Fundamentals of Heat Transfer Muhammad Rashid Usman

Size: px
Start display at page:

Download "Fundamentals of Heat Transfer Muhammad Rashid Usman"

Transcription

1 Fundamentals of Heat Transfer Muammad Rasid Usman Institute of Cemical Engineering and Tecnology University of te Punjab, Laore. Figure taken from: ttp://eatexcanger-design.com/20/0/06/eat-excangers-6/ Dated: 7-Jan-202

2 Course contents final term Convection eat transfer: Free and forced convection. Rate equation for convective eat transfer coefficient. Brief description of ydrodynamic boundary layer and eat transfer coefficient. Units of eat transfer coefficient. Individual and overall eat transfer coefficients: plane wall and ollow cylinder. Numerical problems regarding overall eat transfer coefficient. Determination of eat transfer coefficient. Description of various eat transfer correlations. Log mean temperature difference. Numerical problems involving log mean temperature difference. Heat transfer in coiled and jacketed agitated vessels. Introduction to boiling and condensation. Types of boiling: Pool boiling and film boiling. Critical tickness of insulation. Brief description of eat transfer equipment: Heat excangers, furnaces, and evaporators. Radiation eat transfer: Basics of radiation eat transfer. Stefan-Boltzmann Law. Kircoff s law. Radiation eat transfer coefficient. Radiation to a small object from surroundings. View factors in radiation. Radiation in absorbing gases. 2

3 Te text book Please read and consult to know and learn. Geankoplis, C.J. (2003). Transport processes and separation process principles: includes unit operations. 4 t ed. Prentice- Hall International, Inc. 3

4 Convection eat transfer 4

5 Types of convective eat transfer Free or natural convection eat transfer Forced convection eat transfer 5

6 Free or natural convection eat transfer If te fluid motion is caused by itself due to difference in densities at two different points suc a process is natural or free convection eat transfer. Te density differences may be caused by temperature differences or concentration differences at two locations. In natural convection, no mecanical means are used to produce convective currents and convective mixing is a solely due to natural motion of te fluid. Boiling of milk and water and eating distant parts of a room in te presence of a room eater are common daily examples. 6

7 Forced convection eat transfer If te fluid motion is caused by some external or mecanical means te eat transfer is due to forced convection. Pumps, blowers, fans, agitation devices suc as impellers are employed for forced convection eat transfer. gitation using impellers in reaction vessels and pumping of fluids, at ig velocity, in eat excangers devices are te examples of forced convection. 7

8 Free and forced convection eat transfer In wic of te following cases do you expect greater rate of eat transfer?. Free convection 2. Forced convection 8

9 Newton s rate equation Rate of eat transfer per unit area is equal to te product of eat transfer coefficient and temperature difference between te eated surface and fluid far from te surface. q ( T s Tf ) q ( T s Tf ) q T f T s

10 Heat conduction troug a multilayer (composite) ollow cylinder-4: Problem (modified)-7 [p. 7, 2] ir at 20 C blows over a ot plate 50 by 75 cm wile maintained at 250 C. Te convection eat transfer coefficient is 25 W/m 2 K. Calculate te rate of eat transfer. Wat if eat transfer coefficient for te system is very ig or very low suc as 200 W/m 2 K and 0. W/m 2 K respectively. Wat is te direction of eat flow. T air = 20 C ir 75 cm 50 cm T s = 250 C 0

11 Heat transfer coefficient From te Newton s rate equation, it may be said tat eat transfer coefficient is te ability of te system, for wic it is defined, to transfer eat. Wat are te units of eat transfer coefficient?

12 Units of eat transfer coefficient SI units: J/s m 2 K or W/m 2 K W/m 2 K is equal to W/m 2 C Englis system: Btu/ ft 2 F Compare units of termal conductivity and eat transfer coefficient. 2

13 Heat transfer coefficient based on film model: Hydrodynamic boundary layer [p.58, 6] Fully developed boundary layer 3

14 Heat transfer coefficient based on film model Consider tickness of te film as Δx and k as te termal conductivity of te fluid (material of te film), ten it may be written tat k x Te main resistance to eat transfer is in tis film. Te eat transfer coefficient is sometimes called film coefficient. Note: Liquids and gases ave low termal conductivity. 4

15 Heat transfer coefficient based on film model Excerpt (p. 3.2) from Heat transfer by K.. Gavana, 8 t ed., Nirali Prakasan, Pune (2008). 5

16 Heat transfer coefficient based on film model For convective eat transfer, te film model suggests tat were ever a fluid flows past a solid surface tere is a film formed adjacent to te wall and tat tere is no turbulence in tis film and tis film offers te only resistance to eat transfer. It is important to mention ere tat for te film model, in te turbulent region (beyond te film) of a fluid tere is no problem for eat transfer, i.e. due to intense mixing, eat transfer is greatly enanced and tere is no temperature differential. 6

17 pproximate magnitudes of some eat transfer coefficients [] 7

18 Heat transfer coefficient based on film model Condensing steam (saturated steam) as ig eat transfer coefficient in contrast to supereated steam tat is wy a process engineer would like to eat a system using condensing steam and not by supereated steam. supereated steam beaves like a gas and you know gases ave low eat transfer coefficients. 8

19 Individual and overall eat transfer coefficients: plane wall [p. 249, ] Outside film resistance Inside film resistance Wall resistance 9

20 Individual and overall eat transfer coefficients: plane wall [p. 249, ] For inside film resistance: q i ( T T2) For wall resistance: q k ( T2 T 3) x For outside film: q ( T 3 T4) Wat if we ave two walls? o 20

