Forced Convection Heat Transfer

Size: px
Start display at page:

Download "Forced Convection Heat Transfer"

Transcription

1 Forced onvection Heat raner onvection i the mechanim o heat traner through a luid in the preence o bul luid motion. onvection i claiied a natural (or ree) and orced convection depending on how the luid motion i initiated. In natural convection, any luid motion i caued by natural mean uch a the buoyancy eect, i.e. the rie o warmer luid and all the cooler luid. Wherea in orced convection, the luid i orced to low over a urace or in a tube by eternal mean uch a a pump or an. Mechanim o Forced onvection onvection heat traner i complicated ince it involve luid motion a well a heat conduction. he luid motion enhance heat traner (the higher the velocity the higher the heat traner rate). he rate o convection heat traner i epreed by Newton law o cooling: q Q conv conv h W / m ha W he convective heat traner coeicient h trongly depend on the luid propertie and roughne o the olid urace, and the type o the luid low (laminar or turbulent). V Q conv V Zero velocity at the urace. Q cond Solid hot urace, Fig. 1: Forced convection. It i aumed that the velocity o the luid i zero at the wall, thi aumption i called nolip condition. A a reult, the heat traner rom the olid urace to the luid layer adjacent to the urace i by pure conduction, ince the luid i motionle. hu, M. Bahrami ENS 388 (F09) Forced onvection Heat raner 1

2 q conv q q conv luid y h cond y0 h luid y y0 W / m. K he convection heat traner coeicient, in general, varie along the low direction. he mean or average convection heat traner coeicient or a urace i determined by (properly) averaging the local heat traner coeicient over the entire urace. Velocity Boundary ayer onider the low o a luid over a lat plate, the velocity and the temperature o the luid approaching the plate i uniorm at U and. he luid can be conidered a adjacent layer on top o each other. Fig. : Velocity boundary layer. Auming no lip condition at the wall, the velocity o the luid layer at the wall i zero. he motionle layer low down the particle o the neighboring luid layer a a reult o riction between the two adjacent layer. he preence o the plate i elt up to ome ditance rom the plate beyond which the luid velocity U remain unchanged. hi region i called velocity boundary layer. Boundary layer region i the region where the vicou eect and the velocity change are igniicant and the invicid region i the region in which the rictional eect are negligible and the velocity remain eentially contant. he riction between two adjacent layer between two layer act imilar to a drag orce (riction orce). he drag orce per unit area i called the hear tre: V y y0 N / m where μ i the dynamic vicoity o the luid g/m. or N./m. Vicoity i a meaure o luid reitance to low, and i a trong unction o temperature. he urace hear tre can alo be determined rom: M. Bahrami ENS 388 (F09) Forced onvection Heat raner

3 U N / m where i the riction coeicient or the drag coeicient which i determined eperimentally in mot cae. he drag orce i calculated rom: U FD A N he low in boundary layer tart a mooth and treamlined which i called laminar low. At ome ditance rom the leading edge, the low turn chaotic, which i called turbulent and it i characterized by velocity luctuation and highly diordered motion. he tranition rom laminar to turbulent low occur over ome region which i called tranition region. he velocity proile in the laminar region i approimately parabolic, and become latter in turbulent low. he turbulent region can be conidered o three region: laminar ublayer (where vicou eect are dominant), buer layer (where both laminar and turbulent eect eit), and turbulent layer. he intene miing o the luid in turbulent low enhance heat and momentum traner between luid particle, which in turn increae the riction orce and the convection heat traner coeicient. Non dimenional Group In convection, it i a common practice to non dimenionalize the governing equation and combine the variable which group together into dimenionle number (group). elt number: non dimenional heat traner coeicient h q q where δ i the characteritic length, i.e. D or the tube and or the lat plate. elt number repreent the enhancement o heat traner through a luid a a reult o convection relative to conduction acro the ame luid layer. Reynold number: ratio o inertia orce to vicou orce in the luid Re inertia orce vicou orce conv cond V V At large Re number, the inertia orce, which are proportional to the denity and the velocity o the luid, are large relative to the vicou orce; thu the vicou orce cannot prevent the random and rapid luctuation o the luid (turbulent regime). M. Bahrami ENS 388 (F09) Forced onvection Heat raner 3

