External Forced Convection :
|
|
- Lawrence Day
- 5 years ago
- Views:
Transcription
1 External Forced Convection : Flow over Bluff Objects (Cylinders, Spheres, Packed Beds) and Impinging Jets Chapter 7 Sections 7.4 through 7.8
2 7.4 The Cylinder in Cross Flow Conditions depend on special features of boundary layer development, including onset at a stagnation point and separation, as well as transition to turbulence. Stagnation point: Location of zero velocity ( u = 0) and maximum pressure. Followed by boundary layer development under a favorable pressure gradient ( dp / dx < 0) and hence acceleration of the free stream flow ( du / dx 0). > As the rear of the cylinder is approached, the pressure must begin to increase. Hence, there is a minimum in the pressure distribution, p(x), after which boundary layer development occurs under the influence of an adverse pressure gradient dp / dx > 0, du / dx < 0. ( )
3 Separation occurs when the velocity gradient du / dy y = 0 reduces to zero and is accompanied by flow reversal and a downstream wake. Location of separation depends on boundary layer transition. Re ρ VD VD D = µ ν
4 What features differentiate boundary development for the flat plate in parallel flow from that for flow over a cylinder? Force imposed by the flow is due to the combination of friction and form drag. The dimensionless form of the drag force is C D FD = Figure 7.8 A f 2 ( ρv /2)
5
6 Heat Transfer Considerations The Local Nusselt Number: 5 How does the local Nusselt number vary with for Re 2 x 10? What conditions are associated with maxima and minima in the variation? 5 How does the local Nusselt number vary with θ for Re > 2 10? What conditions are associated with maxima and minima in the variation? The Average Nusselt Number ( Nu D hd k ) θ / : D D < Flow over a circular cylinder [Churchill and Bernstein Correlation]: Nu D 1/2 1/3 5/8 0.62Re Pr D ReD = /3 1/ ,000 + ( 0.4/Pr) 4/5 for ( Re Pr) 0.2 D
7 Cylinders of Noncircular Cross Section: Nu D = hd m 1/3 = C ReD Pr k for Pr 0.7
8 Circular Cylinders [Zukauskas]: Nu D Pr = C m n 1/4 ReD Pr ( ) 0.7 Pr 500 Prs 1 Re 10 D 6 If Pr 10, n = 0.37 ; If Pr 10, n = 0.36.
9
10
11
12
13
14
15
16 7.5 The Sphere See Eqs.. (7.47) - (7.49) Nu sph hd = k µ = Re Re Pr µ s 14 (7.48)
17
18
19 7.6 Flow Across Tube Banks A common geometry for two-fluid heat exchangers. Aligned and Staggered Arrays: Aligned: V max = S T S T V D S T max S D D T T S V max = T V S 2 D D S T D ( S D D) Staggered: V = V if 2( S D) ( S D) or, if 2( ) ( )
20 Nu = C Re N 10 m D 1 D,max L 2000 Re 40, 000 Pr = 0.7 D,max where Re D,max ρvmaxd µ more general form: m 1/3 D = ReD,max Pr L 10 Nu C N 2000 Re 40,000 Pr 0.7 D,max If N L < 10, Nu = C Nu D ( 10) 2 D N < ( N 10) L L
21
22 Flow Conditions: How do convection coefficients vary from row-to-row in an array? How do flow conditions differ between the two configurations? Why should an aligned array not be used for S T /S L < 0.7? Average Nusselt Number for an Isothermal Array [Zukauskas]: Nu C C ( ) 1/4 m 0.36 D = 2 ReD,maxPr Pr/ Prs Cm, Table 7.7 ; C Table 7.8 All properties are evaluated at ( T + T )/2 except for Pr s. i 2 o
23
24
25 Fluid Outlet Temperature (T o ) : Ts T o πdnh = exp T T ρvn S c s i T T p N = N x N T L What may be said about T o as N? Total Heat Rate: = A = N( π DL) q ha T T = m s m ( T T ) ( T T ) s i s o T n T s s T T i o s Pressure Drop: 2 ρvmax p = NLχ f 2 χ, f Figures 7.13 and 7.14
26
27
28
29
30
31
32
33 7.8 The Sphere and Packed Beds Flow over a sphere Boundary layer development is similar to that for flow over a cylinder, involving transition and separation. ( 1/ 2 2/3) 0.4 ( ) 1/ 4 Nu = Re Re Pr µ / µ D D D s What are the limiting values of the Nusselt number and the convection coefficient for slow flows over small spheres. CD Figure 7.8 Gas Flow through a Packed Bed Flow is characterized by tortuous paths through a bed of fixed particles. Large surface area per unit volume renders configuration desirable for the transfer and storage of thermal energy.