21 2 Individual and overall eat transfer coefficients: plane wall [p. 249, ] i o k x T T q 4 k x T T q o i 4 te resistancein series all Sumof Overall temperature difference rate Heat

22 22 Individual and overall eat transfer coefficients: plane wall Reciprocal of overall resistance is overall conductance and frequently written in terms of overall eat transfer coefficient. i o k x U i o k x U ( 4) T T U q, k x U o i

23 Individual and overall eat transfer coefficients: plane wall Case : Wat if tickness of te wall wit ig termal conductivity is very small? Case 2: If one of te two film coefficients is a small value compared to te oter, ten major resistance is offered by te one wit small value and te coefficient is called as controlling film coefficient. Wat will be te form of te eat rate equation if i >>> o? Case 3: Wat if tere are a number of plane walls in series? Tink oter cases! 23

24 Individual and overall eat transfer coefficients: ollow cylinder Pipe wall resistance Outside fluid film resistance r 2 r Inside fluid film resistance 24

25 Individual and overall eat transfer coefficients: ollow cylinder q i i T T4 ln( r2 / r ) 2 k L o o Overall temperature difference Heat rate Sumof all te resistancein series 25

26 Individual and overall eat transfer coefficients: ollow cylinder U i i ln( r2 / r 2 k ) L o o Wic? Unlike plane wall, te inside and outside surface areas are different for cylindrical geometry. Te overall eat transfer coefficient is terefore as to be defined eiter on outside or inside surface of te ollow cylinder. 26

27 27 Individual and overall eat transfer coefficients: ollow cylinder o o i i i i L k r r U 2 ) / ln( 2 o o i i o o L k r r U 2 ) / ln( 2

28 References. Geankoplis, C.J. (2003). Transport processes and separation process principles: includes unit operations. 4 t ed. Prentice-Hall International, Inc. 2. Holman, J.P. (200). Heat transfer. 0 t ed. McGraw-Hill Higer Education, Singapore. 3. Cengel, Y.. (2003). Heat transfer: practical approac. 2 nd ed. McGraw-Hill. 4. Incropera, F.P.; DeWitt, D.P.; Bergman, T.L.; Lavine..S. (2007) Fundamentals of eat and mass transfer. 6 t ed. Jon Wiley & Sons, Inc. 5. Kern, D.Q. (965). Process eat transfer. McGraw-Hill International Book Co., Singapore. 6. McCabe, W.L.; Smit, J.C.; Harriott, P. (993). Unit operations of cemical engineering. 5 t ed. McGraw-Hill, Inc., Singapore. 7. Coulson, J.M.; Ricardson, J.F.; Backurst, J.R.; Harker, J.H. (999). Coulson and Ricardson s Cemical engineering: Fluid flow, eat transfer and mass transfer. vol.. 6 t ed. Butterwot-Heinemann, Oxford. 8. Staff of Researc and Education ssociation. (984). Te eat transfer problem solver. Researc and Education ssociation, New Jersey. 9. Kreit, F.; Manglik, R.M.; Bon, M.S. (20). Principles of eat transfer, 7 t ed., Cengage learning. 0. Mills.F. (995). Heat and mass transfer. Ricard D. Irwin, Inc. 28

Fundamentals of Heat Transfer Muhammad Rashid Usman

Fundamentals of Heat Transfer Muhammad Rashid Usman Fundamentals of Heat Transfer Muhammad Rashid Usman Institute of Chemical Engineering and Technology University of the Punjab, Lahore. Figure taken from: http://heatexchanger-design.com/2011/10/06/heat-exchangers-6/

More information

Fundamentals of Heat Transfer Muhammad Rashid Usman

Fundamentals of Heat Transfer Muhammad Rashid Usman Fundamentals of Heat Transfer Muhammad Rashid Usman Institute of Chemical Engineering and Technology University of the Punjab, Lahore. Figure taken from: http://heatexchanger-design.com/2011/10/06/heat-exchangers-6/

More information

University School of Chemical Technology

University School of Chemical Technology University School of Chemical Technology Guru Gobind Singh Indraprastha University Syllabus of Examination B.Tech/M.Tech Dual Degree (Chemical Engineering) (4 th Semester) (w.e.f. August 2004 Batch) Page

More information

Fundamentals of Heat Transfer Muhammad Rashid Usman

Fundamentals of Heat Transfer Muhammad Rashid Usman Fundamentals of Heat ansfe Muhammad Rashid Usman Institute of Chemical Engineeing and echnology Univesity of the Punjab, ahoe. Figue taen fom: http:heatexchange-design.com0006heat-exchanges-6 Dated: 7-Jan-0

More information

Chapters 19 & 20 Heat and the First Law of Thermodynamics

Chapters 19 & 20 Heat and the First Law of Thermodynamics Capters 19 & 20 Heat and te First Law of Termodynamics Te Zerot Law of Termodynamics Te First Law of Termodynamics Termal Processes Te Second Law of Termodynamics Heat Engines and te Carnot Cycle Refrigerators,

More information

Heat Transfer/Heat Exchanger

Heat Transfer/Heat Exchanger Heat ransfer/heat Excanger How is te eat transfer? Mecanism of Convection Applications. Mean fluid Velocity and Boundary and teir effect on te rate of eat transfer. Fundamental equation of eat transfer

More information

De-Coupler Design for an Interacting Tanks System

De-Coupler Design for an Interacting Tanks System IOSR Journal of Electrical and Electronics Engineering (IOSR-JEEE) e-issn: 2278-1676,p-ISSN: 2320-3331, Volume 7, Issue 3 (Sep. - Oct. 2013), PP 77-81 De-Coupler Design for an Interacting Tanks System

