FORMULA SHEET. General formulas:


 Leonard Todd
 3 years ago
 Views:
Transcription
1 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 2.7. Part 1.1 to 1.7 contain all the formulas that were needed in the basic course The basics of Transport Phenomena and part 2.1 to 2.7 contain new formulas used in Advanced Transport Phenomena. General formulas: Newton s 2 nd law of motion. Kinetic energy. Gravitational energy. Angular velocity of circular motion, where T is the period of the motion. Ideal gas law. R is the Gas constant. Density in mass per unit volume. Specific heat: Heat needed to heat an object by 1 degree Celsius. Units are The conversion of going from Celsius to Kelvin. It is important to note that negative temperatures do not exist on the Kelvin scale, while they do for the Celsius scale, so when calculating with absolute temperatures, use Kelvin. In relative calculations where you take a temperature difference, it doesn t matter since Kelvin and Celsius are the same scale, except they are shifted. F = m a E k = 1 2 mv2 E g = m g h ω = 2π T pv = nrt ρ = m V J. C = Q kg K mδt T K = T C + 273,15 The radius of a circle, where r is the radius (half the diameter) of the circle. s = 2πr The area of a circle. A = πr 2 The volume of a sphere. V = 4 3 πr3
2 Constants N = molecules R = J mol K σ = W m 2 K 4 The number of molecules in a mole, called Avogadro s Constant. The gas constant The StefanBoltzmann constant Quantities &Units Mass m kg Time t s Volume V m 3 Velocity v m/s Density ρ Kg/m 3 Diameter D or d m Force F N Temperature T K Pressure p or P Pa Mass flow φ Kg/s Diffusion coefficient D m 2 /s Internal energy U J Heat Q J Work W Nm Total energy E J Area A m 2 Heat transfer coefficient h W/(m 2 K) Thermal conductivity λ W/(m K) Specific heat C p J/(kg K) Drag coefficient C D  Thermal diffusivity a m 2 /s Viscosity η Pa s Mass transfer coefficient k m/s Specific energy dissipation e J/kg Shear stress τ Pa Wavelength λ m AIR AT 20 ⁰C: WATER AT 20 ⁰C: DENSITY: KG/M 3 DENSITY: KG/M 3 HEAT CAPACITY: KJ/(KG K) HEAT CAPACITY: KJ/(KG K) PRANDTL: PRANDTL: 7.01 THERMAL DIFFUSIVITY: * 105 M 2 /S THERMAL DIFFUSIVITY: * 106 M 2 /S VISCOSITY: 1.82 * 105 PA S VISCOSITY: * 103 PA S
3 WEEK 1.1: The general balance equation. d = in out + production dt WEEK 1.2: Total energy balance First law of Thermodynamics, where ΔWis the net work done on the system. The thermal energy balance in a steady state without energy change. The mechanical energy balance. Bernoulli s equation: Neglects all friction and heat production. h is height. Bernoulli s Principle: The energy per unit volume before is the same as the energy per unit volume after. de dt = φ m,in {U + p ρ v2 + gh}in ΔU = ΔQ + ΔW 0 = φ m (u in u out ) + φ q + φ m e fr 2 ) φ m,out {U + p ρ v2 + gh} out 0 = φ m ( (v in 2 v out + g(h 2 in h out ) + (p in p out ) + φ ρ w φ m E fr ) p ρ + v2 + gh = constant 2 P ρv ρgh 1 = P ρv ρgh 2 WEEK 1.3: Reynolds number, where ρ f is the density of the fluid, v r is the relative velocity, D is the diameter and μ is the viscosity of the fluid The drag force. C D is the drag coefficient, A is the frontal area, v is the relative velocity. Stokes law: The drag force on a sphere with a low Reynolds number (Re < 1). Re = ρ fv r D μ F D = C D A 1 2 ρ fv r 2 F D = 3πDμv r
4 WEEK 1.4: Fourier s law, the transfer of heat. λ is the material conductivity, Δx is the thickness, A is the area, ΔT is the difference in temperature. Fick s law of diffusion, analogous to Fourier s law. D is the diffusion coefficient, A is the area and dc a is the change in concentration over x. dx φ q = λa ΔT Δx φ m = D A ( dc A dx ) WEEK 1.5: Newton s law of cooling. h is the heat transfer coefficient. Nusselt number. Used to make h dimensionless. Mass transfer coefficient, where Sh is the Sherwood number, analogous to Nusselt number. Δx is the size of the object, also called D sometimes. φ q = h A ΔT Nu = D h λ k = Sh D Δx WEEK 1.6: Thermal diffusivity. λ is thermal conductivity, ρ is material density, C p is specific heat. a = λ ρ C p Penetration depth. Only valid while penetration theory still holds, for πat < D, where D is the size of the sheet 2 being penetrated by heat. Fourier number. Nusselt number for penetration theory. x p = πat Fo = at D 2 Nu = 1 πfo WEEK 1.7: No new formulas this week!