4 he Reynold number at which the low become turbulent i called the critical Reynold number. For lat plate the critical Re i eperimentally determined to be approimately Re critical = 10. andtl number: i a meaure o relative thicne o the velocity and thermal boundary layer molecular diuivity o momentum p molecular diuivity o heat where luid propertie are: ma denity : ρ, (g/m 3 ) peciic heat capacity : p (J/g K) dynamic vicoity : µ, (N /m ) inematic vicoity : ν, µ / ρ (m /) thermal conductivity :, (W/m K) thermal diuivity : α, /(ρ p ) (m /) hermal Boundary ayer Similar to velocity boundary layer, a thermal boundary layer develop when a luid at peciic temperature low over a urace which i at dierent temperature. Fig. 3: hermal boundary layer. he thicne o the thermal boundary layer δ t i deined a the ditance at which: 0.99 he relative thicne o the velocity and the thermal boundary layer i decribed by the andtl number. For low andtl number luid, i.e. liquid metal, heat diue much ater than momentum low (remember = ν/α<<1) and the velocity boundary layer i ully contained within the thermal boundary layer. On the other hand, or high andtl number luid, i.e. oil, heat diue much lower than the momentum and the thermal boundary layer i contained within the velocity boundary layer. M. Bahrami ENS 388 (F09) Forced onvection Heat raner 4

5 Flow Over Flat Plate he riction and heat traner coeicient or a lat plate can be determined by olving the conervation o ma, momentum, and energy equation (either approimately or numerically). hey can alo be meaured eperimentally. It i ound that the elt number can be epreed a: h Re where, m, and n are contant and i the length o the lat plate. he propertie o the luid are uually evaluated at the ilm temperature deined a: aminar Flow he local riction coeicient and the elt number at the location or laminar low over a lat plate are, h Re 0.33 Re 1/ 1/ m n 0.6 where i the ditant rom the leading edge o the plate and Re = ρv / μ. he averaged riction coeicient and the elt number over the entire iothermal plate or laminar regime are: h 1.38 Re Re 1/ 1/ 0.6 aing the critical Reynold number to be 10, the length o the plate cr over which the low i laminar can be determined rom urbulent Flow Re cr 10 V he local riction coeicient and the elt number at location or turbulent low over a lat iothermal plate are: cr M. Bahrami ENS 388 (F09) Forced onvection Heat raner

6 , h 0.09 Re Re 1/ 4 / 10 Re Re 10 he averaged riction coeicient and elt number over the iothermal plate in turbulent region are: h 0.04 Re 0.03 Re 1/ 4 / 10 Re ombined aminar and urbulent Flow 10 Re 10 I the plate i uiciently long or the low to become turbulent (and not long enough to diregard the laminar low region), we hould ue the average value or riction coeicient and the elt number. cr 1 0 cr 1 h h, 0,, a min ar a min ar d d cr h cr,, urbulent,, urbulent where the critical Reynold number i aumed to be 10. Ater perorming the integral and impliication, one obtain: 1/ h 0.03 Re Re Re 4 / Re d d 10 Re 10 he above relationhip have been obtained or the cae o iothermal urace, but could alo be ued approimately or the cae o non iothermal urace. In uch cae aume the urace temperature be contant at ome average value. For iolu (uniorm heat lu) plate, the local elt number or laminar and turbulent low can be ound rom: h 0.43Re h Re aminar (iolu plate) urbulent (iolu plate) Note the iolu relationhip give value that are 36% higher or laminar and 4% or turbulent low relative to iothermal plate cae. M. Bahrami ENS 388 (F09) Forced onvection Heat raner 6