More information

Experimental Analysis of Heat Transfer Augmentation in Double Pipe Heat Exchanger using Tangential Entry of Fluid

Experimental Analysis of Heat Transfer Augmentation in Double Pipe Heat Exchanger using Tangential Entry of Fluid ISR Journal of Mecanical & Civil Engineering (ISRJMCE) e-issn: 2278-1684,p-ISSN: 2320-334X PP 29-34 www.iosrjournals.org Experimental Analysis of Heat Transfer Augmentation in Double Pipe Heat Excanger

More information

Effects of Radiation on Unsteady Couette Flow between Two Vertical Parallel Plates with Ramped Wall Temperature

Effects of Radiation on Unsteady Couette Flow between Two Vertical Parallel Plates with Ramped Wall Temperature Volume 39 No. February 01 Effects of Radiation on Unsteady Couette Flow between Two Vertical Parallel Plates wit Ramped Wall Temperature S. Das Department of Matematics University of Gour Banga Malda 73

More information

Use of fin analysis for determination of thermal conductivity of material

Use of fin analysis for determination of thermal conductivity of material RESEARCH ARTICLE OPEN ACCESS Use of fin analysis for determination of termal conductivity of material Nea Sanjay Babar 1, Saloni Suas Desmuk 2,Sarayu Dattatray Gogare 3, Snea Barat Bansude 4,Pradyumna

More information

Chapter 1 INTRODUCTION AND BASIC CONCEPTS

Chapter 1 INTRODUCTION AND BASIC CONCEPTS Heat and Mass Transfer: Fundamentals & Applications 5th Edition in SI Units Yunus A. Çengel, Afshin J. Ghajar McGraw-Hill, 2015 Chapter 1 INTRODUCTION AND BASIC CONCEPTS Mehmet Kanoglu University of Gaziantep

More information

Compressor 1. Evaporator. Condenser. Expansion valve. CHE 323, October 8, Chemical Engineering Thermodynamics. Tutorial problem 5.

Compressor 1. Evaporator. Condenser. Expansion valve. CHE 323, October 8, Chemical Engineering Thermodynamics. Tutorial problem 5. CHE 33, October 8, 014. Cemical Engineering Termodynamics. Tutorial problem 5. In a simple compression refrigeration process, an adiabatic reversible compressor is used to compress propane, used as a refrigerant.

More information

4.2 - Richardson Extrapolation

4.2 - Richardson Extrapolation . - Ricardson Extrapolation. Small-O Notation: Recall tat te big-o notation used to define te rate of convergence in Section.: Definition Let x n n converge to a number x. Suppose tat n n is a sequence

More information

University School of Chemical Technology

University School of Chemical Technology University School of Chemical Technology Guru Gobind Singh Indraprastha University Syllabus of Examination B.Tech/M.Tech Dual Degree (Chemical Engineering) (5 th Semester) (w.e.f. August 2004 Batch) Page

More information

(4.2) -Richardson Extrapolation

(4.2) -Richardson Extrapolation (.) -Ricardson Extrapolation. Small-O Notation: Recall tat te big-o notation used to define te rate of convergence in Section.: Suppose tat lim G 0 and lim F L. Te function F is said to converge to L as

More information

Numerical Differentiation

Numerical Differentiation Numerical Differentiation Finite Difference Formulas for te first derivative (Using Taylor Expansion tecnique) (section 8.3.) Suppose tat f() = g() is a function of te variable, and tat as 0 te function

More information

Department of Chemical Engineering. Year 2 Module Synopses

Department of Chemical Engineering. Year 2 Module Synopses Department of Chemical Engineering Year 2 Module Synopses ENGS203P Mathematical Modelling and Analysis II CENG201P Design and Professional Skills II CENG202P Engineering Experimentation CENG203P Process

More information

Section A 01. (12 M) (s 2 s 3 ) = 313 s 2 = s 1, h 3 = h 4 (s 1 s 3 ) = kj/kgk. = kj/kgk. 313 (s 3 s 4f ) = ln

Section A 01. (12 M) (s 2 s 3 ) = 313 s 2 = s 1, h 3 = h 4 (s 1 s 3 ) = kj/kgk. = kj/kgk. 313 (s 3 s 4f ) = ln 0. (a) Sol: Section A A refrigerator macine uses R- as te working fluid. Te temperature of R- in te evaporator coil is 5C, and te gas leaves te compressor as dry saturated at a temperature of 40C. Te mean

More information

Carnot Factor of a Vapour Power Cycle with Regenerative Extraction

Carnot Factor of a Vapour Power Cycle with Regenerative Extraction Journal of Modern Pysics, 2017, 8, 1795-1808 ttp://www.scirp.org/journal/jmp ISSN Online: 2153-120X ISSN Print: 2153-1196 arnot Factor of a Vapour Power ycle wit Regenerative Extraction Duparquet Alain

More information

1. Consider the trigonometric function f(t) whose graph is shown below. Write down a possible formula for f(t).

1. Consider the trigonometric function f(t) whose graph is shown below. Write down a possible formula for f(t). . Consider te trigonometric function f(t) wose grap is sown below. Write down a possible formula for f(t). Tis function appears to be an odd, periodic function tat as been sifted upwards, so we will use

More information

CFD Analysis and Optimization of Heat Transfer in Double Pipe Heat Exchanger with Helical-Tap Inserts at Annulus of Inner Pipe

CFD Analysis and Optimization of Heat Transfer in Double Pipe Heat Exchanger with Helical-Tap Inserts at Annulus of Inner Pipe IOR Journal Mecanical and Civil Engineering (IOR-JMCE) e-in: 2278-1684,p-IN: 2320-334X, Volume 13, Issue 3 Ver. VII (May- Jun. 2016), PP 17-22 www.iosrjournals.org CFD Analysis and Optimization Heat Transfer

More information

S.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100

S.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100 Total No. of Questions 12] [Total No. of Printed Pages 7 Seat No. [4162]-187 S.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100 N.B.

