Chapter 6 Fundamental Concepts of Convection
|
|
- Shonda Cummings
- 5 years ago
- Views:
Transcription
1 Chapter 6 Fundamental Concepts of Convection
2 6.1 The Convection Boundary Layers Velocity boundary layer: τ surface shear stress: s = μ u local friction coeff.: C f y y=0 τ s ρu / (6.) (6.1) Thermal boundary layer: local heat flux: q s = k T f local heat transfer coeff.: y y=0 q " kf T / y s y= 0 h = = T T T T s s (6.3) (6.5)
3 Concentration boundary layer: local species flux: " CA NA = DAB [kmol/s m ] y y= 0 " ρ or (mass basis): A na = DAB [kg/s m ] y y= 0 " N D C / y As, local mass transfer coeff.: hm = = C C C C AB A y= 0 As, A, As, A, (6.6) (6.9) or (mass basis): h m = D ABρ A / y y=0 ρ A,s ρ A,
4 6.1.4 Significance of the Boundary Layers Velocity boundary layer: always exists for flow over any surface Thermal boundary layer: exists if the surface and free stream temperature differ Concentration boundary layer: exists if the surface concentration of a species differs from the free stream value The principal manifestations and boundary layer parameters are Velocity boundary layer: surface friction and friction coefficient C f Thermal boundary layer: convection heat transfer and heat transfer convection coefficient h Concentration boundary layer: convection mass transfer and mass transfer convection coefficient h m
5 6. Local and Average Convection Coefficients 6..1 Heat Transfer The local heat flux q may be expressed as (Newton's law of cooling) q = h(t s -T ), h = heat transfer convection coeff. = f (fluid properties, surface geometry, flow conditions) The total heat transfer rate q may be obtained by integration q = qda = ( T T ), if T s is uniform A s s hda s s As (6.10-1) = ha ( T ), s 1 where h = hdas. A A s s (6.13) s T
6 6.. Mass Transfer Similar for mass transfer of species A, we have N = h ( C C ) [kmol/s m ] where or " A m A, s A, N = h A ( C C ) [kmol/s] A m s A, s A, n n h = m A m s s h da = h ( ρ ρ ) [kg/s m ] " A m A, s A, = h A ( ρ ρ ) [kg/s] A m s A, s A, --local --average --Molar transfer rate (6.15) (6.16) (6.18) --Mass transfer rate (6.19)
7 We can also write Fick s law on a mass basis by multiplying Eq. 6.7 by M A to yield " ρa na = DAB = hm( ρa, s ρa, ) y h m = y= 0 D ρ / y AB A y= 0 ρ ρ A, s A, (6.0) (6.1) The value of C A,s or ρ A,s can be determined by assuming thermodynamic equilibrium at the interface between the gas and the liquid or solid surface. Thus, C A, s p ( T ) sat s = R T (6.)
8 6..3 The Problem of Convection The local flux and/or the total transfer rate are of paramount importance in any convection problem. So, determination of these coefficients (local h or h m and average h or h m ) is viewed as the problem of convection. However, the problem is not a simple one, as h or h = f m (fluid properties, surface geometry, flow conditions) i.e., ρμ,, k, c f p, f EXs
9 6.3 Laminar and Turbulent Flow Critical Reynolds no. where transition from laminar boundary layer to turbulent occurs: Re x,c = ρu x c μ = EX 6.4
10 6.4 The Boundary Layer Equations (-D, Steady) Boundary Layer Equations for Laminar Flow For the steady, two-dimensional flow of an incompressible fluid with constant properties, the following equations are involved. (Read 6S.1 for detailed derivation.) u x v y continuity eq.: + = 0 (D.1)
11 momentum eq. (incompressible): energy equation: species equations: X y u x u x p y u v x u u = + μ ρ Y y v x v y p y v v x v u = + μ ρ y-dir. x-dir. A AB N y C x C D y C v x C u A A A A & + + = + (D.6) (D.) (D.3) q y T x T k y T v x T u c p & Φ = + μ ρ where u v u v y x x y μ μ Φ= (D.4) (D.5) energy transport thru convection heat transport thru conduction heat generation viscous dissipation
12
13 Boundary layer approximations: u >> v u u v v Velocity boundary layer >>,, y x y x T y T >> x Thermal boundary layer CA CA >> y x Concentration boundary layer Usual additional simplifications: incompressible, constant properties, negligible body forces, nonreacting, no energy generation
14 Eqs. 6.7 is unchanged and the x-mom equation reduces to u u 1 dp u u + v = + ν x y ρ dx y (6.8) The energy equation reduces to T u x T + v y energy transport thru convection and the species equation becomes C A C A CA u + v = DAB x y y T = α y ν u + c p y heat transport thru conduction usually negligible (6.9) (6.30) For incompressible, constant property flow, Eq. (6.8) is uncoupled from (6.9) & (6.30). Eqs. (6.7) & (6.8) need to be solved first, for the velocity field u(x, y) and v(x, y), before (6.9) & (6.30) can be solved, i.e., the temperature and species fields are coupled to the velocity field.
