g/m, 477 J/g. C, α.95 0-6 m /s Analyss Frst the Bt number s alulated t be hr B (60 W/m. C(0.75 m 0.705 (4.9 W/m. C The nstants and A rresndng t ths Bt number are, frm Table -,.0904 and A.548 The Furer number s 6 αt (.95 0 m /s(0 60 s τ 0.548 (0.75 m whh s very lse t the value f 0.. Therefre, the ne-term arxmate slutn (r the transent temerature harts an stll be used, wth the understandng that the errr nvlved wll be a lttle mre than erent. Then the temerature at the enter f the shaft bemes τ (.0904 (0.548 θ 0, yl Ae (.548 e 0.9607 T 50 0.9607 90 C 400 50 The mum heat an be transferred frm the ylnder er meter f ts length s m ρv ρπr (7900 g/m [ π (0.75 m (m] 760. g m [ T ] (760. g(0.477 J/g. C(400 50 C 90,640 J One the nstant J 0.4679 s determned frm Table - rresndng t the nstant.0904, the atual heat transfer bemes yl T T J( 90 50 400 50 0.76(90,640 J 5,960 J 0.4679.0904 0.76 Ar T 50 C Steel shaft T 400 C PROPRIETARY MATERIA. 008 The MGraw-Hll Cmanes, In. mted dstrbutn ermtted nly t teahers and eduatrs fr urse rearatn. If yu are a student usng ths Manual, yu are usng t wthut ermssn.

-0-46 A rb s rasted n an ven. The heat transfer effent at the surfae f the rb, the temerature f the uter surfae f the rb and the amunt f heat transfer when t s rare dne are t be determned. The tme t wll tae t rast ths rb t medum level s als t be determned. Assumtns The rb s a hmgeneus sheral bjet. Heat ndutn n the rb s ne-dmensnal beause f symmetry abut the mdnt. The thermal rertes f the rb are nstant. 4 The heat transfer effent s nstant and unfrm ver the entre surfae. 5 The Furer number s τ > 0. s that the ne-term arxmate slutns (r the transent temerature harts are alable (ths assumtn wll be verfed. Prertes The rertes f the rb are gven t be 0.45 W/m. C, ρ 00 g/m, 4. J/g. C, and α 0.9 0-7 m /s. Analyss (a The radus f the rast s determned t be m. g m ρv V 0.00667 m ρ 00 g/m 4 V (0.00667 m V πr r 0.0860 m 4π 4π The Furer number s 7 αt (0.9 0 m /s( 600 + 45 60s τ 0.7 (0.0860 m r whh s smewhat belw the value f 0.. Therefre, the ne-term arxmate slutn (r the transent temerature harts an stll be used, wth the understandng that the errr nvlved wll be a lttle mre than erent. Then the ne-term slutn an be wrtten n the frm τ 60 6 (0.7 θ 0, sh Ae 0. 65 Ae T 4.5 6 It s determned frm Table - by tral and errr that ths equatn s satsfed when B 0, whh rresnds t.07 and A.9898. Then the heat transfer effent an be determned frm hr B h B r (0.45 W/m. C(0 56.9 W/m. C (0.0860 m Ths value seems t be larger than exeted fr rblems f ths nd. Ths s rbably due t the Furer number beng less than 0.. (b The temerature at the surfae f the rb s T ( r, sn( / t T sn(.07 rad τ r r (.07 (0.7 θ ( r sh Ae (.9898 e T r / r.07 T ( r 6 0.0 T ( r 59.5 C 4.5 6 ( The mum ssble heat transfer s m ( T (. g(4. J/g. C(6 4.5 C 080 J Then the atual amunt f heat transfer bemes sn( s( sn(.07 (.07 s(.07 θ, sh (0.65 0.78 (.07 0.78 (0.78(080 J 69 J (d The ng tme fr medum-dne rb s determned t be 7 6 τ θ 0, sh Ae (.9898 e T 4.5 6 τr (0.6(0.0860 m t α 7 (0.9 0 m /s (.07 τ 0,866 s 8 mn hr Oven 6 C τ 0.6 Rb 4.5 C Ths result s lse t the lsted value f hurs and 0 mnutes. The dfferene between the tw results s due t the Furer number beng less than 0. and thus the errr n the ne-term arxmatn. Dsussn The temerature f the uter arts f the rb s greater than that f the nner arts f the rb after t s taen ut f the ven. Therefre, there wll be a heat transfer frm uter arts f the rb t the nner arts as a result f ths temerature dfferene. The remmendatn s lgal. PROPRIETARY MATERIA. 008 The MGraw-Hll Cmanes, In. mted dstrbutn ermtted nly t teahers and eduatrs fr urse rearatn. If yu are a student usng ths Manual, yu are usng t wthut ermssn.