7 Eample 1 Engine oil at 60 low over a m long lat plate whoe temperature i 0 with a velocity o m/. Determine the total drag orce and the rate o heat traner per unit width o the entire plate. oil = 60 V = m/ Q =0 = m We aume the critical Reynold number i 10. he propertie o the oil at the ilm temperature are: he Re number or the plate i: g / m W /( m. K) m / Re = V / ν = which i le than the critical Re. hu we have laminar low. he riction coeicient and the drag orce can be ound rom: F D 1.38 Re V A he elt number i determined rom: 3 g m m m 86 / / 1.N h hen, W h. m K Q ha 0664 Re 11040W M. Bahrami ENS 388 (F09) Forced onvection Heat raner

8 Flow acro ylinder and Sphere he characteritic length or a circular tube or phere i the eternal diameter, D, and the Reynold number i deined: V D Re he critical Re or the low acro phere or tube i 10. he approaching luid to the cylinder (a phere) will branch out and encircle the body, orming a boundary layer. Fig. 4: ypical low pattern over phere and treamlined body and drag orce. At low Re (Re < 4) number the luid completely wrap around the body. At higher Re number, the luid i too at to remain attached to the urace a it approache the top o the cylinder. hu, the boundary layer detache rom the urace, orming a wae behind the body. hi point i called the eparation point. o reduce the drag coeicient, treamlined bodie are more uitable, e.g. airplane are built to reemble bird and ubmarine to reemble ih, Fig. 4. In low pat cylinder or phere, low eparation occur around 80 or laminar low and 140 or turbulent low. V FD D AN N AN : rontal area where rontal area o a cylinder i A N = D, and or a phere i A N = πd / 4. M. Bahrami ENS 388 (F09) Forced onvection Heat raner 8

9 he drag orce acting on a body i caued by two eect: the riction drag (due to the hear tre at the urace) and the preure drag which i due to preure dierential between the ront and rear ide o the body. A a reult o tranition to turbulent low, which move the eparation point urther to the rear o the body, a large reduction in the drag coeicient occur. A a reult, the urace o gol ball i intentionally roughened to induce turbulent at a lower Re number, ee Fig.. Fig. : Roughened gol ball reduce D. he average heat traner coeicient or cro low over a cylinder can be ound rom the correlation preented by hurchill and Berntein: 1/ / 8 hd 0.6 Re Re yl / 3 1/ ,000 where luid propertie are evaluated at the ilm temperature = ( + ) /. For low over a phere, Whitaer recommended the ollowing: Sph 4 / 0.4Re 1 / 0.06 Re / / 1/ 4 hd / M. Bahrami ENS 388 (F09) Forced onvection Heat raner 9

10 which i valid or 3. < Re < 80,000 and 0. < < 380. he luid propertie are evaluated at the ree tream temperature, ecept or μ which i evaluated at urace temperature. he average elt number or low acro circular and non circular cylinder can be ound rom able 10 3 engel boo. Eample he decorative platic ilm on a copper phere o 10 mm diameter i cured in an oven at. Upon removal rom the oven, the phere i ubjected to an air tream at 1 atm and 3 having a velocity o 10 m/, etimate how long it will tae to cool the phere to 3. P = 1 atm. V = 10 m/ = 3 opper phere D = 10 mm i = = 3 Aumption: 1. Negligible thermal reitance and capacitance or the platic layer.. Spatially iothermal phere. 3. Negligible Radiation. opper at 38 K ρ = 8933 g / m 3 = 399 W / m.k p = 38 J / g.k Air at 96 K μ = N. / m v = m / = 0.08 W / m.k = 0.09 μ = N. / m he time required to complete the cooling proce may be obtained rom the reult or a lumped capacitance. V t ha P i ln p D i ln 6h Whitaer relationhip can be ued to ind h or the low over phere: Sph where Re = ρvd / μ = 610. Hence, 0.4Re 1 / 0.06 Re / / 1/ 4 hd / M. Bahrami ENS 388 (F09) Forced onvection Heat raner 10

