# FORMULA SHEET. General formulas:

Save this PDF as:

Size: px
Start display at page:

## 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 Stefan-Boltzmann 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: * 10-5 M 2 /S THERMAL DIFFUSIVITY: * 10-6 M 2 /S VISCOSITY: 1.82 * 10-5 PA S VISCOSITY: * 10-3 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 visco-elastic fluids, where λ is a elasticity parameter Hagen-Poiseuille 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: Stefan-Boltzman 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

### 6. 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

### Transport 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

### Lecture 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

### Heat 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

### Fluid 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

### PHYSICAL 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

### Convection 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

### Outline. 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

### Tutorial 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,

### Level 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

### Chapter 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,

### Nicholas 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

### 1. 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

### EXAMPLE 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

### Convection. 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 -

### Lesson 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

### Thermodynamics, 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

### Reynolds, 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

### Friction 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

### Physics 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, UW-Madison 1 Fluids Density

### MIXED CONVECTION SLIP FLOW WITH TEMPERATURE JUMP ALONG A MOVING PLATE IN PRESENCE OF FREE STREAM

THERMAL SCIENCE, Year 015, Vol. 19, No. 1, pp. 119-18 119 MIXED CONVECTION SLIP FLOW WITH TEMPERATURE JUMP ALONG A MOVING PLATE IN PRESENCE OF FREE STREAM by Gurminder SINGH *a and Oluwole Daniel MAKINDE

### PIPE 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,

### TALLINN 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.

### Rate 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

### OUTCOME 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,

### 1. 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

### Mechanical 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

### Contents. 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. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors

### Chapter 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

### Masters 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 =

### Shell 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

### PHY121 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

### Figure 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)

### Momentum 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

### ME 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 non-circular ducts) are very common. Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared

### Forced 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

### BME 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

### 150A 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

### PHYSICS. 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

### In 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

### Piping 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

### DEPARTMENT OF MECHANICAL ENGINEERING. ME 6502 Heat and Mass Transfer III YEAR-V SEMESTER

ME650 HEAT AND MASS TRNSFER MARKS & 16 MARKS QUESTION AND ANSWER ME 650 Heat and Mass Transfer III YEAR-V SEMESTER NAME :. REG.NO :. BRANCH :... YEAR & SEM :. 1 ME650 HEAT AND MASS TRNSFER MARKS & 16 MARKS

### Temperature 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

### So 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

### PROBLEM 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

### Chapter 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

### PART 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

### Pressure in stationary and moving fluid Lab- Lab On- On Chip: Lecture 2

Pressure in stationary and moving fluid Lab-On-Chip: 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;

### CLASS 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

### Laminar 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

### Today 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

### R09. d water surface. Prove that the depth of pressure is equal to p +.

Code No:A109210105 R09 SET-1 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

### MHD Non-Newtonian Power Law Fluid Flow and Heat Transfer Past a Non-Linear 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 Non-Newtonian Power Law Fluid Flow and Heat Transfer Past a Non-Linear Stretching Surface

### Steven 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

### Forced 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

### Analysis 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

### HEAT 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

### Computational 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

### Thermal 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

### Analytical 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

### ME 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

### 7.2 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

### AMRITA 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

### 3.8 The First Law of Thermodynamics and the Energy Equation

CEE 3310 Control Volume Analysis, Sep 30, 2011 65 Review Conservation of angular momentum 1-D 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

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

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

### Hydraulics 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

### Lecture 4. Differential Analysis of Fluid Flow Navier-Stockes equation

Lecture 4 Differential Analysis of Fluid Flow Navier-Stockes equation Newton second law and conservation of momentum & momentum-of-momentum A jet of fluid deflected by an object puts a force on the object.

### Internal 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

### Fall 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

### Conceptual Study of the Effect of Radiation on Free Convective Flow of Mass and Heat Transfer over a Vertical Plate

Applied Mathematics 014, 4(): 56-63 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,*,

### Chapters 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,

### CFD 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

### Combined Effect of Buoyancy Force and Navier Slip on Entropy Generation in a Vertical Porous Channel

Entropy 0, 4, 08-044; doi:0.3390/e40608 Article OPEN ACCESS entropy ISSN 099-4300 www.mdpi.com/journal/entropy Combined Effect of Buoyancy Force and Navier Slip on Entropy Generation in a Vertical Porous

### Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet

Meccanica (2006) 41:509 518 DOI 10.1007/s11012-006-0009-4 Mied convection boundary layers in the stagnation-point flow toward a stretching vertical sheet A. Ishak R. Nazar I. Pop Received: 17 June 2005

### Module 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

### Liquids 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

### Countercurrent 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

### HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION

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

### NUMERICAL SOLUTION OF MHD FLOW OVER A MOVING VERTICAL POROUS PLATE WITH HEAT AND MASS TRANSFER

Int. J. Chem. Sci.: 1(4), 14, 1487-1499 ISSN 97-768X www.sadgurupublications.com NUMERICAL SOLUTION OF MHD FLOW OVER A MOVING VERTICAL POROUS PLATE WITH HEAT AND MASS TRANSFER R. LAKSHMI a, K. JAYARAMI

### EFFECT OF STAGGERED RIB LENGTH ON PERFORMANCE OF SOLAR AIR HEATER USING V-RIB WITH SYMMETRICAL GAP AND STAGGERED RIB

EFFECT OF STAGGERED RIB LENGTH ON PERFORMANCE OF SOLAR AIR HEATER USING V-RIB WITH SYMMETRICAL GAP AND STAGGERED RIB Piyush Kumar Jain and Atul Lanjewar Department of Mechanical Engineering, Maulana Azad

### Lecture 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.

### Heat 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

### Chapter 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

### Heat 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

### Fluids. Fluids in Motion or Fluid Dynamics

Fluids Fluids in Motion or Fluid Dynamics Resources: Serway - Chapter 9: 9.7-9.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT - 8: Hydrostatics, Archimedes' Principle,

### NUMERICAL 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

### Experiment 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

### Calculation 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 2010-13th Conference on Process Integration, Modelling

### Pressure in stationary and moving fluid. Lab-On-Chip: Lecture 2

Pressure in stationary and moving fluid Lab-On-Chip: Lecture Fluid Statics No shearing stress.no relative movement between adjacent fluid particles, i.e. static or moving as a single block Pressure at

### Physics 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

### Unsteady 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

### Part 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

### Aerodynamics. 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

### Transport 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,

### Unsteady Magnetohydrodynamic Free Convective Flow Past a Vertical Porous Plate

International Journal of Applied Science and Engineering 2013. 11, 3: 267-275 Unsteady Magnetohydrodynamic Free Convective Flow Past a Vertical Porous Plate Murali Gundagania,*, Sivaiah Sheria, Ajit Paulb,

### UNIVERSITY 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

### N. SENAPATI 1 & R. K. DHAL 2

IMPACT: International Journal of Research in Humanities, Arts and Literature (IMPACT: IJRHAL) ISSN(E): 2321-8878; ISSN(P): 2347-4564 Vol. 2, Issue 1, Jan 2014, 19-28 Impact Journals MAGNETIC EFFECTS OF