-7-5 A ersn uts ales nt the freezer t l them quly. The enter and surfae temeratures f the ales, and the amunt f heat transfer frm eah ale n h are t be determned. Assumtns The ales are sheral n shae wth a dameter f 9 m. Heat ndutn n the ales s ne-dmensnal beause f symmetry abut the mdnt. The thermal rertes f the ales are nstant. 4 The heat transfer effent s nstant and unfrm ver the entre surfae. 5 The Furer number s τ > 0. s that the ne-term arxmate slutns (r the transent temerature harts are alable (ths assumtn wll be verfed. Prertes The rertes f the ales are gven t be 0.48 W/m. C, ρ 840 g/m,.8 J/g. C, and α. 0-7 m /s. Analyss The Bt number s Ar hr (8 W/m. C(0.045 m B 0.86 T 5 C (0.48 W/m. C The nstants and A rresndng t ths Ale Bt number are, frm Table -, T 0 C.476 and A.90 The Furer number s 7 αt (. 0 m /s(h 600 s/h τ 0. > 0. r (0.045 m Then the temerature at the enter f the ales bemes 0 ( 5 τ T (.476 (0. θ 0, sh Ae (.9 e 0. 749. C T 0 ( 5 The temerature at the surfae f the ales s θ ( r sh T( r T A e T ( r ( 5 0.505 T ( r 0 ( 5 τ The mum ssble heat transfer s 4 m ρv ρ πr m ( T sn( r r / r.7 C / r (.9 e (.476 (0. 4. (840 g/m π (0.045 m 0.06 g (0.06 g(.8 J/g. C T Then the atual amunt f heat transfer bemes θ 0.40, sh (0.40(4.75 J 7. J sn(.476 rad.476 [ 0 ( 5 ] C 4.75 J 0.505 sn( s( sn(.476 rad (.476 s(.476 rad (0.749 0.40 (.476 PROPRIETARY MATERIA. 008 The MGraw-Hll Cmanes, In. mted dstrbutn ermtted nly t teahers and eduatrs fr urse rearatn. If yu are a student usng ths Manual, yu are usng t wthut ermssn.

-90 04 Internal mbustn engne valves are quenhed n a large l bath. The tme t taes fr the valve temerature t dr t sefed temeratures and the mum heat transfer are t be determned. Assumtns The thermal rertes f the valves are nstant. The heat transfer effent s nstant and unfrm ver the entre surfae. Deendng n the sze f the l bath, the l bath temerature wll nrease durng quenhng. Hwever, an average anstant temerature as sefed n the rblem wll be used. 4 The Bt number s B < 0. s that the lumed system analyss s alable (ths assumtn wll be verfed. Prertes The thermal ndutvty, densty, and sef heat f the balls are gven t be 48 W/m. C, ρ 7840 g/m, and 440 J/g. C. Analyss (a The haraterst length f the balls and the Bt number are V.8( πd / 4.8D.8(0.008 m 0.008 m A πd 8 8 s h (800 W/m. C(0.008 m B 0.0 < 0. 48 W/m. C Therefre, we an use lumed system analyss. Then the tme fr a fnal valve temerature f 400 C bemes has 8h 8(800 W/m. C b 0.88 s ρ V.8ρ D.8(7840 g/m (440 J/g. C(0.008 m 400 50 (0.88 s t e e t 5.9 s T 800 50 (b The tme fr a fnal valve temerature f 00 C s 00 50 (0.88 s e e T 800 50 ( The tme fr a fnal valve temerature f 5 C s 5 50 (0.88 s e e T 800 50 t t t.5 s t 5.4 s (d The mum amunt f heat transfer frm a sngle valve s determned frm.8πd.8π (0.008 m (0.0 m m ρv ρ (7840 g/m 0.0709 g 4 4 m [ T ] (0.0709 g(440 J/g. C(800 50 C,400 J.4 J (er valve f Ol T 50 C Engne valve T 800 C PROPRIETARY MATERIA. 008 The MGraw-Hll Cmanes, In. mted dstrbutn ermtted nly t teahers and eduatrs fr urse rearatn. If yu are a student usng ths Manual, yu are usng t wthut ermssn.

2024 © sciencedocbox.com Privacy Policy | Terms of Service | Feedback