15 6.5 Boundary Layer Similarity: The Normalized Convection Transfer Equations Boundary Layer Similarity Parameters Defining x* x and y* y L is the characteristic length L L u* u and v* V V v V is the free stream velocity T* T T s T and T C A * C C A A,s s C A, C A,s we arrive at the convection transfer equations and their boundary conditions in nondimensional form, as shown in Table 6.1. Dimensionless groups: Reynolds no.: ReL Prandtl no.: Pr v Schmidt no.: Sc α v D VL v AB
16 The final dimensionless governing eqs.: (6.35)-(6.37)--similar in form u* u * x* u* T * x * u * x * + v * y * = 0 u* + v* y* = dp* dx * + Re 1 u * L y* + v* T * y* = 1 Re L Pr T * y* u* C A * x * + v* C A * y* = 1 C A * Re L Sc y* (6.35) (6.36) (6.37)
17 6.5. Functional Form of the Solutions From (6.35), we can write u* = f x*, y*, Re L, dp dx where dp*/dx* depends on the surface geometry. * * The shear stress and the friction coefficient at the surface are τ s = μ u = μv y L u* y=0 y* y*= 0 C f = τ s ρv / = Re u * = f ( x*, ReL) (6.45, 46) L y * y*=0 Re For a prescribed geometry, (6.45) is universally applicable. L (6.44)
18 From (6.36) T* = f x*, y*, Re h = k f (T T s ) L (T s T ) EX 6.5 L, Pr, dp dx T * =+ k f T * y* L y*=0 y * y*=0 Nusselt number can be defined as Nu hl =+ T * k f y* y*=0 For a prescribed geometry, from (6.47) Nu = f ( x *, ReL, Pr) The spatially average Nusselt number is then hl Nu = = f ( ReL, Pr) k f Similarly for mass transfer, h L Sh = = f Re D * * ( Sc) m L, AB (6.47) (6.48) (6.49) (6.50) (6.54)
19 6.6 Physical Significance of the Dimensionless Parameters See Table 6.. For heat transfer, the important dimensionless parameters are: Re, Nu, Pr, Bi, Fo, Pe (= RePr), Gr For mass transfer, Re, Sh, Sc, Bi m, Fo m, Le (= α/d AB ) For boundary layer thicknesses, δ n δ n δ n 1 Pr, Sc, t Le n = for laminar boundary layer δt δc δc 3 (6.55, 56, 58) δ δ δ for turbulent boundary layer (why?) t c
20 6.7 Boundary Layer Analogies The Heat and Mass Transfer Analogy Since the dimensionless relations that govern the thermal and the concentration boundary layers are the same, the heat and mass transfer relations for a particular geometry are interchangeable.