11 Sph h hd / 0.4(610) D 1 W / m K 1/ he required time or cooling i then t 0.06(610) / g / m 38J / g. K 0.01m 61W / m. K (0.09) ln 69. ec 3 3 1/ M. Bahrami ENS 388 (F09) Forced onvection Heat raner 11

Heat transfer to or from a fluid flowing through a tube

Heat transfer to or from a fluid flowing through a tube Heat tranfer to or from a fluid flowing through a tube R. Shankar Subramanian A common ituation encountered by the chemical engineer i heat tranfer to fluid flowing through a tube. Thi can occur in heat

More information

6. Friction, Experiment and Theory

6. Friction, Experiment and Theory 6. Friction, Experiment and Theory The lab thi wee invetigate the rictional orce and the phyical interpretation o the coeicient o riction. We will mae ue o the concept o the orce o gravity, the normal

More information

Pipe Flow Calculations

Pipe Flow Calculations Pipe Flow Calculation R. Shankar Subramanian epartment o Chemical and Biomolecular Engineering Clarkon Univerity We begin with ome reult that we hall ue when making riction lo calculation or teady, ully

More information

1D STEADY STATE HEAT

1D STEADY STATE HEAT D SEADY SAE HEA CONDUCION () Prabal alukdar Aociate Profeor Department of Mechanical Engineering II Delhi E-mail: prabal@mech.iitd.ac.in Convection Boundary Condition Heat conduction at the urface in a

More information

Figure 2.1. a. Block diagram representation of a system; b. block diagram representation of an interconnection of subsystems

Figure 2.1. a. Block diagram representation of a system; b. block diagram representation of an interconnection of subsystems Figure. a. Block diagram repreentation o a ytem; b. block diagram repreentation o an interconnection o ubytem REVIEW OF THE LAPLACE TRANSFORM Table. Laplace tranorm table Table. Laplace tranorm theorem

More information

FLUID MECHANICS. TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES

FLUID MECHANICS. TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES FLUID MECHANICS TUTORIAL No.4 FLOW THROUGH POROUS PASSAGES In thi tutorial you will continue the work on laminar flow and develop Poieuille' equation to the form known a the Carman - Kozeny equation. Thi

More information

Ohm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power

Ohm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power Ohm Law Ohmic relationhip V=IR Ohm law tate that current through the conductor i directly proportional to the voltage acro it if temperature and other phyical condition do not change. In many material,

More information

Advanced Multiphase Modeling of Solidification

Advanced Multiphase Modeling of Solidification Advanced Multiphae Modeling o Solidiication with OpenFOAM A. Vakhruhev 1, A. Ludwig 2, M. Wu 1, Y. Tang 3, G. Hackl 3, G. Nitzl 4 1 Chritian Doppler Laboratory or Advanced roce Simulation o Solidiication

More information

Natural Convection. Buoyancy force

Natural Convection. Buoyancy force Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

More information

Darcy Friction Factor Formulae in Turbulent Pipe Flow

Darcy Friction Factor Formulae in Turbulent Pipe Flow Darcy Friction Factor Formulae in Turbulent Pipe Flow Jukka Kiijärvi Lunowa Fluid Mechanics Paper 110727 July 29, 2011 Abstract The Darcy riction actor in turbulent pipe low must be solved rom the Colebrook

More information

XI / PHYSICS FLUIDS IN MOTION 11/PA

XI / PHYSICS FLUIDS IN MOTION 11/PA Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A

More information

Basic Equations, Boundary Conditions and Dimensionless Parameters

Basic Equations, Boundary Conditions and Dimensionless Parameters Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were

More information

σ m using Equation 8.1 given that σ

σ m using Equation 8.1 given that σ 8. Etimate the theoretical fracture trength of a brittle material if it i known that fracture occur by the propagation of an elliptically haped urface crack of length 0.8 mm and having a tip radiu of curvature

