FORMULA SHEET. General formulas:


 Leonard Todd
 10 months 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
Summary 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationRate of change of velocity. a=dv/dt. Acceleration is a vector quantity.
9.7 CENTRIFUGATION The centrifuge is a widely used instrument in clinical laboratories for the separation of components. Various quantities are used for the description and the calculation of the separation
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 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 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 informationContents. Microfluidics  Jens Ducrée Physics: Laminar and Turbulent Flow 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. InkJet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationChapter 2 Mass Transfer Coefficient
Chapter 2 Mass Transfer Coefficient 2.1 Introduction The analysis reported in the previous chapter allows to describe the concentration profile and the mass fluxes of components in a mixture by solving
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 informationShell Balances in Fluid Mechanics
Shell Balances in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University When fluid flow occurs in a single direction everywhere in a system, shell
More informationPHY121 Physics for the Life Sciences I
PHY Physics for the Life Sciences I Lecture 0. Fluid flow: kinematics describing the motion. Fluid flow: dynamics causes and effects, Bernoulli s Equation 3. Viscosity and Poiseuille s Law for narrow tubes
More informationFigure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m
1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)
More informationMomentum Circular Motion and Gravitation Rotational Motion Fluid Mechanics
Momentum Circular Motion and Gravitation Rotational Motion Fluid Mechanics Momentum Momentum Collisions between objects can be evaluated using the laws of conservation of energy and of momentum. Momentum
More informationME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts. Flow in Pipes and Ducts. Flow in Pipes and Ducts (cont d)
ME 305 Fluid Mechanics I Flow in Pipes and Ducts Flow in closed conduits (circular pipes and noncircular ducts) are very common. Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared
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 informationBME 419/519 Hernandez 2002
Vascular Biology 2  Hemodynamics A. Flow relationships : some basic definitions Q v = A v = velocity, Q = flow rate A = cross sectional area Ohm s Law for fluids: Flow is driven by a pressure gradient
More information150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces
Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with
More informationPHYSICS. Course Structure. Unit Topics Marks. Physical World and Measurement. 1 Physical World. 2 Units and Measurements.
PHYSICS Course Structure Unit Topics Marks I Physical World and Measurement 1 Physical World 2 Units and Measurements II Kinematics 3 Motion in a Straight Line 23 4 Motion in a Plane III Laws of Motion
More informationIn steady flow the velocity of the fluid particles at any point is constant as time passes.
Chapter 10 Fluids Fluids in Motion In steady flow the velocity of the fluid particles at any point is constant as time passes. Unsteady flow exists whenever the velocity of the fluid particles at a point
More informationPiping Systems and Flow Analysis (Chapter 3)
Piping Systems and Flow Analysis (Chapter 3) 2 Learning Outcomes (Chapter 3) Losses in Piping Systems Major losses Minor losses Pipe Networks Pipes in series Pipes in parallel Manifolds and Distribution
More informationDEPARTMENT OF MECHANICAL ENGINEERING. ME 6502 Heat and Mass Transfer III YEARV SEMESTER
ME650 HEAT AND MASS TRNSFER MARKS & 16 MARKS QUESTION AND ANSWER ME 650 Heat and Mass Transfer III YEARV SEMESTER NAME :. REG.NO :. BRANCH :... YEAR & SEM :. 1 ME650 HEAT AND MASS TRNSFER MARKS & 16 MARKS
More informationTemperature Thermal Expansion Ideal Gas Law Kinetic Theory Heat Heat Transfer Phase Changes Specific Heat Calorimetry
Temperature Thermal Expansion Ideal Gas Law Kinetic Theory Heat Heat Transfer Phase Changes Specific Heat Calorimetry Zeroeth Law Two systems individually in thermal equilibrium with a third system (such
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 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 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 informationPART 1B EXPERIMENTAL ENGINEERING. SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) BOUNDARY LAYERS AND DRAG
1 PART 1B EXPERIMENTAL ENGINEERING SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) EXPERIMENT T3 (LONG) BOUNDARY LAYERS AND DRAG OBJECTIVES a) To measure the velocity
More informationPressure in stationary and moving fluid Lab Lab On On Chip: Lecture 2
Pressure in stationary and moving fluid LabOnChip: Lecture Lecture plan what is pressure e and how it s distributed in static fluid water pressure in engineering problems buoyancy y and archimedes law;
More informationCLASS SCHEDULE 2013 FALL
CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties
More informationLaminar Forced Convection Heat Transfer from Two Heated Square Cylinders in a Bingham Plastic Fluid
Laminar Forced Convection Heat Transfer from Two Heated Square Cylinders in a Bingham Plastic Fluid E. Tejaswini 1*, B. Sreenivasulu 2, B. Srinivas 3 1,2,3 Gayatri Vidya Parishad College of Engineering
More informationToday s menu. Last lecture. A/D conversion. A/D conversion (cont d...) Sampling
Last lecture Capacitive sensing elements. Inductive sensing elements. Reactive Deflection bridges. Electromagnetic sensing elements. Thermoelectric sensing elements. Elastic sensing elements. Piezoelectric
More informationR09. d water surface. Prove that the depth of pressure is equal to p +.