21 With and and equivalent functions, f (x*, Re L ), Then, and we have Nu = f *, Sh = f *, n ( x Re L ) Pr ( ) n x Re L Sc Nu Sh hl k hl/ D = = n n n n Pr Sc Pr Sc h h m = / m AB k D AB Le n = ρc p Le 1 n (6.60), n=1/3 for most applications EX 6.6
22 6.7.3 The Reynolds Analogy For dp*/dx* = 0 and Pr = Sc = 1, Eqs are of precisely the same form. Moreover, if dp*/dx*=0, the boundary conditions, also have the same form. From Equations 6.45, 6.48, 6.5, it follows that Re C L f = Nu = Sh (6.66) Replacing Nu and Sh with Stanton number (St) and mass transfer Stanton number (St m ), as defined in (6.67) and (6.68), we have Cf /= St = Stm -- Reynolds Analogy (6.69) h Nu hm Sh St =, Stm = ρvcp RePr V ReSc The modified Reynolds Analogy (or Chilton-Colburn Analogy) is C f C /3 Nu f /3 Sh = StPr j ; H = = StmSc jm = 1/3 1/3 (6.70,71) RePr ReSc Eqs. 6.70, 71 are appropriate for laminar flow when dp*/dx* ~ 0; for turbulent flow, conditions are less sensitive to pressure gradient.
23 6.7. Evaporative Cooling For evaporative cooling shown in Fig. 6.10, where " q add " q conv " q evap + q add If is absent, then " = n A " h fg " = q evap h(t T s ) = h fg h m [ρ A,sat (T s ) ρ A, ] hm T Ts = hfg [ A,sat ( Ts) A, ] h ρ ρ (6.64) Using the heat and mass transfer analogy, (6.64) becomes M A h fg (T T s ) = Rρc p Le /3 [ p A,sat (T s ) T p A, s T ] (6.65) Note: Gas properties ρ, c p, Le should be evaluated at the arithmetic mean temperature of the thermal b. l., T am = (T s +T )/. EX 6.7 (6.6)
24 Special Topic Heat Pipes Representative Ranges of Convection Thermal Resistance h (W/m K) Areal R th,conv (Kcm /W) Natural Convection Air ~5 5,000~400 Oils 0~00 500~50 Water 100~1, ~10 Forced Convection Air 0~00 500~50 Oils 00~,000 50~5 Water 1,000~10,000 10~1 Microchannel Cooling 40, Impinging Jet Cooling,400~49, ~0.0 Heat Pipe 0.049* * based on THERMACORE 5 mm heat pipe having capacity of 0W with ΔT=5K.
25 The Working Principle of Heat Pipes --Based on phase-change heat transfer Evaporation Section Adiabatic Section Condensation Section The performance of a heat pipe is dictated by its thermal resistance R th and maximum heat load, Q max, which are mainly determined by the evaporation characteristics.
26 A small amount of working fluid (mostly water) is filled in the heat pipe after it is evacuated. 管壁 container Working fluid wick 溝槽燒結金屬金屬網 Advantages of Heat Pipes superior heat spreading ability fast thermal response light weight and flexible low cost simple without active units
Fundamental 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 information6. Laminar and turbulent boundary layers
6. Laminar and turbulent boundary layers John Richard Thome 8 avril 2008 John Richard Thome (LTCM - SGM - EPFL) Heat transfer - Convection 8 avril 2008 1 / 34 6.1 Some introductory ideas Figure 6.1 A boundary
More informationTransport processes. 7. Semester Chemical Engineering Civil Engineering
Transport processes 7. Semester Chemical Engineering Civil Engineering 1 Course plan 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite Control Volume nalysis 4. Differential nalysis of Fluid Flow
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 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 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 informationMechanical Engineering. Postal Correspondence Course HEAT TRANSFER. GATE, IES & PSUs
Heat Transfer-ME GATE, IES, PSU 1 SAMPLE STUDY MATERIAL Mechanical Engineering ME Postal Correspondence Course HEAT TRANSFER GATE, IES & PSUs Heat Transfer-ME GATE, IES, PSU 2 C O N T E N T 1. INTRODUCTION
More informationSummary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer
1. Nusselt number Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer Average Nusselt number: convective heat transfer Nu L = conductive heat transfer = hl where L is the characteristic
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 informationIntroduction to Heat and Mass Transfer. Week 12