More information

Desalination by vacuum membrane distillation: sensitivity analysis

Desalination by vacuum membrane distillation: sensitivity analysis Separation and Purification Tecnology 33 (2003) 75/87 www.elsevier.com/locate/seppur Desalination by vacuum membrane distillation: sensitivity analysis Fawzi Banat *, Fami Abu Al-Rub, Kalid Bani-Melem

More information

Elmahdy, A.H.; Haddad, K. NRCC-43378

Elmahdy, A.H.; Haddad, K. NRCC-43378 Experimental procedure and uncertainty analysis of a guarded otbox metod to determine te termal transmission coefficient of skyligts and sloped glazing Elmady, A.H.; Haddad, K. NRCC-43378 A version of

More information

Determination of heat transfer intensity between free streaming water film and rigid surface using thermography

Determination of heat transfer intensity between free streaming water film and rigid surface using thermography IV Conferencia Panamericana de END Buenos Aires Octubre 2007 Determination of eat transfer intensity between free ing water film and rigid surface using termograpy Ivanka Boras and Srecko Svaic Faculty

More information

Lecture 10: Carnot theorem

Lecture 10: Carnot theorem ecture 0: Carnot teorem Feb 7, 005 Equivalence of Kelvin and Clausius formulations ast time we learned tat te Second aw can be formulated in two ways. e Kelvin formulation: No process is possible wose

More information

HEAT TRANSFER. PHI Learning PfcO too1. Principles and Applications BINAY K. DUTTA. Delhi Kolkata. West Bengal Pollution Control Board

HEAT TRANSFER. PHI Learning PfcO too1. Principles and Applications BINAY K. DUTTA. Delhi Kolkata. West Bengal Pollution Control Board HEAT TRANSFER Principles and Applications BINAY K. DUTTA West Bengal Pollution Control Board Kolkata PHI Learning PfcO too1 Delhi-110092 2014 Contents Preface Notations ix xiii 1. Introduction 1-8 1.1

More information

If there is convective heat transfer from outer surface to fluid maintained at T W.

If there is convective heat transfer from outer surface to fluid maintained at T W. Heat Transfer 1. What are the different modes of heat transfer? Explain with examples. 2. State Fourier s Law of heat conduction? Write some of their applications. 3. State the effect of variation of temperature

More information

Solution for the Homework 4

Solution for the Homework 4 Solution for te Homework 4 Problem 6.5: In tis section we computed te single-particle translational partition function, tr, by summing over all definite-energy wavefunctions. An alternative approac, owever,

More information

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127 C ONTENTS Preface xviii Nomenclature xxvi CHAPTER ONE BASICS OF HEAT TRANSFER 1 1-1 Thermodynamics and Heat Transfer 2 Application Areas of Heat Transfer 3 Historical Background 3 1-2 Engineering Heat

More information

INTRODUCTION DEFINITION OF FLUID. U p F FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION

INTRODUCTION DEFINITION OF FLUID. U p F FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION INTRODUCTION DEFINITION OF FLUID plate solid F at t = 0 t > 0 = F/A plate U p F fluid t 0 t 1 t 2 t 3 FLUID IS A SUBSTANCE THAT CAN NOT SUPPORT SHEAR FORCES OF ANY MAGNITUDE WITHOUT CONTINUOUS DEFORMATION

More information

DEVELOPMENT AND PERFORMANCE EVALUATION OF THERMAL CONDUCTIVITY EQUIPMENT FOR LABORATORY USES

DEVELOPMENT AND PERFORMANCE EVALUATION OF THERMAL CONDUCTIVITY EQUIPMENT FOR LABORATORY USES . Sunday Albert LAWAL,. Benjamin Iyenagbe UGHEOKE DEVELOPMENT AND PERFORMANCE EVALUATION OF THERMAL CONDUCTIVITY EQUIPMENT FOR LABORATORY USES. DEPARTMENT OF MECHANICAL ENGINEERING, FEDERAL UNIVERSITY

More information

A = h w (1) Error Analysis Physics 141

A = h w (1) Error Analysis Physics 141 Introduction In all brances of pysical science and engineering one deals constantly wit numbers wic results more or less directly from experimental observations. Experimental observations always ave inaccuracies.

More information

Some Review Problems for First Midterm Mathematics 1300, Calculus 1

Some Review Problems for First Midterm Mathematics 1300, Calculus 1 Some Review Problems for First Midterm Matematics 00, Calculus. Consider te trigonometric function f(t) wose grap is sown below. Write down a possible formula for f(t). Tis function appears to be an odd,

More information

Study of Convective Heat Transfer through Micro Channels with Different Configurations

Study of Convective Heat Transfer through Micro Channels with Different Configurations International Journal of Current Engineering and Tecnology E-ISSN 2277 4106, P-ISSN 2347 5161 2016 INPRESSCO, All Rigts Reserved Available at ttp://inpressco.com/category/ijcet Researc Article Study of

More information

Simulation and verification of a plate heat exchanger with a built-in tap water accumulator

Simulation and verification of a plate heat exchanger with a built-in tap water accumulator Simulation and verification of a plate eat excanger wit a built-in tap water accumulator Anders Eriksson Abstract In order to test and verify a compact brazed eat excanger (CBE wit a built-in accumulation

More information

Heat and Mass Transfer Unit-1 Conduction

Heat and Mass Transfer Unit-1 Conduction 1. State Fourier s Law of conduction. Heat and Mass Transfer Unit-1 Conduction Part-A The rate of heat conduction is proportional to the area measured normal to the direction of heat flow and to the temperature

More information

(a) At what number x = a does f have a removable discontinuity? What value f(a) should be assigned to f at x = a in order to make f continuous at a?