34 For a packed bed of spheres: ε j H = 2.06 Re D ε void fraction (0.3 < ε < 0.5) A q ha T = p, t m, total surface area of particles pt Ts T ha o pt, = exp Ts T i ρvac, bc p Acb, cross-sectional area of bed
35 7.7 Impinging Jet Characterized by large convection coefficients and used for cooling and heating in numerous manufacturing, electronic and aeronautic applications. Flow and Heat Transfer for a Circular or Rectangular Jet: Significant Features: Mixing and velocity profile development in the free jet. Stagnation point and zone. Velocity profile development in the wall jet.
36 Local Nusselt number distribution: Average Nusselt number: hd k VD e Re = ν ( ) h Nu = = f Re, Pr, A r,h / Dh h, A r from Fig Correlations Section Jet Arrays Slot Jets What is the nature and effect of jet interactions and discharge conditions? Nusselt number correlations for arrays of circular and slot jets Section
37
38 Problem: Extrusion Process Problem 7.63: Cooling of extruded copper wire by convection and radiation. KNOWN: Velocity, diameter, initial temperature and properties of extruded wire. Temperature and velocity of air. Temperature of surroundings. FIND: (a) Differential equation for temperature distribution T(x) along the wire, (b) Exact solution for negligible radiation and corresponding value of temperature at prescribed length ( x = L = 5m) of wire, (c) Effect of radiation on temperature of wire at prescribed length. Effect of wire velocity and emissivity on temperature distribution.
39 Problem: 7.78 Measurement of combustion gas temperature with a spherical thermocouple junction. KNOWN: Velocity and temperature of combustion gases. Diameter and emissivity of thermocouple junction. Combustor temperature. FIND: (a) Time to achieve 98% of maximum thermocouple temperature rise for negligible radiation, (b) Steady-state thermocouple temperature, (c) Effect of gas velocity and thermocouple emissivity on measurement error. SCHEMATIC:
40 ASSUMPTIONS: (1) Validity of lumped capacitance analysis, (2) Constant properties, (3) Negligible conduction through lead wires, (4) Radiation exchange between small surface and a large enclosure (parts b and c). PROPERTIES: Thermocouple: 0.1 ε 1.0, k = 100 W/m K, c = 385 J/kg K, ρ = 8920 kg/m 3 ; Gases: k = 0.05 W/m K, ν = m 2 /s, Pr = ANALYSIS: (a) If the lumped capacitance analysis may be used, it follows from Equation 5.5 that ρvc Ti T Dρc t = ln = ln 50 has T T 6h ( ). Neglecting the viscosity ratio correlation for variable property effects, use of V = 5 m/s with the Whitaker correlation yields ( ) ( 1/2 2/3) 0.4 VD 5 m s( 0.001m) NuD = hd k = ReD ReD Pr ReD = = = 100 ν m s ( ( ) ( ) )( ) 0.05 W m K h = / / = 328 W m 2 K 0.001m Since Bi = h( ro 3) k = , the lumped capacitance method may be used. ( 3 ) 0.001m 8920 kg m 385J kg K t = ln( 50) = 6.83s 6 328W m 2 K
41 (b) Performing an energy balance on the junction, q conv = q rad. Hence, evaluating radiation exchange from Equation 1.7 and with ε = 0.5, ( ) ε σ ( 4 4) = has T T As T Tc W m 2 K T K T 400 K W m 2 K ( ) = ( ) T = 936 K Parametric calculations to determine the effects of V and ε yield the following results: Temperature, T(K) 950 Temperature, T(K) Velocity, V(m/s) Emissivity, epsilon = Emissivity Velocity, V = 5 m/s
42 Since the temperature recorded by the thermocouple junction increases with increasing V and decreasing ε, the measurement error, T - T, decreases with increasing V and decreasing ε. The error is due to net radiative transfer from the junction (which depresses T) and hence should decrease with decreasing ε. For a prescribed heat loss, the temperature difference ( T - T) decreases with decreasing convection resistance, and hence with increasing h(v). COMMENTS: To infer the actual gas temperature (1000 K) from the measured result (936 K), correction would have to be made for radiation exchange with the cold surroundings. What measures may be taken to reduce the error associated with radiation effects?