Code No:A109210105 R09 SET1 B.Tech II Year  I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal
More informationMHD NonNewtonian Power Law Fluid Flow and Heat Transfer Past a NonLinear Stretching Surface with Thermal Radiation and Viscous Dissipation
Journal of Applied Science and Engineering, Vol. 17, No. 3, pp. 267274 (2014) DOI: 10.6180/jase.2014.17.3.07 MHD NonNewtonian Power Law Fluid Flow and Heat Transfer Past a NonLinear Stretching Surface
More informationSteven Burian Civil & Environmental Engineering September 25, 2013
Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering September 25, 2013 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session
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 informationAnalysis of Heat Transfer in Pipe with Twisted Tape Inserts
Proceedings of the 2 nd International Conference on Fluid Flow, Heat and Mass Transfer Ottawa, Ontario, Canada, April 30 May 1, 2015 Paper No. 143 Analysis of Heat Transfer in Pipe with Twisted Tape Inserts
More informationHEAT EXCHANGER. Objectives
HEAT EXCHANGER Heat exchange is an important unit operation that contributes to efficiency and safety of many processes. In this project you will evaluate performance of three different types of heat exchangers
More informationComputational Fluid Dynamics 2
Seite 1 Introduction Computational Fluid Dynamics 11.07.2016 Computational Fluid Dynamics 2 Turbulence effects and Particle transport Martin Pietsch Computational Biomechanics Summer Term 2016 Seite 2
More informationThermal physics revision questions
Thermal physics revision questions ONE SECTION OF QUESTIONS TO BE COMPLETED AND MARKED EVERY WEEK AFTER HALF TERM. Section 1: Energy 1. Define the law of conservation of energy. Energy is neither created
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/aoter20140031 Analytical solutions of heat transfer for laminar flow in rectangular channels WITOLD RYBIŃSKI 1 JAROSŁAW MIKIELEWICZ
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 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 informationAMRITA VISHWA VIDYAPEETHAM DEPARTMENT OF CHEMICAL ENGINEERING AND MATERIALS SCIENCE. PhD Entrance Examination  Syllabus
AMRITA VISHWA VIDYAPEETHAM DEPARTMENT OF CHEMICAL ENGINEERING AND MATERIALS SCIENCE PhD Entrance Examination  Syllabus The research being carried out in the department of Chemical Engineering & Materials
More information3.8 The First Law of Thermodynamics and the Energy Equation
CEE 3310 Control Volume Analysis, Sep 30, 2011 65 Review Conservation of angular momentum 1D form ( r F )ext = [ˆ ] ( r v)d + ( r v) out ṁ out ( r v) in ṁ in t CV 3.8 The First Law of Thermodynamics and
More informationHEAT TRANSFER. Mechanisms of Heat Transfer: (1) Conduction
HEAT TRANSFER Mechanisms of Heat Transfer: (1) Conduction where Q is the amount of heat, Btu, transferred in time t, h k is the thermal conductivity, Btu/[h ft 2 ( o F/ft)] A is the area of heat transfer
More informationHydraulics for Urban Storm Drainage
Urban Hydraulics Hydraulics for Urban Storm Drainage Learning objectives: understanding of basic concepts of fluid flow and how to analyze conduit flows, free surface flows. to analyze, hydrostatic pressure
More informationLecture 4. Differential Analysis of Fluid Flow NavierStockes equation
Lecture 4 Differential Analysis of Fluid Flow NavierStockes equation Newton second law and conservation of momentum & momentumofmomentum A jet of fluid deflected by an object puts a force on the object.
More informationInternal Forced Convection. Copyright The McGrawHill Companies, Inc. Permission required for reproduction or display.