Introduction to Heat and Mass Transfer Week 12 Next Topic Convective Heat Transfer» Heat and Mass Transfer Analogy» Evaporative Cooling» Types of Flows Heat and Mass Transfer Analogy Equations governing
More informationENGR Heat Transfer II
ENGR 7901 - Heat Transfer II Convective Heat Transfer 1 Introduction In this portion of the course we will examine convection heat transfer principles. We are now interested in how to predict the value
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 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 informationHeat 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 information10. Buoyancy-driven flow
10. Buoyancy-driven flow For such flows to occur, need: Gravity field Variation of density (note: not the same as variable density!) Simplest case: Viscous flow, incompressible fluid, density-variation
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 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 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 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 informationHeat processes. Heat exchange
Heat processes Heat exchange Heat energy transported across a surface from higher temperature side to lower temperature side; it is a macroscopic measure of transported energies of molecular motions Temperature
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 informationProblem 4.3. Problem 4.4
Problem 4.3 Problem 4.4 Problem 4.5 Problem 4.6 Problem 4.7 This is forced convection flow over a streamlined body. Viscous (velocity) boundary layer approximations can be made if the Reynolds number Re
More informationNumerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15-Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis
More informationMECHANISM BEHIND FREE /NATURAL CONVECTION
CONVECTIVE HEAT TRANSFER By: Prof K. M. Joshi, Assi. Professor, MED, SSAS Institute of Technology, Surat. MECHANISM BEHIND FREE /NATURAL CONVECTION The stagnate layer of fluid in immediate vicinity of
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 informationCONVECTIVE HEAT TRANSFER
CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 3 LAMINAR BOUNDARY LAYER FLOW LAMINAR BOUNDARY LAYER FLOW Boundary
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 informationCONVECTIVE HEAT TRANSFER
CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 4 HEAT TRANSFER IN CHANNEL FLOW BASIC CONCEPTS BASIC CONCEPTS Laminar
More informationLecture 30 Review of Fluid Flow and Heat Transfer
Objectives In this lecture you will learn the following We shall summarise the principles used in fluid mechanics and heat transfer. It is assumed that the student has already been exposed to courses in
More informationUnit operations of chemical engineering
1 Unit operations of chemical engineering Fourth year Chemical Engineering Department College of Engineering AL-Qadesyia University Lecturer: 2 3 Syllabus 1) Boundary layer theory 2) Transfer of heat,
More informationOutline. Definition and mechanism Theory of diffusion Molecular diffusion in gases Molecular diffusion in liquid Mass transfer
Diffusion 051333 Unit operation in gro-industry III Department of Biotechnology, Faculty of gro-industry Kasetsart University Lecturer: Kittipong Rattanaporn 1 Outline Definition and mechanism Theory of
More informationLevel 7 Post Graduate Diploma in Engineering Heat and mass transfer
9210-221 Level 7 Post Graduate Diploma in Engineering Heat and mass transfer 0 You should have the following for this examination one answer book non programmable calculator pen, pencil, drawing instruments
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 informationDimensionless Numbers
1 06.10.2017, 09:49 Dimensionless Numbers A. Salih Dept. of Aerospace Engineering IIST, Thiruvananthapuram The nondimensionalization of the governing equations of fluid flow is important for both theoretical
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 informationForced Convection: Inside Pipe HANNA ILYANI ZULHAIMI