5 WEEK 2.1: The general microbalance equation. Where β is the dependent variable of interest dβ dt = φ β x φ β x+dx + P β WEEK 2.2: Momentum balance d dt (m v x) = φ m,in v x,in φ m,out v x,out + F x Fanning pressure drop equation Δp = 4f L 1 ρ < v >2 D 2 Hydraulic diameter, S is the wetted perimeter. D h = 4A S The fanning friction factor for the laminar regime: Re < f = 64 Re The fanning friction factor for the turbulent regime (formula of Blasius): 4000 < Re < f = Re 1/4 The specific energy dissipation is modelled as the sum of e diss = (e fr ) i + (e L ) j dissipation in pipelines parts and appendage parts Specific energy dissipation in appendages for turbulent flow i e L = K L 1 < v >2 2 j GATE VALVE open 3/4 1/2 1/4 K L KINK α K L
6 WEEK 2.3: DIMENSIONLESS NUMBERS: Greatz number: Fraction of conductive over convective heat transfer Grashof number: Fraction of buoyancy forces over viscous forces Lewis number: Fraction of thickness of thermal boundary layer over mass transfer boundary layer Peclet (heat) number: Fraction convective heat transfer over conductive heat transfer Peclet (mas) number: Fraction convective mass transfer over diffusive mass transfer Prandtl number: Fraction of hydrodynamic boundary layer thickness over thermal boundary layer thickness Schmidt number: Fraction of hydrodynamic boundary layer over mass transfer boundary layer Gz = al d 2 v Gr = d3 g γ ΔT v 2 Le = a D Pe = vd a Pe = vd D Pr = ν a Sc = ν D (D is the mass diffusion constant) (D is the mass diffusion constant) (ν is the kinematic viscosity) (ν is the kinematic viscosity, D is the mass diffusion constant) DIMENSIONLESS CORRELATIONS FOR HEAT TRANSFER: Laminar flow in tubes: Gz < 0.05 Laminar flow in tubes: Gz > 0.1 Turbulent flow in tubes: Re > 10 4 and Pr 0.7 Flat plate parallel to flow: Re < Long cylinders perpendicular to the flow: 10 < Re < 10 4 and Pr > 0.7 and Pe >> 1 Long cylinders perpendicular to the flow: Re > 10 4 and Pr > 0.7 Flow around spheres: 10 < Re < 10 4 and Pr > 0.7 and Pe >> 1 Nu = 1.08 Gz 1/3 and < Nu > = 1.62 Gz 1/3 Nu = < Nu > = 3.66 < Nu > = Re 0.8 Pr 0.33 Nu = Re 1/2 Pr 1/3 < Nu > = 0.57 Re 1/2 Pr 1/3 < Nu > = Re 0.8 Pr 0.33 < Nu > = Re 1/2 Pr 1/3
7 DIMENSIONLESS CORRELATIONS FOR MASS TRANSFER: Laminar flow in tubes: Gz < 0.05 Laminar flow in tubes: Gz > 0.1 Turbulent flow in tubes: Re > 10 4 and Sc 0.7 Flat plate parallel to flow: Re < Long cylinders perpendicular to the flow: 1 < Re < 10 4 and Sc > 0.7 and Pe >> 1 Flow around spheres: 10 < Re < 10 4 and Sc > 0.7 and Pe >> 1 Sh = 1.08 Gz 1/3 and < Sh > = 1.62 Gz 1/3 Sh = < Sh > = 3.66 < Sh > = Re 0.8 Sc 0.33 Sh = Re 1/2 Sc < Sh > = 0.42 Sc 1/ Re 1/2 Sc 1/3 < Sh > = Re 1/2 Sc 1/3 OTHER FORMULAS: Sieder and Tate correction, this equation is used in Nu = Re 0.8 Pr 0.33 ( µ ) 0.14 situations with a viscosity gradient in turbulent pipe flow µ s The Chilton and Colburn relations combines heat and h mass flow coefficients k = Le 2/3 ρ C p WEEK 2.4: The partition coefficient, in which you may assign phases to superscript 1 and 2 Henry s Law: with p the partial pressure, H the henry s coefficient and y the fraction dissolved in the liquid m = C1 C 2 p A = H A y A
8 WEEK 2.5: Shear stress in Newtonian fluids τ yx = µ dv x dy Shear stress for liquids that follow the power law (Ostwald De Waele model) τ yx = K v x dy n 1 dv x dy Shear stress for Bingham liquids Shear stress for viscoelastic fluids, where λ is a elasticity parameter HagenPoiseuille law is used to calculate flow rates from velocity profiles in tubes τ yx τ 0 = µ dv x dy for τ yx τ 0 dv x dy for τ yx < τ 0 τ yx + λ dτ yx dt = µ dv x dy R φ v = v x (r) 2π r dr 0 WEEK 2.6: StefanBoltzman Law for grey radiators. Note if e = 1 the object is a black radiator φ q " = e σ T 4 Wiens Law that relates the temperature of a radiator to its maximum in radiation wavelength λ max T = m K Heat radiation with the help of visibility factors φ net,1 2 = F 1 2 A 1 σt F 2 1 A 2 σt 2
9 4f
10 GRAPHS:
11
12 FOR A SPHERE
Convective 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 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 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 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 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 informationMechanical Engineering. Postal Correspondence Course HEAT TRANSFER. GATE, IES & PSUs
Heat TransferME GATE, IES, PSU 1 SAMPLE STUDY MATERIAL Mechanical Engineering ME Postal Correspondence Course HEAT TRANSFER GATE, IES & PSUs Heat TransferME GATE, IES, PSU 2 C O N T E N T 1. INTRODUCTION
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 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 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 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 informationNumerical Heat and Mass Transfer
Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis
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 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 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 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 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 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 informationHeat and Mass Transfer Unit1 Conduction
1. State Fourier s Law of conduction. Heat and Mass Transfer Unit1 Conduction PartA The rate of heat conduction is proportional to the area measured normal to the direction of heat flow and to the temperature
More informationMODULE CODE: ENGG08021 INTRODUCTION TO THERMOFLUIDS. Date: 15 January 2016 Time: 10:00 12:00
School of Engineering & Computing Session 201516 Paisley Campus Trimester 1 MODULE CODE: ENGG08021 INTRODUCTION TO THERMOFLUIDS Date: 15 January 2016 Time: 10:00 12:00 Attempt FOUR QUESTIONS IN TOTAL
More informationChapter 7: Natural Convection
71 Introduction 7 The Grashof Number 73 Natural Convection over Surfaces 74 Natural Convection Inside Enclosures 75 Similarity Solution 76 Integral Method 77 Combined Natural and Forced Convection
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 informationChapter 6 Fundamental Concepts of Convection
Chapter 6 Fundamental Concepts of Convection 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
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 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 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 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 informationConvection Heat Transfer. Introduction
Convection Heat Transfer Reading Problems 121 128 1240, 1249, 1268, 1270, 1287, 1298 131 136 1339, 1347, 1359 141 144 1418, 1424, 1445, 1482 Introduction Newton s Law of Cooling Controlling
More informationChemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017
Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering
More informationOutline. Definition and mechanism Theory of diffusion Molecular diffusion in gases Molecular diffusion in liquid Mass transfer
Diffusion 051333 Unit operation in groindustry III Department of Biotechnology, Faculty of groindustry Kasetsart University Lecturer: Kittipong Rattanaporn 1 Outline Definition and mechanism Theory of
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 informationWhat s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube
PHYS 101 Lecture 29x  Viscosity 29x  1 Lecture 29x Viscosity (extended version) What s important: viscosity Poiseuille's law Stokes' law Demo: dissipation in flow through a tube Viscosity We introduced
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 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 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 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 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 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 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 informationLevel 7 Post Graduate Diploma in Engineering Heat and mass transfer
9210221 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 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 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 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 informationINDIAN INSTITUTE OF TECHNOOGY, KHARAGPUR Date:  AN No. of Students: 5 Sub. No.: ME64/ME64 Time: Hours Full Marks: 6 Mid Autumn Semester Examination Sub. Name: Convective Heat and Mass Transfer Instructions:
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 informationChapter 3 NATURAL CONVECTION
Fundamentals of ThermalFluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGrawHill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGrawHill Companies,
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 informationNicholas J. Giordano. Chapter 10 Fluids
Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according
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 informationBAE 820 Physical Principles of Environmental Systems
BAE 820 Physical Principles of Environmental Systems Stokes' law and Reynold number Dr. Zifei Liu The motion of a particle in a fluid environment, such as air or water m dv =F(t)  F dt d  1 4 2 3 πr3
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 information1. Introduction, tensors, kinematics
1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and
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 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 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 informationFluid Mechanics Theory I
Fluid Mechanics Theory I Last Class: 1. Introduction 2. MicroTAS or Lab on a Chip 3. Microfluidics Length Scale 4. Fundamentals 5. Different Aspects of Microfluidcs Today s Contents: 1. Introduction to
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 informationCHME 302 CHEMICAL ENGINEERING LABOATORYI EXPERIMENT 302V FREE AND FORCED CONVECTION
CHME 302 CHEMICAL ENGINEERING LABOATORYI EXPERIMENT 302V FREE AND FORCED CONVECTION OBJECTIVE The objective of the experiment is to compare the heat transfer characteristics of free and forced convection.