External Flow: Flow over Bluff Objects (Cylinders, Spheres, Packed Beds) and Impinging Jets
External Flow: Flow over Bluff Object (Cylinder, Sphere, Packed Bed) and Impinging Jet he Cylinder in Cro Flow - Condition depend on pecial feature of boundary layer development, including onet at a tagnation
More informationChapter 7: External Forced Convection. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University
Chapter 7: External Forced Convection Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Objectives When you finish studying this chapter, you should be able to: Distinguish between
More informationExternal Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
External Forced Convection Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Drag and Heat Transfer in External flow Fluid flow over solid bodies is responsible
More informationQUESTION ANSWER. . e. Fourier number:
QUESTION 1. (0 pts) The Lumped Capacitance Method (a) List and describe the implications of the two major assumptions of the lumped capacitance method. (6 pts) (b) Define the Biot number by equations and
More informationENGR Heat Transfer II
ENGR 7901 - Heat Transfer II External Flows 1 Introduction In this chapter we will consider several fundamental flows, namely: the flat plate, the cylinder, the sphere, several other body shapes, and banks
More informationUNIT II CONVECTION HEAT TRANSFER
UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid
More informationPROBLEM Node 5: ( ) ( ) ( ) ( )
PROBLEM 4.78 KNOWN: Nodal network and boundary conditions for a water-cooled cold plate. FIND: (a) Steady-state temperature distribution for prescribed conditions, (b) Means by which operation may be extended
More informationChapter 7: External Forced Convection
Chapter 7: External Forced Convection Yoav Peles Department of Mechanical, Aerospace and Nuclear Engineering Rensselaer Polytechnic Institute Copyright The McGraw-Hill Companies, Inc. Permission required
More informationINSTRUCTOR: 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 informationTime-Dependent Conduction :
Time-Dependent Conduction : The Lumped Capacitance Method Chapter Five Sections 5.1 thru 5.3 Transient Conduction A heat transfer process for which the temperature varies with time, as well as location
More informationTransient Heat Transfer Experiment. ME 331 Introduction to Heat Transfer. June 1 st, 2017
Transient Heat Transfer Experiment ME 331 Introduction to Heat Transfer June 1 st, 2017 Abstract The lumped capacitance assumption for transient conduction was tested for three heated spheres; a gold plated
More informationConvection Heat Transfer. Introduction
Convection Heat Transfer Reading Problems 12-1 12-8 12-40, 12-49, 12-68, 12-70, 12-87, 12-98 13-1 13-6 13-39, 13-47, 13-59 14-1 14-4 14-18, 14-24, 14-45, 14-82 Introduction Newton s Law of Cooling Controlling
More informationIntroduction to Heat and Mass Transfer. Week 5
Introduction to Heat and Mass Transfer Week 5 Critical Resistance Thermal resistances due to conduction and convection in radial systems behave differently Depending on application, we want to either maximize
More informationIn Chapter 6 we considered the general and theoretical aspects of forced
cen58933_ch07.qxd 9/4/2002 12:12 PM Page 367 EXTERNAL FORCED CONVECTION CHAPTER 7 In Chapter 6 we considered the general and theoretical aspects of forced convection, with emphasis on differential formulation
More informationFundamental Concepts of Convection : Flow and Thermal Considerations. Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.