+ Forced Convection: Inside Pipe HANNA ILYANI ZULHAIMI + OUTLINE u Introduction and Dimensionless Numbers u Heat Transfer Coefficient for Laminar Flow inside a Pipe u Heat Transfer Coefficient for Turbulent
More informationLiquid or gas flow through pipes or ducts is commonly used in heating and
cen58933_ch08.qxd 9/4/2002 11:29 AM Page 419 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications. The fluid in such applications
More informationA NUMERICAL APPROACH FOR ESTIMATING THE ENTROPY GENERATION IN FLAT HEAT PIPES
A NUMERICAL APPROACH FOR ESTIMATING THE ENTROPY GENERATION IN FLAT HEAT PIPES Dr. Mahesh Kumar. P Department of Mechanical Engineering Govt College of Engineering, Kannur Parassinikkadavu (P.O), Kannur,
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 informationInternal Flow: Heat Transfer in Pipes
Internal Flow: Heat Transfer in Pipes V.Vuorinen Aalto University School of Engineering Heat and Mass Transfer Course, Autumn 2016 November 15 th 2016, Otaniemi ville.vuorinen@aalto.fi First about the
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 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 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 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 informationFluid Mechanics II Viscosity and shear stresses
Fluid Mechanics II Viscosity and shear stresses Shear stresses in a Newtonian fluid A fluid at rest can not resist shearing forces. Under the action of such forces it deforms continuously, however small
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 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 informationOE4625 Dredge Pumps and Slurry Transport. Vaclav Matousek October 13, 2004
OE465 Vaclav Matousek October 13, 004 1 Dredge Vermelding Pumps onderdeel and Slurry organisatie Transport OE465 Vaclav Matousek October 13, 004 Dredge Vermelding Pumps onderdeel and Slurry organisatie
More informationThermal and Fluids in Architectural Engineering
hermal and Fluids in Architectural Engineering 12. Convection heat transfer Jun-Seo Par, Dr. Eng., Prof. Dept. of Architectural Engineering Hanyang Univ. Where do we learn in this chaper 1. Introduction
More informationExternal Forced Convection :
External Forced Convection : Flow over Bluff Objects (Cylinders, Spheres, Packed Beds) and Impinging Jets Chapter 7 Sections 7.4 through 7.8 7.4 The Cylinder in Cross Flow Conditions depend on special
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 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 informationTutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k)
Tutorial 1 1. Explain in detail the mechanism of forced convection. Show by dimensional analysis (Rayleigh method) that data for forced convection may be correlated by an equation of the form Nu = φ (Re,
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 informationStudies on flow through and around a porous permeable sphere: II. Heat Transfer
Studies on flow through and around a porous permeable sphere: II. Heat Transfer A. K. Jain and S. Basu 1 Department of Chemical Engineering Indian Institute of Technology Delhi New Delhi 110016, India
More informationModule 9: Mass Transfer Lecture 40: Analysis of Concentration Boundary Layer. The Lecture Contains: The concentration boundary layer
The Lecture Contains: The concentration boundary layer Heat and Mass Transfer Analogy Evaporate Cooling file:///d /Web%20Course%20(Ganesh%20Rana)/Dr.%20gautam%20biswas/Final/convective_heat_and_mass_transfer/lecture40/40_1.html[12/24/2014
More informationME 144: Heat Transfer Introduction to Convection. J. M. Meyers
ME 144: Heat Transfer Introduction to Convection Introductory Remarks Convection heat transfer differs from diffusion heat transfer in that a bulk fluid motion is present which augments the overall heat
More informationSo far, we have considered conduction, which is the mechanism of heat
cen58933_ch06.qxd 9/4/2002 12:05 PM Page 333 FUNDAMENTALS OF CONVECTION CHAPTER 6 So far, we have considered conduction, which is the mechanism of heat transfer through a solid or a quiescent fluid. We