(a) At what number x = a does f have a removable discontinuity? What value f(a) should be assigned to f at x = a in order to make f continuous at a? Solutions to Test 1 Fall 016 1pt 1. Te grap of a function f(x) is sown at rigt below. Part I. State te value of eac limit. If a limit is infinite, state weter it is or. If a limit does not exist (but is

More information

HEAT TRANSFER. Mechanisms of Heat Transfer: (1) Conduction

HEAT TRANSFER. Mechanisms of Heat Transfer: (1) Conduction HEAT TRANSFER Mechanisms of Heat Transfer: (1) Conduction where Q is the amount of heat, Btu, transferred in time t, h k is the thermal conductivity, Btu/[h ft 2 ( o F/ft)] A is the area of heat transfer

More information

Heat Transfer with Phase Change

Heat Transfer with Phase Change CM3110 Transport I Part II: Heat Transfer Heat Transfer with Phase Change Evaporators and Condensers Professor Faith Morrison Department of Chemical Engineering Michigan Technological University 1 Heat

More information

The entransy dissipation minimization principle under given heat duty and heat transfer area conditions

The entransy dissipation minimization principle under given heat duty and heat transfer area conditions Article Engineering Termopysics July 2011 Vol.56 No.19: 2071 2076 doi: 10.1007/s11434-010-4189-x SPECIAL TOPICS: Te entransy dissipation minimization principle under given eat duty and eat transfer area

More information

LOSSES DUE TO PIPE FITTINGS

LOSSES DUE TO PIPE FITTINGS LOSSES DUE TO PIPE FITTINGS Aim: To determine the losses across the fittings in a pipe network Theory: The resistance to flow in a pipe network causes loss in the pressure head along the flow. The overall

More information

Fluids and Buoyancy. 1. What will happen to the scale reading as the mass is lowered?

Fluids and Buoyancy. 1. What will happen to the scale reading as the mass is lowered? Fluids and Buoyancy. Wat will appen to te scale reading as te mass is lowered? M Using rcimedes Principle: any body fully or partially submerged in a fluid is buoyed up by a force equal to te weigt of

More information

MAT 145. Type of Calculator Used TI-89 Titanium 100 points Score 100 possible points

MAT 145. Type of Calculator Used TI-89 Titanium 100 points Score 100 possible points MAT 15 Test #2 Name Solution Guide Type of Calculator Used TI-89 Titanium 100 points Score 100 possible points Use te grap of a function sown ere as you respond to questions 1 to 8. 1. lim f (x) 0 2. lim

More information

Chapter: Heat and States

Chapter: Heat and States Table of Contents Chapter: Heat and States of Matter Section 1: Temperature and Thermal Energy Section 2: States of Matter Section 3: Transferring Thermal Energy Section 4: Using Thermal Energy 1 Temperature

More information

LAMINAR FORCED CONVECTION TO FLUIDS IN COILED PIPE SUBMERGED IN AGITATED VESSEL

LAMINAR FORCED CONVECTION TO FLUIDS IN COILED PIPE SUBMERGED IN AGITATED VESSEL Int. J. Mec. Eng. & Rob. Res. 05 Ansar Ali S K et al., 05 Researc Paper LAMIAR FORCED COVECTIO TO FLUIDS I COILED PIPE SUBMERGED I AGITATED VESSEL Ansar Ali S K *, L P Sing and S Gupta 3 ISS 78 049 www.ijmerr.com

More information

Phase space in classical physics

Phase space in classical physics Pase space in classical pysics Quantum mecanically, we can actually COU te number of microstates consistent wit a given macrostate, specified (for example) by te total energy. In general, eac microstate

More information

Consider the element shown in Figure 2.1. The statement of energy conservation applied to this element in a time period t is that:

Consider the element shown in Figure 2.1. The statement of energy conservation applied to this element in a time period t is that: . Conduction. e General Conduction Equation Conduction occurs in a stationary medium wic is most liely to be a solid, but conduction can also occur in s. Heat is transferred by conduction due to motion

More information

Exam 1 Review Solutions

Exam 1 Review Solutions Exam Review Solutions Please also review te old quizzes, and be sure tat you understand te omework problems. General notes: () Always give an algebraic reason for your answer (graps are not sufficient),

More information

Chapter 3 Thermoelectric Coolers

Chapter 3 Thermoelectric Coolers 3- Capter 3 ermoelectric Coolers Contents Capter 3 ermoelectric Coolers... 3- Contents... 3-3. deal Equations... 3-3. Maximum Parameters... 3-7 3.3 Normalized Parameters... 3-8 Example 3. ermoelectric

More information

Logarithmic functions

Logarithmic functions Roberto s Notes on Differential Calculus Capter 5: Derivatives of transcendental functions Section Derivatives of Logaritmic functions Wat ou need to know alread: Definition of derivative and all basic

More information

Unit B-4: List of Subjects

Unit B-4: List of Subjects ES312 Energy Transfer Fundamentals Unit B: First Law of Thermodynamics ROAD MAP... B-1: The Concept of Energy B-2: Work Interactions B-3: First Law of Thermodynamics B-4: Heat Transfer Fundamentals Unit