Fundamental Concepts of Convection : Flow and Thermal Considerations Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.3 6.1 Boundary Layers: Physical Features Velocity Boundary Layer
More informationExamination Heat Transfer
Examination Heat Transfer code: 4B680 date: June 13, 2008 time: 14.00-17.00 Note: There are 4 questions in total. The first one consists of independent subquestions. If possible and necessary, guide numbers
More information11. Advanced Radiation
. Advanced adiation. Gray Surfaces The gray surface is a medium whose monochromatic emissivity ( λ does not vary with wavelength. The monochromatic emissivity is defined as the ratio of the monochromatic
More informationAutumn 2005 THERMODYNAMICS. Time: 3 Hours
CORK INSTITUTE OF TECHNOOGY Bachelor of Engineering (Honours) in Mechanical Engineering Stage 3 (Bachelor of Engineering in Mechanical Engineering Stage 3) (NFQ evel 8) Autumn 2005 THERMODYNAMICS Time:
More informationHeat Transfer Convection
Heat ransfer Convection Previous lectures conduction: heat transfer without fluid motion oday (textbook nearly 00 pages) Convection: heat transfer with fluid motion Research methods different Natural Convection
More informationConvection Workshop. Academic Resource Center
Convection Workshop Academic Resource Center Presentation Outline Understanding the concepts Correlations External Convection (Chapter 7) Internal Convection (Chapter 8) Free Convection (Chapter 9) Solving
More informationPROBLEM 9.3. KNOWN: Relation for the Rayleigh number. FIND: Rayleigh number for four fluids for prescribed conditions. SCHEMATIC:
PROBEM.3 KNOWN: Relation for the Rayleigh number. FIND: Rayleigh number for four fluids for prescribed conditions. ASSUMPTIONS: (1 Perfect gas behavior for specified gases. PROPERTIES: Table A-4, Air (400K,
More informationChapter 10: Steady Heat Conduction
Chapter 0: Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another hermodynamics gives no indication of
More informationFIND: (a) Sketch temperature distribution, T(x,t), (b) Sketch the heat flux at the outer surface, q L,t as a function of time.
PROBLEM 5.1 NOWN: Electrical heater attached to backside of plate while front surface is exposed to convection process (T,h); initially plate is at a uniform temperature of the ambient air and suddenly
More informationECE309 INTRODUCTION TO THERMODYNAMICS & HEAT TRANSFER. 3 August 2004
ECE309 INTRODUCTION TO THERMODYNAMICS & HEAT TRANSFER 3 August 004 Final Examination R. Culham This is a 3 hour, closed-book examination. You are permitted to use one 8.5 in. in. crib sheet (both sides),
More informationChapter 4: Transient Heat Conduction. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University
Chapter 4: Transient Heat Conduction Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Objectives When you finish studying this chapter, you should be able to: Assess when the spatial
More informationExamination Heat Transfer
Examination Heat Transfer code: 4B680 date: 17 january 2006 time: 14.00-17.00 hours NOTE: There are 4 questions in total. The first one consists of independent sub-questions. If necessary, guide numbers
More informationLaminar Flow. Chapter ZERO PRESSURE GRADIENT
Chapter 2 Laminar Flow 2.1 ZERO PRESSRE GRADIENT Problem 2.1.1 Consider a uniform flow of velocity over a flat plate of length L of a fluid of kinematic viscosity ν. Assume that the fluid is incompressible
More informationIf 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 informationForced Convection Around Obstacles
Chapter 4 Forced Convection Around Obstacles 4.1. Description of the flow This chapter is devoted to heat transfer on bodies immersed in a stream. We consider a solid characterized by the length scale
More informationPROBLEM 7.2 1/3. (b) The local convection coefficient, Eq. 7.23, and heat flux at x = L are 1/2 1/3
PROBLEM 7. KNOWN: Temperature and velocity of engine oil. Temperature and length of flat plate. FIND: (a) Velocity and thermal boundary layer thickness at trailing edge, (b) Heat flux and surface shear
More informationIntroduction to Heat and Mass Transfer. Week 7
Introduction to Heat and Mass Transfer Week 7 Example Solution Technique Using either finite difference method or finite volume method, we end up with a set of simultaneous algebraic equations in terms
More informationTrue/False. Circle the correct answer. (1pt each, 7pts total) 3. Radiation doesn t occur in materials that are transparent such as gases.
ME 323 Sample Final Exam. 120pts total True/False. Circle the correct answer. (1pt each, 7pts total) 1. A solid angle of 2π steradians defines a hemispherical shell. T F 2. The Earth irradiates the Sun.