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 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 informationAP Physics Laboratory #6.1: Analyzing Terminal Velocity Using an Interesting Version of Atwood s Machine
AP Physics Laboratory #6.1: Analyzing Terminal Velocity Using an Interesting Version of Atwood s Machine Name: Date: Lab Partners: PURPOSE The purpose of this Laboratory is to study a system as it approaches
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 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 informationMicrofluidics 1 Basics, Laminar flow, shear and flow profiles
MT0.6081 Microfluidics and BioMEMS Microfluidics 1 Basics, Laminar flow, shear and flow profiles 11.1.2017 Ville Jokinen Outline of the next 3 weeks: Today: Microfluidics 1: Laminar flow, flow profiles,
More informationLectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6
Lectures on Nuclear Power Safety Lecture No 6 Title: Introduction to ThermalHydraulic Analysis of Nuclear Reactor Cores Department of Energy Technology KTH Spring 2005 Slide No 1 Outline of the Lecture
More informationPhysics 201 Chapter 13 Lecture 1
Physics 201 Chapter 13 Lecture 1 Fluid Statics Pascal s Principle Archimedes Principle (Buoyancy) Fluid Dynamics Continuity Equation Bernoulli Equation 11/30/2009 Physics 201, UWMadison 1 Fluids Density
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 informationLecturer, Department t of Mechanical Engineering, SVMIT, Bharuch
Fluid Mechanics By Ashish J. Modi Lecturer, Department t of Mechanical Engineering, i SVMIT, Bharuch Review of fundamentals Properties of Fluids Introduction Any characteristic of a system is called a
More informationReynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment:
7 STEADY FLOW IN PIPES 7.1 Reynolds Number Reynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment: Laminar flow Turbulent flow Reynolds apparatus
More informationFINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT OF A HEATED SQUARE HOLLOW CYLINDER IN A LIDDRIVEN RECTANGULAR ENCLOSURE
Proceedings of the International Conference on Mechanical Engineering 2011 (ICME2011) 1820 December 2011, Dhaka, Bangladesh ICME11TH014 FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT
More informationFriction Factors and Drag Coefficients
Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the
More informationThermodynamics, Fluid Dynamics, and Heat Transfer
Chapter 2 Thermodynamics, Fluid Dynamics, and Heat Transfer 2. Introduction In this chapter we will review fundamental concepts from Thermodynamics, Fluid Dynamics, and Heat Transfer. Each section first
More information2. FLUIDFLOW EQUATIONS SPRING 2019
2. FLUIDFLOW EQUATIONS SPRING 2019 2.1 Introduction 2.2 Conservative differential equations 2.3 Nonconservative differential equations 2.4 Nondimensionalisation Summary Examples 2.1 Introduction Fluid
More informationQuick Recapitulation of Fluid Mechanics
Quick Recapitulation of Fluid Mechanics Amey Joshi 07Feb018 1 Equations of ideal fluids onsider a volume element of a fluid of density ρ. If there are no sources or sinks in, the mass in it will change
More informationV/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0
UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and nonuniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and irrotational
More informationTALLINN UNIVERSITY OF TECHNOLOGY, DIVISION OF PHYSICS 13. STOKES METHOD
13. STOKES METHOD 1. Objective To determine the coefficient of viscosity of a known fluid using Stokes method.. Equipment needed A glass vessel with glycerine, micrometer calliper, stopwatch, ruler. 3.