More information

LIMITS AND DERIVATIVES CONDITIONS FOR THE EXISTENCE OF A LIMIT

LIMITS AND DERIVATIVES CONDITIONS FOR THE EXISTENCE OF A LIMIT LIMITS AND DERIVATIVES Te limit of a function is defined as te value of y tat te curve approaces, as x approaces a particular value. Te limit of f (x) as x approaces a is written as f (x) approaces, as

More information

SECTION 3.2: DERIVATIVE FUNCTIONS and DIFFERENTIABILITY

SECTION 3.2: DERIVATIVE FUNCTIONS and DIFFERENTIABILITY (Section 3.2: Derivative Functions and Differentiability) 3.2.1 SECTION 3.2: DERIVATIVE FUNCTIONS and DIFFERENTIABILITY LEARNING OBJECTIVES Know, understand, and apply te Limit Definition of te Derivative

More information

Law of Heat Transfer

Law of Heat Transfer Law of Heat Transfer The Fundamental Laws which are used in broad area of applications are: 1. The law of conversion of mass 2. Newton s second law of motion 3. First and second laws of thermodynamics

More information

Analysis: The speed of the proton is much less than light speed, so we can use the

Analysis: The speed of the proton is much less than light speed, so we can use the Section 1.3: Wave Proerties of Classical Particles Tutorial 1 Practice, age 634 1. Given: 1.8! 10 "5 kg # m/s; 6.63! 10 "34 J #s Analysis: Use te de Broglie relation, λ. Solution:! 6.63 " 10#34 kg $ m

More information

Test 2 Review. 1. Find the determinant of the matrix below using (a) cofactor expansion and (b) row reduction. A = 3 2 =

Test 2 Review. 1. Find the determinant of the matrix below using (a) cofactor expansion and (b) row reduction. A = 3 2 = Test Review Find te determinant of te matrix below using (a cofactor expansion and (b row reduction Answer: (a det + = (b Observe R R R R R R R R R Ten det B = (((det Hence det Use Cramer s rule to solve:

More information

Department of Mechanical Engineering ME 96. Free and Forced Convection Experiment. Revised: 25 April Introduction

Department of Mechanical Engineering ME 96. Free and Forced Convection Experiment. Revised: 25 April Introduction CALIFORNIA INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering ME 96 Free and Forced Convection Experiment Revised: 25 April 1994 1. Introduction The term forced convection refers to heat transport

More information

Grade: 11 International Physics Olympiad Qualifier Set: 2

Grade: 11 International Physics Olympiad Qualifier Set: 2 Grade: 11 International Pysics Olympiad Qualifier Set: 2 --------------------------------------------------------------------------------------------------------------- Max Marks: 60 Test ID: 12111 Time

More information

INSTRUCTOR: PM DR MAZLAN ABDUL WAHID

INSTRUCTOR: PM DR MAZLAN ABDUL WAHID SMJ 4463: HEAT TRANSFER INSTRUCTOR: PM ABDUL WAHID http://www.fkm.utm.my/~mazlan TEXT: Introduction to Heat Transfer by Incropera, DeWitt, Bergman, Lavine 6 th Edition, John Wiley and Sons Chapter 7 External

More information

Optimization of flat tubular molten salt receivers

Optimization of flat tubular molten salt receivers Optimization of flat tubular molten salt receivers Meige Zeng, Jon Pye Researc Scool of Engineering, Australian National University, Canberra, Australia Abstract E-mail: meige.zeng@anu.edu.au, jon.pye@anu.edu.au

More information

Chapter 2 HEAT CONDUCTION EQUATION

Chapter 2 HEAT CONDUCTION EQUATION Heat and Mass Transfer: Fundamentals & Applications 5th Edition in SI Units Yunus A. Çengel, Afshin J. Ghajar McGraw-Hill, 2015 Chapter 2 HEAT CONDUCTION EQUATION Mehmet Kanoglu University of Gaziantep

More information

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds. Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

More information

Taylor Series and the Mean Value Theorem of Derivatives

Taylor Series and the Mean Value Theorem of Derivatives 1 - Taylor Series and te Mean Value Teorem o Derivatives Te numerical solution o engineering and scientiic problems described by matematical models oten requires solving dierential equations. Dierential

More information

Physics 207 Lecture 23

Physics 207 Lecture 23 ysics 07 Lecture ysics 07, Lecture 8, Dec. Agenda:. Finis, Start. Ideal gas at te molecular level, Internal Energy Molar Specific Heat ( = m c = n ) Ideal Molar Heat apacity (and U int = + W) onstant :

More information

Click here to see an animation of the derivative

Click here to see an animation of the derivative Differentiation Massoud Malek Derivative Te concept of derivative is at te core of Calculus; It is a very powerful tool for understanding te beavior of matematical functions. It allows us to optimize functions,

More information

Exam in Fluid Mechanics SG2214

Exam in Fluid Mechanics SG2214 Exam in Fluid Mecanics G2214 Final exam for te course G2214 23/10 2008 Examiner: Anders Dalkild Te point value of eac question is given in parentesis and you need more tan 20 points to pass te course including

More information

Combining functions: algebraic methods

Combining functions: algebraic methods Combining functions: algebraic metods Functions can be added, subtracted, multiplied, divided, and raised to a power, just like numbers or algebra expressions. If f(x) = x 2 and g(x) = x + 2, clearly f(x)

More information

Thermodynamics Lecture Series

Thermodynamics Lecture Series Termodynamics Lecture Series Ideal Ranke Cycle Te Practical Cycle Applied Sciences Education Researc Group (ASERG) Faculty of Applied Sciences Universiti Teknologi MARA email: drjjlanita@otmail.com ttp://www5.uitm.edu.my/faculties/fsg/drjj1.tml