More informationIntroduction to Heat Transfer
FIFTH EDITION Introduction to Heat Transfer FRANK P. INCROPERA College of Engineering University ofnotre Dame DAVID P. DEWITT School of Mechanical Purdue University Engineering THEODORE L. BERGMAN Department
More informationApplication of Thermocouples in Steady Laminar Flames
Appendix A Application of Thermocouples in Steady Laminar Flames Despite the simplicity of thermocouple theory [Wright, 1995] and construction, thermocouple thermometry in combustion environments is anything
More informationME 331 Homework Assignment #6
ME 33 Homework Assignment #6 Problem Statement: ater at 30 o C flows through a long.85 cm diameter tube at a mass flow rate of 0.020 kg/s. Find: The mean velocity (u m ), maximum velocity (u MAX ), and
More informationCHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW
CHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW 4.1 Introduction Boundary layer concept (Prandtl 1904): Eliminate selected terms in the governing equations Two key questions (1) What are the
More informationMECH 375, Heat Transfer Handout #5: Unsteady Conduction
1 MECH 375, Heat Transfer Handout #5: Unsteady Conduction Amir Maleki, Fall 2018 2 T H I S PA P E R P R O P O S E D A C A N C E R T R E AT M E N T T H AT U S E S N A N O PA R T I - C L E S W I T H T U
More informationHeat Transfer F12-ENG Lab #4 Forced convection School of Engineering, UC Merced.
1 Heat Transfer F12-ENG-135 - Lab #4 Forced convection School of Engineering, UC Merced. October 23, 2012 1 General purpose of the Laboratory To gain a physical understanding of the behavior of the average
More informationChapter 11: Heat Exchangers. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University
Chapter 11: Heat Exchangers Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Objectives When you finish studying this chapter, you should be able to: Recognize numerous types of
More informationASSUMPTIONS: (1) One-dimensional, radial conduction, (2) Constant properties.
PROBLEM 5.5 KNOWN: Diameter and radial temperature of AISI 00 carbon steel shaft. Convection coefficient and temperature of furnace gases. FIND: me required for shaft centerline to reach a prescribed temperature.
More information1 Conduction Heat Transfer
Eng690 - Formula Sheet 2 Conduction Heat Transfer. Cartesian Co-ordinates q x xa x A x dt dx R th A 2 T x 2 + 2 T y 2 + 2 T z 2 + q T T x) plane wall of thicness 2, x 0 at centerline, T s, at x, T s,2
More informationPHYSICAL MECHANISM OF CONVECTION
Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter
More informationEmpirical Co - Relations approach for solving problems of convection 10:06:43
Empirical Co - Relations approach for solving problems of convection 10:06:43 10:06:44 Empirical Corelations for Free Convection Use T f or T b for getting various properties like Re = VL c / ν β = thermal
More information1 Conduction Heat Transfer
Eng6901 - Formula Sheet 3 (December 1, 2015) 1 1 Conduction Heat Transfer 1.1 Cartesian Co-ordinates q x = q xa x = ka x dt dx R th = L ka 2 T x 2 + 2 T y 2 + 2 T z 2 + q k = 1 T α t T (x) plane wall of
More informationFINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT OF A HEATED SQUARE HOLLOW CYLINDER IN A LID-DRIVEN RECTANGULAR ENCLOSURE
Proceedings of the International Conference on Mechanical Engineering 2011 (ICME2011) 18-20 December 2011, Dhaka, Bangladesh ICME11-TH-014 FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT
More informationMYcsvtu Notes HEAT TRANSFER BY CONVECTION
www.mycsvtunotes.in HEAT TRANSFER BY CONVECTION CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in
More informationRelationship to Thermodynamics. Chapter One Section 1.3
Relationship to Thermodynamics Chapter One Section 1.3 Alternative Formulations Alternative Formulations Time Basis: CONSERVATION OF ENERGY (FIRST LAW OF THERMODYNAMICS) An important tool in heat transfer
More informationTankExampleNov2016. Table of contents. Layout
Table of contents Task... 2 Calculation of heat loss of storage tanks... 3 Properties ambient air Properties of air... 7 Heat transfer outside, roof Heat transfer in flow past a plane wall... 8 Properties
More informationECE309 INTRODUCTION TO THERMODYNAMICS & HEAT TRANSFER. 10 August 2005