More informationMOMENTUM TRANSPORT Velocity Distributions in Turbulent Flow
TRANSPORT PHENOMENA MOMENTUM TRANSPORT Velocity Distributions in Turbulent Flow Introduction to Turbulent Flow 1. Comparisons of laminar and turbulent flows 2. Time-smoothed equations of change for incompressible
More informationChapter 5 Principles of Convection heat transfer (Text: J. P. Holman, Heat Transfer, 8 th ed., McGraw Hill, NY)
hapter 5 Principles of onvection heat transfer (Tet: J. P. Holman, Heat Transfer, 8 th ed., McGra Hill, NY) onsider a fluid flo over a flat plate ith different temperatures (Fig 5-1) q A ha( T T ) since
More informationLesson 6 Review of fundamentals: Fluid flow
Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass
More informationNUMERICAL STUDY OF HEAT AND MASS TRANSFER DURING EVAPORATION OF A THIN LIQUID FILM
THERMAL SCIENCE, Year 2015, Vol. 19, No. 5, pp. 1805-1819 1805 NUMERICAL STUDY OF HEAT AND MASS TRANSFER DURING EVAPORATION OF A THIN LIQUID FILM by M hand OUBELLA a, M barek FEDDAOUI b *, and Rachid MIR
More informationAnalytical solutions of heat transfer for laminar flow in rectangular channels
archives of thermodynamics Vol. 35(2014), No. 4, 29 42 DOI: 10.2478/aoter-2014-0031 Analytical solutions of heat transfer for laminar flow in rectangular channels WITOLD RYBIŃSKI 1 JAROSŁAW MIKIELEWICZ
More informationMASS TRANSFER AND GAS ABSORPTION EQUIPMENT
MASS TRANSFER AND GAS ABSORPTION EQUIPMENT Mark J McCready University of Notre Dame Indiana, USA TOPICS Review of heat transfer and heat exchangers Some fundamental aspects of mass transfer Analysis of
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 informationSpecific heat capacity. Convective heat transfer coefficient. Thermal diffusivity. Lc ft, m Characteristic length (r for cylinder or sphere; for slab)
Important Heat Transfer Parameters CBE 150A Midterm #3 Review Sheet General Parameters: q or or Heat transfer rate Heat flux (per unit area) Cp Specific heat capacity k Thermal conductivity h Convective
More informationIntroduction to Heat and Mass Transfer. Week 10
Introduction to Heat and Mass Transfer Week 10 Concentration Boundary Layer No concentration jump condition requires species adjacent to surface to have same concentration as at the surface Owing to concentration
More informationFLUID MECHANICS PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES 5.1.3. Pressure and Shear Stress
More informationOutlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer
Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer
More informationFORCED CONVECTION FILM CONDENSATION OF DOWNWARD-FLOWING VAPOR ON HORIZONTAL TUBE WITH WALL SUCTION EFFECT
Journal of Marine Science and Technology, Vol., No. 5, pp. 5-57 () 5 DOI:.69/JMST--5- FORCED CONVECTION FILM CONDENSATION OF DOWNWARD-FLOWING VAPOR ON HORIZONTAL TUBE WITH WALL SUCTION EFFECT Tong-Bou
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 informationHeat transfer enhancement in natural convection in micropolar nanofluids
Arch. Mech., 68, 4, pp. 327 344, Warszawa 2016 Heat transfer enhancement in natural convection in micropolar nanofluids K. RUP, K. NERING Faculty of Mechanical Engineering Cracow University of Technology
More informationBasic Fluid Mechanics
Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible
More informationheat transfer process where a liquid undergoes a phase change into a vapor (gas)
Two-Phase: Overview Two-Phase two-phase heat transfer describes phenomena where a change of phase (liquid/gas) occurs during and/or due to the heat transfer process two-phase heat transfer generally considers
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 informationHeat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay
Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Lecture No. 18 Forced Convection-1 Welcome. We now begin our study of forced convection
More informationBERNOULLI EQUATION. The motion of a fluid is usually extremely complex.
BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over
More informationCFD Modelling of Horizontal Water Film Evaporation
CFD Modelling of Horizontal Water Film Evaporation Master s Thesis Bc. Radomír Kalinay Prague, 2017 Annotation Sheet Title: Author: CFD Modelling of Horizontal Water Film Evaporation Bc. Radomír Kalinay
More informationIntroduction to Aerospace Engineering
Introduction to Aerospace Engineering Lecture slides Challenge the future 3-0-0 Introduction to Aerospace Engineering Aerodynamics 5 & 6 Prof. H. Bijl ir. N. Timmer Delft University of Technology 5. Compressibility
More informationLectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6
Lectures on Nuclear Power Safety Lecture No 6 Title: Introduction to Thermal-Hydraulic Analysis of Nuclear Reactor Cores Department of Energy Technology KTH Spring 2005 Slide No 1 Outline of the Lecture
More informationNumber of pages in the question paper : 05 Number of questions in the question paper : 48 Modeling Transport Phenomena of Micro-particles Note: Follow the notations used in the lectures. Symbols have their
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 informationEXAMPLE SHEET FOR TOPIC 3 AUTUMN 2013
EXAMPLE SHEET FOR TOPIC ATMN 01 Q1. se dimensional analysis to investigate how the capillary rise h of a liquid in a tube varies with tube diameter d, gravity g, fluid density ρ, surface tension σ and
More informationطراحی مبدل های حرارتی مهدي کریمی ترم بهار HEAT TRANSFER CALCULATIONS
طراحی مبدل های حرارتی مهدي کریمی ترم بهار 96-97 HEAT TRANSFER CALCULATIONS ١ TEMPERATURE DIFFERENCE For any transfer the driving force is needed General heat transfer equation : Q = U.A. T What T should
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 informationPIPE FLOWS: LECTURE /04/2017. Yesterday, for the example problem Δp = f(v, ρ, μ, L, D) We came up with the non dimensional relation
/04/07 ECTURE 4 PIPE FOWS: Yesterday, for the example problem Δp = f(v, ρ, μ,, ) We came up with the non dimensional relation f (, ) 3 V or, p f(, ) You can plot π versus π with π 3 as a parameter. Or,
More informationLECTURE 1 THE CONTENTS OF THIS LECTURE ARE AS FOLLOWS:
LECTURE 1 THE CONTENTS OF THIS LECTURE ARE AS FOLLOWS: 1.0 INTRODUCTION TO FLUID AND BASIC EQUATIONS 2.0 REYNOLDS NUMBER AND CRITICAL VELOCITY 3.0 APPROACH TOWARDS REYNOLDS NUMBER REFERENCES Page 1 of
More informationPHYSICAL MECHANISM OF NATURAL CONVECTION
1 NATURAL CONVECTION In this chapter, we consider natural convection, where any fluid motion occurs by natural means such as buoyancy. The fluid motion in forced convection is quite noticeable, since a
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 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 informationV (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)
IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common
More information7.2 Sublimation. The following assumptions are made in order to solve the problem: Sublimation Over a Flat Plate in a Parallel Flow
7..1 Sublimation Over a Flat Plate in a Parallel Flow The following assumptions are made in order to solve the problem: 1.. 3. The flat plate is very thin and so the thermal resistance along the flat plate
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 informationOUTCOME 2 - TUTORIAL 1
Unit 4: Heat Transfer and Combustion Unit code: K/60/44 QCF level: 5 Credit value: 5 OUTCOME - TUTORIAL Heat transfer coefficients Dimensional analysis: dimensionless groups; Reynolds, Nusselt, Prandtl,
More informationPROBLEM h fg ρ v ρ l σ 10 3 T sat (kj/kg) (kg/m 3 ) (N/m) (K)
PROBLEM 10.9 KNOWN: Fluids at 1 atm: mercury, ethanol, R-1. FIND: Critical heat flux; compare with value for water also at 1 atm. ASSUMPTIONS: (1) Steady-state conditions, () Nucleate pool boiling. PROPERTIES:
More informationFluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture - 17 Laminar and Turbulent flows
Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture - 17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In
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 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 informationCONVECTIVE HEAT TRANSFER
CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 5 NATURAL CONVECTION HEAT TRANSFER BASIC CONCEPTS MECHANISM OF NATURAL
More informationAdvanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell
Laminar external natural convection on vertical and horizontal flat plates, over horizontal and vertical cylinders and sphere, as well as plumes, wakes and other types of free flow will be discussed in
More information