More information

Large eddy simulation of turbulent flow downstream of a backward-facing step

Large eddy simulation of turbulent flow downstream of a backward-facing step Available online at www.sciencedirect.com Procedia Engineering 31 (01) 16 International Conference on Advances in Computational Modeling and Simulation Large eddy simulation of turbulent flow downstream

More information

Recall from our discussion of continuity in lecture a function is continuous at a point x = a if and only if

Recall from our discussion of continuity in lecture a function is continuous at a point x = a if and only if Computational Aspects of its. Keeping te simple simple. Recall by elementary functions we mean :Polynomials (including linear and quadratic equations) Eponentials Logaritms Trig Functions Rational Functions

More information

Section 2.7 Derivatives and Rates of Change Part II Section 2.8 The Derivative as a Function. at the point a, to be. = at time t = a is

Section 2.7 Derivatives and Rates of Change Part II Section 2.8 The Derivative as a Function. at the point a, to be. = at time t = a is Mat 180 www.timetodare.com Section.7 Derivatives and Rates of Cange Part II Section.8 Te Derivative as a Function Derivatives ( ) In te previous section we defined te slope of te tangent to a curve wit

More information

Order of Accuracy. ũ h u Ch p, (1)

Order of Accuracy. ũ h u Ch p, (1) Order of Accuracy 1 Terminology We consider a numerical approximation of an exact value u. Te approximation depends on a small parameter, wic can be for instance te grid size or time step in a numerical

More information

ME-662 CONVECTIVE HEAT AND MASS TRANSFER

ME-662 CONVECTIVE HEAT AND MASS TRANSFER ME-66 CONVECTIVE HEAT AND MASS TRANSFER A. W. Date Mechanical Engineering Department Indian Institute of Technology, Bombay Mumbai - 400076 India LECTURE- INTRODUCTION () March 7, 00 / 7 LECTURE- INTRODUCTION

More information

CFD calculation of convective heat transfer coefficients and validation Part I: Laminar flow Neale, A.; Derome, D.; Blocken, B.; Carmeliet, J.E.

CFD calculation of convective heat transfer coefficients and validation Part I: Laminar flow Neale, A.; Derome, D.; Blocken, B.; Carmeliet, J.E. CFD calculation of convective eat transfer coefficients and validation Part I: Laminar flow Neale, A.; Derome, D.; Blocken, B.; Carmeliet, J.E. Publised in: IEA Annex 41 working meeting, Kyoto, Japan Publised:

More information

HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION

HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION 11 Fourier s Law of Heat Conduction, General Conduction Equation Based on Cartesian Coordinates, Heat Transfer Through a Wall, Composite Wall

More information

The Basics of Vacuum Technology

The Basics of Vacuum Technology Te Basics of Vacuum Tecnology Grolik Benno, Kopp Joacim January 2, 2003 Basics Many scientific and industrial processes are so sensitive tat is is necessary to omit te disturbing influence of air. For

More information

The Laplace equation, cylindrically or spherically symmetric case

The Laplace equation, cylindrically or spherically symmetric case Numerisce Metoden II, 7 4, und Übungen, 7 5 Course Notes, Summer Term 7 Some material and exercises Te Laplace equation, cylindrically or sperically symmetric case Electric and gravitational potential,

More information

INSTRUCTOR: PM DR MAZLAN ABDUL WAHID

INSTRUCTOR: PM DR MAZLAN ABDUL WAHID SMJ 4463: HEAT TRANSFER INSTRUCTOR: PM DR MAZLAN ABDUL WAHID http://www.fkm.utm.my/~mazlan TEXT: Introduction to Heat Transfer by Incropera, DeWitt, Bergman, Lavine 5 th Edition, John Wiley and Sons DR

More information

Problem Solving. Problem Solving Process

Problem Solving. Problem Solving Process Problem Solving One of te primary tasks for engineers is often solving problems. It is wat tey are, or sould be, good at. Solving engineering problems requires more tan just learning new terms, ideas and

More information

Temperature control of two interacting rooms with decoupled PI Control

Temperature control of two interacting rooms with decoupled PI Control Preprints of te 19t World Congress Te International Federation of Automatic Control Cape Town, Sout Africa August 24-29, 2014 Temperature control of two interacting rooms wit decoupled PI Control Meike

More information

3.1 Extreme Values of a Function

3.1 Extreme Values of a Function .1 Etreme Values of a Function Section.1 Notes Page 1 One application of te derivative is finding minimum and maimum values off a grap. In precalculus we were only able to do tis wit quadratics by find

More information

Performance Prediction of Commercial Thermoelectric Cooler. Modules using the Effective Material Properties

Performance Prediction of Commercial Thermoelectric Cooler. Modules using the Effective Material Properties Performance Prediction of Commercial ermoelectric Cooler Modules using te Effective Material Properties HoSung Lee, Alaa M. Attar, Sean L. Weera Mecanical and Aerospace Engineering, Western Micigan University,

More information

Hall Effcts Eon Unsteady MHD Free Convection Flow Over A Stretching Sheet With Variable Viscosity And Viscous Dissipation

Hall Effcts Eon Unsteady MHD Free Convection Flow Over A Stretching Sheet With Variable Viscosity And Viscous Dissipation IOSR Journal of Matematics (IOSR-JM) e-issn: 78-578, p-issn: 39-765X. Volume, Issue 4 Ver. I (Jul - Aug. 5), PP 59-67 www.iosrjournals.org Hall Effcts Eon Unsteady MHD Free Convection Flow Over A Stretcing