ECE309 INTRODUCTION TO THERMODYNAMICS & HEAT TRANSFER 0 August 2005 Final Examination R. Culham & M. Bahrami This is a 2 - /2 hour, closed-book examination. You are permitted to use one 8.5 in. in. crib
More informationFORMULA SHEET. General formulas:
FORMULA SHEET You may use this formula sheet during the Advanced Transport Phenomena course and it should contain all formulas you need during this course. Note that the weeks are numbered from 1.1 to
More informationConvective Mass Transfer
Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface
More informationChapter 7: Natural Convection
7-1 Introduction 7- The Grashof Number 7-3 Natural Convection over Surfaces 7-4 Natural Convection Inside Enclosures 7-5 Similarity Solution 7-6 Integral Method 7-7 Combined Natural and Forced Convection
More informationCircle one: School of Mechanical Engineering Purdue University ME315 Heat and Mass Transfer. Exam #2. April 3, 2014
Circle one: Div. 1 (12:30 pm, Prof. Choi) Div. 2 (9:30 am, Prof. Xu) School of Mechanical Engineering Purdue University ME315 Heat and Mass Transfer Exam #2 April 3, 2014 Instructions: Write your name
More informationFLUID MECHANICS. Chapter 9 Flow over Immersed Bodies
FLUID MECHANICS Chapter 9 Flow over Immersed Bodies CHAP 9. FLOW OVER IMMERSED BODIES CONTENTS 9.1 General External Flow Characteristics 9.3 Drag 9.4 Lift 9.1 General External Flow Characteristics 9.1.1
More informationHEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1
HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1 CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the
More informationIntroduction to Heat and Mass Transfer. Week 14
Introduction to Heat and Mass Transfer Week 14 Next Topic Internal Flow» Velocity Boundary Layer Development» Thermal Boundary Layer Development» Energy Balance Velocity Boundary Layer Development Velocity
More informationPROBLEM 1.3. dt T1 T dx L 0.30 m
PROBLEM 1.3 KNOWN: Inner surface temperature and thermal conductivity of a concrete wall. FIND: Heat loss by conduction through the wall as a function of outer surface temperatures ranging from -15 to
More informationChapter 9 NATURAL CONVECTION
Heat and Mass Transfer: Fundamentals & Applications Fourth Edition in SI Units Yunus A. Cengel, Afshin J. Ghajar McGraw-Hill, 2011 Chapter 9 NATURAL CONVECTION PM Dr Mazlan Abdul Wahid Universiti Teknologi
More informationChapter 3 NATURAL CONVECTION
Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGraw-Hill Companies,
More information6 Empirical and Practical
6 Empirical and Practical Forced-Convection Relations for Heat Transfer CHAPTER 6-1 INTRODUCTION The discussion and analyses of Chapter 5 have shown how forced-convection heat transfer may be calculated
More information( )( ) PROBLEM 9.5 (1) (2) 3 (3) Ra g TL. h L (4) L L. q ( ) 0.10/1m ( C /L ) Ra 0.59/0.6m L2
PROBEM 9.5 KNOWN: Heat transfer rate by convection from a vertical surface, 1m high by 0.m wide, to quiescent air that is 0K cooler. FIND: Ratio of the heat transfer rate for the above case to that for
More informationInternal Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Internal Forced Convection Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Introduction Pipe circular cross section. Duct noncircular cross section. Tubes small-diameter
More informationNatural convection heat transfer around a horizontal circular cylinder near an isothermal vertical wall
Natural convection heat transfer around a horizontal circular cylinder near an isothermal vertical wall Marcel Novomestský 1, Richard Lenhard 1, and Ján Siažik 1 1 University of Žilina, Faculty of Mechanical
More information1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used?
1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used?. During unsteady state heat transfer, can the temperature
More informationPrinciples of Convection
Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid
More informationConvection. 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 informationIntroduction to Heat and Mass Transfer. Week 9
Introduction to Heat and Mass Transfer Week 9 補充! Multidimensional Effects Transient problems with heat transfer in two or three dimensions can be considered using the solutions obtained for one dimensional
More informationPROBLEM 8.3 ( ) p = kg m 1m s m 1000 m = kg s m = bar < P = N m 0.25 m 4 1m s = 1418 N m s = 1.