More informationMIXED CONVECTION SLIP FLOW WITH TEMPERATURE JUMP ALONG A MOVING PLATE IN PRESENCE OF FREE STREAM
THERMAL SCIENCE, Year 015, Vol. 19, No. 1, pp. 11918 119 MIXED CONVECTION SLIP FLOW WITH TEMPERATURE JUMP ALONG A MOVING PLATE IN PRESENCE OF FREE STREAM by Gurminder SINGH *a and Oluwole Daniel MAKINDE
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 informationFor more info
Characteristic of Ideal fluid: (a) It is incompressible (b) It is nonviscous (c) Flow of ideal fluid is irrational (d) It is capable of exhibiting steady flow Stream line flow: Flow of a liquid fluid
More informationMass Transfer Operations I Prof. Bishnupada Mandal Department of Chemical Engineering Indian Institute of Technology, Guwahati
Mass Transfer Operations I Prof. Bishnupada Mandal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module  2 Mass Transfer Coefficient Lecture  4 Boundary Layer Theory and
More informationAnalysis, Design and Fabrication of Forced Convection Apparatus
Analysis, Design and Fabrication of Forced Convection Apparatus Shajan K. Thomas 1, Vishnukumar C M 2, Vishnu C J 3, Alex Baby 4 Assistant Professor, Dept. of Mechanical Engineering, Toc H Institute of
More information6 Empirical and Practical
6 Empirical and Practical ForcedConvection Relations for Heat Transfer CHAPTER 61 INTRODUCTION The discussion and analyses of Chapter 5 have shown how forcedconvection heat transfer may be calculated
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 informationUnit operations of chemical engineering
1 Unit operations of chemical engineering Fourth year Chemical Engineering Department College of Engineering ALQadesyia University Lecturer: 2 3 Syllabus 1) Boundary layer theory 2) Transfer of heat,
More informationFinal Mock Exam PH 2211D
Final Mock Exam PH 2211D April 18, 2015 You will have 2 hours to complete this exam. You must answer 8 questions to make a perfect score of 80. 1 Chapter Concept Summary Equations: Cutnell & Johnson
More informationFluid Mechanics. Jim Emery 9/3/ Bernoulli s Law 2. 2 Torricelli s Law 3. 3 Time to Empty a Tank 3. 4 Viscosity 4. 5 The Acceleration 5
Fluid Mechanics Jim Emery 9/3/2010 Contents 1 Bernoulli s Law 2 2 Torricelli s Law 3 3 Time to Empty a Tank 3 4 Viscosity 4 5 The Acceleration 5 6 The Equation of Motion Due to Cauchy 7 7 The Deformation
More informationPlease remember all the unit that you use in your calculation. There are no marks for correct answer without unit.
CHAPTER 1 : PROPERTIES OF FLUIDS What is fluid? A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called
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 informationModelling of dispersed, multicomponent, multiphase flows in resource industries. Section 3: Examples of analyses conducted for Newtonian fluids
Modelling of dispersed, multicomponent, multiphase flows in resource industries Section 3: Examples of analyses conducted for Newtonian fluids Globex Julmester 017 Lecture # 04 July 017 Agenda Lecture
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 informationMechanical Engineering Programme of Study
Mechanical Engineering Programme of Study Fluid Mechanics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy SOLVED EXAMPLES ON VISCOUS FLOW 1. Consider steady, laminar flow between two fixed parallel
More information1. Introduction, fluid properties (1.1, 2.8, 4.1, and handouts)
1. Introduction, fluid properties (1.1, 2.8, 4.1, and handouts) Introduction, general information Course overview Fluids as a continuum Density Compressibility Viscosity Exercises: A1 Fluid mechanics Fluid
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 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 informationLiquids and solids are essentially incompressible substances and the variation of their density with pressure is usually negligible.
Properties of Fluids Intensive properties are those that are independent of the mass of a system i.e. temperature, pressure and density. Extensive properties are those whose values depend on the size of
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 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 NonDimensional form of the Equations of Motion.......... 4
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 informationLecture 28. Key words: Heat transfer, conduction, convection, radiation, furnace, heat transfer coefficient
Lecture 28 Contents Heat transfer importance Conduction Convection Free Convection Forced convection Radiation Radiation coefficient Illustration on heat transfer coefficient 1 Illustration on heat transfer
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 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 information