Internal Forced Convection Copyright The McGrawHill Companies, Inc. Permission required for reproduction or display. Introduction Pipe circular cross section. Duct noncircular cross section. Tubes smalldiameter
More informationFall 2012 Qualifying Exam. Part I
Fall 2012 Qualifying Exam Part I Calculators are allowed. No reference material may be used. Please clearly mark the problems you have solved and want to be graded. Do only mark the required number of
More informationConceptual Study of the Effect of Radiation on Free Convective Flow of Mass and Heat Transfer over a Vertical Plate
Applied Mathematics 014, 4(): 5663 DOI: 10.593/j.am.014040.03 Conceptual Study of the Effect of Radiation on Free Convective Flow of Mass and Heat Transfer over a Vertical Plate Abah Sunday Ojima 1,*,
More informationChapters 16 Temperature and Heat
Chapters 16 Temperature and Heat 1 Overview of Chapter 16 Temperature and the Zeroth Law of Thermodynamics Temperature Scales Thermal Expansion Heat and Mechanical Work Specific Heat Conduction, Convection,
More informationCFD Investigation of Heat Transfer and Flow Patterns in Tube Side Laminar Flow and the Potential for Enhancement
A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 35, 2013 Guest Editors: Petar Varbanov, Jiří Klemeš, Panos Seferlis, Athanasios I. Papadopoulos, Spyros Voutetakis Copyright 2013, AIDIC Servizi
More informationCombined Effect of Buoyancy Force and Navier Slip on Entropy Generation in a Vertical Porous Channel
Entropy 0, 4, 08044; doi:0.3390/e40608 Article OPEN ACCESS entropy ISSN 0994300 www.mdpi.com/journal/entropy Combined Effect of Buoyancy Force and Navier Slip on Entropy Generation in a Vertical Porous
More informationMixed convection boundary layers in the stagnationpoint flow toward a stretching vertical sheet
Meccanica (2006) 41:509 518 DOI 10.1007/s1101200600094 Mied convection boundary layers in the stagnationpoint flow toward a stretching vertical sheet A. Ishak R. Nazar I. Pop Received: 17 June 2005
More informationModule 6: Free Convections Lecture 26: Evaluation of Nusselt Number. The Lecture Contains: Heat transfer coefficient. Objectives_template
The Lecture Contains: Heat transfer coefficient file:///d /Web%20Course%20(Ganesh%20Rana)/Dr.%20gautam%20biswas/Final/convective_heat_and_mass_transfer/lecture26/26_1.html[12/24/2014 6:08:23 PM] Heat transfer
More informationLiquids CHAPTER 13 FLUIDS FLUIDS. Gases. Density! Bulk modulus! Compressibility. To begin with... some important definitions...
CHAPTER 13 FLUIDS FLUIDS Liquids Gases Density! Bulk modulus! Compressibility Pressure in a fluid! Hydraulic lift! Hydrostatic paradox Measurement of pressure! Manometers and barometers Buoyancy and Archimedes
More informationCountercurrent heat exchanger
Countercurrent heat exchanger 1. Theoretical summary The basic operating principles and the simplified calculations regarding the counter current heat exchanger were discussed in the subject Chemical Unit
More informationHEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION
HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION 11 Fourier s Law of Heat Conduction, General Conduction Equation Based on Cartesian Coordinates, Heat Transfer Through a Wall, Composite Wall
More informationNUMERICAL SOLUTION OF MHD FLOW OVER A MOVING VERTICAL POROUS PLATE WITH HEAT AND MASS TRANSFER
Int. J. Chem. Sci.: 1(4), 14, 14871499 ISSN 97768X www.sadgurupublications.com NUMERICAL SOLUTION OF MHD FLOW OVER A MOVING VERTICAL POROUS PLATE WITH HEAT AND MASS TRANSFER R. LAKSHMI a, K. JAYARAMI
More informationEFFECT OF STAGGERED RIB LENGTH ON PERFORMANCE OF SOLAR AIR HEATER USING VRIB WITH SYMMETRICAL GAP AND STAGGERED RIB
EFFECT OF STAGGERED RIB LENGTH ON PERFORMANCE OF SOLAR AIR HEATER USING VRIB WITH SYMMETRICAL GAP AND STAGGERED RIB Piyush Kumar Jain and Atul Lanjewar Department of Mechanical Engineering, Maulana Azad
More informationLecture 9 Laminar Diffusion Flame Configurations
Lecture 9 Laminar Diffusion Flame Configurations 9.1 Different Flame Geometries and Single Droplet Burning Solutions for the velocities and the mixture fraction fields for some typical laminar flame configurations.