PROBLEM 8.3 KNOWN: Temperature and velocity of water flow in a pipe of prescribed dimensions. FIND: Pressure drop and pump power requirement for (a) a smooth pipe, (b) a cast iron pipe with a clean surface,
More informationINSTRUCTOR: 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 5 th Edition, John Wiley and Sons Chapter 9 Natural
More informationPROBLEM 1.2 ( ) 25 C 15 C dx L 0.30 m Ambient air temperature, T2 (C)
PROBLEM 1.2 KNOWN: Inner surface temperature and thermal conductivity of a concrete wall. FIND: Heat loss by conduction through the wall as a function of ambient air temperatures ranging from -15 to 38
More informationConvection. U y. U u(y) T s. T y
Convection Heat transfer in the presence of a fluid motion on a solid surface Various mechanisms at play in the fluid: - advection physical transport of the fluid - diffusion conduction in the fluid -
More informationMIXED CONVECTION HEAT TRANSFER FROM A PARTICLE IN SUPERCRITICAL WATER
THERMAL SCIENCE, Year 2016, Vol. 20, No. 2, pp. 483-492 483 MIXED CONVECTION HEAT TRANSFER FROM A PARTICLE IN SUPERCRITICAL WATER by Liping WEI, Youjun LU*, and Jinjia WEI State Key Laboratory of Multiphase
More informationDepartment of Mechanical Engineering
Department of Mechanical Engineering AMEE401 / AUTO400 Aerodynamics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy HOMEWORK ASSIGNMENT #2 QUESTION 1 Clearly there are two mechanisms responsible
More informationELEC9712 High Voltage Systems. 1.2 Heat transfer from electrical equipment
ELEC9712 High Voltage Systems 1.2 Heat transfer from electrical equipment The basic equation governing heat transfer in an item of electrical equipment is the following incremental balance equation, with
More informationCHME 302 CHEMICAL ENGINEERING LABOATORY-I EXPERIMENT 302-V FREE AND FORCED CONVECTION
CHME 302 CHEMICAL ENGINEERING LABOATORY-I EXPERIMENT 302-V FREE AND FORCED CONVECTION OBJECTIVE The objective of the experiment is to compare the heat transfer characteristics of free and forced convection.
More informationCoolant. Circuits Chip
1) A square isothermal chip is of width w=5 mm on a side and is mounted in a subtrate such that its side and back surfaces are well insulated, while the front surface is exposed to the flow of a coolant
More informationCalculations on a heated cylinder case
Calculations on a heated cylinder case J. C. Uribe and D. Laurence 1 Introduction In order to evaluate the wall functions in version 1.3 of Code Saturne, a heated cylinder case has been chosen. The case
More informationMaximum Heat Transfer Density From Finned Tubes Cooled By Natural Convection
Maximum Heat Transfer Density From Finned Tubes Cooled By Natural Convection Ahmed Waheed Mustafa 1 Mays Munir Ismael 2 AL-Nahrain University College of Engineering Mechanical Engineering Department ahmedwah@eng.nahrainuniv.edu.iq
More informationTable of Contents. Foreword... xiii. Preface... xv
Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...
More informationReview: Conduction. Breaking News
CH EN 3453 Heat Transfer Review: Conduction Breaking News No more homework (yay!) Final project reports due today by 8:00 PM Email PDF version to report@chen3453.com Review grading rubric on Project page
More informationANALYSIS OF HEAT AND MASS TRANSFER OF THE DIFFERENT MOIST OBJECT GEOMETRIES WITH AIR SLOT JET IMPINGING FOR FORCED CONVECTION DRYING Doğan Engin ALNAK a, Koray KARABULUT b* a Cumhuriyet University, Technology
More informationTransport processes. 7. Semester Chemical Engineering Civil Engineering
Transport processes 7. Semester Chemical Engineering Civil Engineering 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite Control Volume Analysis 4. Differential Analysis of Fluid Flow 5. Viscous
More informationChapter 5 Time-Dependent Conduction
Chapter 5 Time-Dependent Conduction 5.1 The Lumped Capacitance Method This method assumes spatially uniform solid temperature at any instant during the transient process. It is valid if the temperature
More informationHeat Transfer. Solutions for Vol I _ Classroom Practice Questions. Chapter 1 Conduction
Heat ransfer Solutions for Vol I _ lassroom Practice Questions hapter onduction r r r K K. ns: () ase (): Higher thermal conductive material is inside and lo thermal conductive material is outside K K
More information6.2 Governing Equations for Natural Convection
6. Governing Equations for Natural Convection 6..1 Generalized Governing Equations The governing equations for natural convection are special cases of the generalized governing equations that were discussed
More informationStudy of Temperature Distribution Along the Fin Length
Heat Transfer Experiment No. 2 Study of Temperature Distribution Along the Fin Length Name of the Student: Roll No: Department of Mechanical Engineering for Women, Pune. Aim: ˆ Measuring the temperature
More informationLumped Mass Heat Transfer Experiment
Lumped Mass Heat Transfer Experiment Thermal Network Solution with TNSolver Bob Cochran Applied Computational Heat Transfer Seattle, WA TNSolver@heattransfer.org ME 331 Introduction to Heat Transfer University
More informationa. Fourier s law pertains to conductive heat transfer. A one-dimensional form of this law is below. Units are given in brackets.