More information

FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES

FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES FREESTUDY HEAT TRANSFER TUTORIAL ADVANCED STUDIES This is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection. The tutorials are designed to bring the

More information

Steady Heat Conduction

Steady Heat Conduction Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long

More information

The Analysis of Two-Phase Condensation Heat Transfer Models Based on the Comparison of the Boundary Condition

The Analysis of Two-Phase Condensation Heat Transfer Models Based on the Comparison of the Boundary Condition Acta Polytechnica Hungarica Vol. 9, No. 6, 2012 The Analysis o Two-Phase Condensation Heat Transer Models Based on the Comparison o the Boundary Condition Róbert Sánta College o Applied Sciences Subotica

More information

Turbulent Mixing and Chemical Reaction in Stirred Tanks

Turbulent Mixing and Chemical Reaction in Stirred Tanks Turbulent Mixing and Chemical Reaction in Stirred Tank André Bakker Julian B. Faano Blend time and chemical product ditribution in turbulent agitated veel can be predicted with the aid of Computational

More information

Incline and Friction Examples

Incline and Friction Examples Incline and riction Eample Phic 6A Prepared b Vince Zaccone riction i a force that oppoe the motion of urface that are in contact with each other. We will conider 2 tpe of friction in thi cla: KINETIC

More information

BUILT-IN DUAL FREQUENCY ANTENNA WITH AN EMBEDDED CAMERA AND A VERTICAL GROUND PLANE

BUILT-IN DUAL FREQUENCY ANTENNA WITH AN EMBEDDED CAMERA AND A VERTICAL GROUND PLANE Progre In Electromagnetic Reearch Letter, Vol. 3, 51, 08 BUILT-IN DUAL FREQUENCY ANTENNA WITH AN EMBEDDED CAMERA AND A VERTICAL GROUND PLANE S. H. Zainud-Deen Faculty of Electronic Engineering Menoufia

More information

MECH 2110 - Statics & Dynamics

MECH 2110 - Statics & Dynamics Chapter D Problem 3 Solution 1/7/8 1:8 PM MECH 11 - Static & Dynamic Chapter D Problem 3 Solution Page 7, Engineering Mechanic - Dynamic, 4th Edition, Meriam and Kraige Given: Particle moving along a traight

More information

Linear Momentum and Collisions

Linear Momentum and Collisions Chapter 7 Linear Momentum and Colliion 7.1 The Important Stuff 7.1.1 Linear Momentum The linear momentum of a particle with ma m moving with velocity v i defined a p = mv (7.1) Linear momentum i a vector.

More information

EXPERIMENT 11 CONSOLIDATION TEST

EXPERIMENT 11 CONSOLIDATION TEST 119 EXPERIMENT 11 CONSOLIDATION TEST Purpoe: Thi tet i performed to determine the magnitude and rate of volume decreae that a laterally confined oil pecimen undergoe when ubjected to different vertical

More information

v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t

v = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement

More information

SOLUTION OF BOUNDARY LAYER

SOLUTION OF BOUNDARY LAYER SOUION OF BOUNDARY AYER EQUAIONS Prabal alkar Aociate Proeor Department o Mechanical Engineering II Delhi E-mail: prabal@mech.iit.ac.in P.alkar/Mech-IID Bonar laer Approimation X momentm: ρ μ P Appling

More information

How To Design A Wind Turbine

How To Design A Wind Turbine Critical iue in wind turbine deign (Uncertaintie) IEA-meeting Trondheim, Norway June 4-5 005 Proect idea: To ignificantly improve deign bai for offhore wind turbine by: Analying all deign proce component

More information

Transient turbulent flow in a pipe

Transient turbulent flow in a pipe Tranient turbulent flow in a pipe M. S. Ghidaoui A. A. Kolyhkin Rémi Vaillancourt CRM-3176 January 25 Thi work wa upported in part by the Latvian Council of Science, project 4.1239, the Natural Science