More information

Mathematics 5 Worksheet 11 Geometry, Tangency, and the Derivative

Mathematics 5 Worksheet 11 Geometry, Tangency, and the Derivative Matematics 5 Workseet 11 Geometry, Tangency, and te Derivative Problem 1. Find te equation of a line wit slope m tat intersects te point (3, 9). Solution. Te equation for a line passing troug a point (x

More information

Math 1241 Calculus Test 1

Math 1241 Calculus Test 1 February 4, 2004 Name Te first nine problems count 6 points eac and te final seven count as marked. Tere are 120 points available on tis test. Multiple coice section. Circle te correct coice(s). You do

More information

Chapter 4 Optimal Design

Chapter 4 Optimal Design 4- Capter 4 Optimal Design e optimum design of termoelectric devices (termoelectric generator and cooler) in conjunction wit eat sins was developed using dimensional analysis. ew dimensionless groups were

More information

Practice Problem Solutions: Exam 1

Practice Problem Solutions: Exam 1 Practice Problem Solutions: Exam 1 1. (a) Algebraic Solution: Te largest term in te numerator is 3x 2, wile te largest term in te denominator is 5x 2 3x 2 + 5. Tus lim x 5x 2 2x 3x 2 x 5x 2 = 3 5 Numerical

More information

Derivatives and Rates of Change

Derivatives and Rates of Change Section.1 Derivatives and Rates of Cange 2016 Kiryl Tsiscanka Derivatives and Rates of Cange Measuring te Rate of Increase of Blood Alcool Concentration Biomedical scientists ave studied te cemical and

More information

8-4 P 2. = 12 kw. AIR T = const. Therefore, Q &

8-4 P 2. = 12 kw. AIR T = const. Therefore, Q & 8-4 8-4 Air i compreed teadily by a compreor. e air temperature i mataed contant by eat rejection to te urroundg. e rate o entropy cange o air i to be determed. Aumption i i a teady-low proce ce tere i

More information

Continuity and Differentiability Worksheet

Continuity and Differentiability Worksheet Continuity and Differentiability Workseet (Be sure tat you can also do te grapical eercises from te tet- Tese were not included below! Typical problems are like problems -3, p. 6; -3, p. 7; 33-34, p. 7;

More information

CFD calculation of convective heat transfer coefficients and validation Part I: Laminar flow. Annex 41 Kyoto, April 3 rd to 5 th, 2006

CFD calculation of convective heat transfer coefficients and validation Part I: Laminar flow. Annex 41 Kyoto, April 3 rd to 5 th, 2006 CFD calculation of convective eat transfer coefficients and validation Part I: Laminar flow Annex 41 Kyoto, April 3 rd to 5 t, 2006 Adam Neale 1, Dominique Derome 1, Bert Blocken 2 and Jan Carmeliet 2,3

More information

Prediction of Oil-Water Two Phase Flow Pressure Drop by Using Homogeneous Model

Prediction of Oil-Water Two Phase Flow Pressure Drop by Using Homogeneous Model FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November 008 Prediction of Oil-Water Two Pase Flow Pressure Drop by Using Nay Zar Aung a, Triyogi Yuwono b a Department of Mecanical Engineering, Institute

More information

Exam 1 Solutions. x(x 2) (x + 1)(x 2) = x

Exam 1 Solutions. x(x 2) (x + 1)(x 2) = x Eam Solutions Question (0%) Consider f() = 2 2 2 2. (a) By calculating relevant its, determine te equations of all vertical asymptotes of te grap of f(). If tere are none, say so. f() = ( 2) ( + )( 2)

More information

PREFACE. Julian C. Smith Peter Harriott. xvii

PREFACE. Julian C. Smith Peter Harriott. xvii PREFACE This sixth edition of the text on the unit operations of chemical engineering has been extensively revised and updated, with much new material and considerable condensation of some sections. Its

More information

Handling Missing Data on Asymmetric Distribution

Handling Missing Data on Asymmetric Distribution International Matematical Forum, Vol. 8, 03, no. 4, 53-65 Handling Missing Data on Asymmetric Distribution Amad M. H. Al-Kazale Department of Matematics, Faculty of Science Al-albayt University, Al-Mafraq-Jordan

More information

y = 3 2 x 3. The slope of this line is 3 and its y-intercept is (0, 3). For every two units to the right, the line rises three units vertically.

y = 3 2 x 3. The slope of this line is 3 and its y-intercept is (0, 3). For every two units to the right, the line rises three units vertically. Mat 2 - Calculus for Management and Social Science. Understanding te basics of lines in te -plane is crucial to te stud of calculus. Notes Recall tat te and -intercepts of a line are were te line meets

More information

10 Derivatives ( )

10 Derivatives ( ) Instructor: Micael Medvinsky 0 Derivatives (.6-.8) Te tangent line to te curve yf() at te point (a,f(a)) is te line l m + b troug tis point wit slope Alternatively one can epress te slope as f f a m lim

More information

Journal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article

Journal of Chemical and Pharmaceutical Research, 2013, 5(12): Research Article Available online.jocpr.com Journal of emical and Parmaceutical Researc, 013, 5(1):55-531 Researc Article ISSN : 0975-7384 ODEN(USA) : JPR5 Performance and empirical models of a eat pump ater eater system

More information

3 Minority carrier profiles (the hyperbolic functions) Consider a

3 Minority carrier profiles (the hyperbolic functions) Consider a Microelectronic Devices and Circuits October 9, 013 - Homework #3 Due Nov 9, 013 1 Te pn junction Consider an abrupt Si pn + junction tat as 10 15 acceptors cm -3 on te p-side and 10 19 donors on te n-side.

More information