QUESTION An understanding of the basic laws governing heat transfer is imperative to everything you will learn this semester. Write the equation for and explain the following laws governing the three basic
More informationPROBLEM ρ v (kg/m 3 ) ANALYSIS: The critical heat flux can be estimated by Eq with C = 0.
PROBLEM 10.10 KNOWN: Fluids at 1 atm: mercury, ethanol, R-14a. FIND: Critical heat flux; compare with value for water also at 1 atm. ASSUMPTIONS: (1) Steady-state conditions, () Nucleate pool boiling.
More informationENG Heat Transfer II 1. 1 Forced Convection: External Flows Flow Over Flat Surfaces... 4
ENG7901 - Heat Transfer II 1 Contents 1 Forced Convection: External Flows 4 1.1 Flow Over Flat Surfaces............................. 4 1.1.1 Non-Dimensional form of the Equations of Motion.......... 4
More informationTHE INFLUENCE OF INCLINATION ANGLE ON NATURAL CONVECTION IN A RECTANGULAR ENCLOSURE
THE INFLUENCE OF INCLINATION ANGLE ON NATURAL CONVECTION IN A RECTANGULAR ENCLOSURE Thamer Khalif Salem Mechanical Engineering, College of Engineering, Tikrit University, IRAQ. thamer_khalif@yahoo.com
More informationModeling of Fluid Flow and Heat Transfer for Optimization of Pin-Fin Heat Sinks
Modeling of Fluid Flow and Heat Transfer for Optimization of Pin-Fin Heat Sinks by Waqar Ahmed Khan Athesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree
More informationChapter 10: Boiling and Condensation 1. Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI.
Chapter 10: Boiling and Condensation 1 1 Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI. Objectives When you finish studying this chapter, you should be able to: Differentiate between evaporation
More informationMasters in Mechanical Engineering. Problems of incompressible viscous flow. 2µ dx y(y h)+ U h y 0 < y < h,
Masters in Mechanical Engineering Problems of incompressible viscous flow 1. Consider the laminar Couette flow between two infinite flat plates (lower plate (y = 0) with no velocity and top plate (y =
More informationFall 2014 Qualifying Exam Thermodynamics Closed Book
Fall 2014 Qualifying Exam Thermodynamics Closed Book Saturated ammonia vapor at 200 O F flows through a 0.250 in diameter tube. The ammonia passes through a small orifice causing the pressure to drop very
More informationPhone: , For Educational Use. SOFTbank E-Book Center, Tehran. Fundamentals of Heat Transfer. René Reyes Mazzoco
8 Fundamentals of Heat Transfer René Reyes Mazzoco Universidad de las Américas Puebla, Cholula, Mexico 1 HEAT TRANSFER MECHANISMS 1.1 Conduction Conduction heat transfer is explained through the molecular
More informationChapter 6 Laminar External Flow
Chapter 6 aminar Eternal Flow Contents 1 Thermal Boundary ayer 1 2 Scale analysis 2 2.1 Case 1: δ t > δ (Thermal B.. is larger than the velocity B..) 3 2.2 Case 2: δ t < δ (Thermal B.. is smaller than
More informationUniversity of Rome Tor Vergata
University of Rome Tor Vergata Faculty of Engineering Department of Industrial Engineering THERMODYNAMIC AND HEAT TRANSFER HEAT TRANSFER dr. G. Bovesecchi gianluigi.bovesecchi@gmail.com 06-7259-727 (7249)
More informationOn the influence of tube row number for mixed convection around micro tubes
Thessaloniki, Greece, 22-24 August 211 On the influence of tube row number for mixed convection around micro tubes Chuanshan DAI, Qiuxiang WANG, Biao LI * Corresponding author: Tel.: +86-22274183; Fax:
More informationBen Wolfe 11/3/14. Figure 1: Theoretical diagram showing the each step of heat loss.
Condenser Analysis Water Cooled Model: For this condenser design there will be a coil of stainless steel tubing suspended in a bath of cold water. The cold water will be stationary and begin at an ambient
More information