More informationHeat transfer and thermal properties of materials
Heat transfer and thermal properties of materials Background Effects of temperature on the properties of materials Heat transfer mechanisms Conduction Radiation Convection Background: Thermal management
More informationChapter 4: Fundamental Forces
Chapter 4: Fundamental Forces Newton s Second Law: F=ma In atmospheric science it is typical to consider the force per unit mass acting on the atmosphere: Force mass = a In order to understand atmospheric
More informationHeat source/sink and thermal conductivity effects on micropolar nanofluid flow over a MHD radiative stretching surface
Heat source/sink and thermal conductivity effects on micropolar nanofluid flow over a MHD radiative stretching surface Srinivas Maripala 1 and Kishan Naikoti 2 1Department of mathematics, Sreenidhi Institute
More informationFluids. Fluids in Motion or Fluid Dynamics
Fluids Fluids in Motion or Fluid Dynamics Resources: Serway  Chapter 9: 9.79.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT  8: Hydrostatics, Archimedes' Principle,
More informationNUMERICAL STUDY OF HEAT AND MASS TRANSFER DURING EVAPORATION OF A THIN LIQUID FILM
THERMAL SCIENCE, Year 2015, Vol. 19, No. 5, pp. 18051819 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 informationExperiment 1. Measurement of Thermal Conductivity of a Metal (Brass) Bar
Experiment 1 Measurement of Thermal Conductivity of a Metal (Brass) Bar Introduction: Thermal conductivity is a measure of the ability of a substance to conduct heat, determined by the rate of heat flow
More informationCalculation of Power and Flow Capacity of Rotor / Stator Devices in VisiMix RSD Program.
Calculation of Power and Flow Capacity of Rotor / Stator Devices in VisiMix RSD Program. L.N.Braginsky, D.Sc. (Was invited to be presented on the CHISA 201013th Conference on Process Integration, Modelling
More informationPressure in stationary and moving fluid. LabOnChip: Lecture 2
Pressure in stationary and moving fluid LabOnChip: Lecture Fluid Statics No shearing stress.no relative movement between adjacent fluid particles, i.e. static or moving as a single block Pressure at
More informationPhysics Final Exam  Summer 2014 Version 31  Answer Key Page 1 of 20
Physics 220  Final Exam  Summer 2014 Version 31  Answer Key Page 1 of 20 1. A pendulum on the Earth has a period T. The acceleration due to gravity on Mars is less than that on the Earth, and the acceleration
More informationUnsteady Laminar Free Convection from a Vertical Cone with Uniform Surface Heat Flux
Nonlinear Analysis: Modelling and Control, 2008, Vol. 13, No. 1, 47 60 Unsteady Laminar Free Convection from a Vertical Cone with Uniform Surface Heat Flux Bapuji Pullepu 1, K. Ekambavanan 1, A. J. Chamkha
More informationPart I.
Part I bblee@unimp . Introduction to Mass Transfer and Diffusion 2. Molecular Diffusion in Gasses 3. Molecular Diffusion in Liquids Part I 4. Molecular Diffusion in Biological Solutions and Gels 5. Molecular
More informationAerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)
Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation
More informationTransport Properties: Momentum Transport, Viscosity
Transport Properties: Momentum Transport, Viscosity 13th February 2011 1 Introduction Much as mass(material) is transported within luids (gases and liquids), linear momentum is also associated with transport,
More informationUnsteady Magnetohydrodynamic Free Convective Flow Past a Vertical Porous Plate
International Journal of Applied Science and Engineering 2013. 11, 3: 267275 Unsteady Magnetohydrodynamic Free Convective Flow Past a Vertical Porous Plate Murali Gundagania,*, Sivaiah Sheria, Ajit Paulb,
More informationUNIVERSITY OF OSLO. Faculty of Mathematics and Natural Sciences. MEK4300/9300 Viscous flow og turbulence
UNIVERSITY OF OSLO Faculty of Mathematics and Natural Sciences Examination in: Day of examination: Friday 15. June 212 Examination hours: 9. 13. This problem set consists of 5 pages. Appendices: Permitted
More informationN. SENAPATI 1 & R. K. DHAL 2
IMPACT: International Journal of Research in Humanities, Arts and Literature (IMPACT: IJRHAL) ISSN(E): 23218878; ISSN(P): 23474564 Vol. 2, Issue 1, Jan 2014, 1928 Impact Journals MAGNETIC EFFECTS OF
More informationChapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian
Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite
More informationINTRODUCTION TO FLUID MECHANICS June 27, 2013
INTRODUCTION TO FLUID MECHANICS June 27, 2013 PROBLEM 3 (1 hour) A perfect liquid of constant density ρ and constant viscosity µ fills the space between two infinite parallel walls separated by a distance
More information