More information

Calibration and Uncertainties of Pipe Roughness Height

Calibration and Uncertainties of Pipe Roughness Height 9 th IWA/IAHR Conerence on Urban Drainage Modelling Calibration and Uncertainties o Pipe Roughness Height Kailin Yang, Yongxin Guo, Xinlei Guo,Hui Fu and Tao Wang China Institute o Water Resources and

More information

Polyethylene (PE) pipes Dimensions

Polyethylene (PE) pipes Dimensions DEUTSCHE NORM Augut 1999 Polyethylene (PE) pipe Dimenion { 8074 ICS 23.040.20 Rohre au Polyethylen (PE) PE 63, PE 80, PE 100, PE HD Maße Superede September 1987 edition. In keeping with current practice

More information

Unit 11 Using Linear Regression to Describe Relationships

Unit 11 Using Linear Regression to Describe Relationships Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory

More information

Engineering Bernoulli Equation

Engineering Bernoulli Equation Engineering Bernoulli Equation R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkon Univerity The Engineering Bernoulli equation can be derived from the principle of conervation

More information

Investigation of the Benzene Molecule Adsorbed on Faujasite Zeolite Using Double Quantum Filtered NMR Spectral Analysis

Investigation of the Benzene Molecule Adsorbed on Faujasite Zeolite Using Double Quantum Filtered NMR Spectral Analysis 5070 J. Phy. Chem. B 1999, 103, 5070-5080 Invetigation o the Benzene Molecule Adorbed on Faujaite Zeolite Uing Double Quantum Filtered NMR Spectral Analyi Yu-Huei Chen and Lian-Pin Hwang* Department o

More information

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD

GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Earth Material Lecture 13 Earth Material Hooke law of elaticity Force = E Area Hooke law n = E n Extenion Length Robert Hooke (1635-1703) wa a virtuoo cientit contributing to geology, palaeontology, biology

More information

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy

More information

Report 4668-1b 30.10.2010. Measurement report. Sylomer - field test

Report 4668-1b 30.10.2010. Measurement report. Sylomer - field test Report 4668-1b Meaurement report Sylomer - field tet Report 4668-1b 2(16) Contet 1 Introduction... 3 1.1 Cutomer... 3 1.2 The ite and purpoe of the meaurement... 3 2 Meaurement... 6 2.1 Attenuation of

More information

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

More information

MODELLING HIGH TEMPERATURE FLOW STRESS CURVES OF TITANIUM ALLOYS

MODELLING HIGH TEMPERATURE FLOW STRESS CURVES OF TITANIUM ALLOYS MODELLING HIGH TEMPERATURE FLOW STRESS CURVES OF TITANIUM ALLOYS Z. Guo, N. Saunder, J.P. Schillé, A.P. Miodownik Sente Software Ltd, Surrey Technology Centre, Guildford, GU2 7YG, U.K. Keyword: Titanium

More information

LAB1 2D and 3D step-index waveguides. TE and TM modes.

LAB1 2D and 3D step-index waveguides. TE and TM modes. LAB1 2D and 3D tep-index waveguide. T and TM mode. 1. Getting tarted 1.1. The purpoe o thi laboratory are: - T/TM mode propagation in 2D (lab waveguide) tep-index waveguide a a unction o guide peciic parameter

More information

Basic Principles in Microfluidics

Basic Principles in Microfluidics Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces

More information

Mathematical Modeling of Molten Slag Granulation Using a Spinning Disk Atomizer (SDA)

Mathematical Modeling of Molten Slag Granulation Using a Spinning Disk Atomizer (SDA) Mathematical Modeling of Molten Slag Granulation Uing a Spinning Dik Atomizer (SDA) Hadi Purwanto and Tomohiro Akiyama Center for Advanced Reearch of Energy Converion Material, Hokkaido Univerity Kita

More information

FLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions

FLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or

More information

THE MODELING AND CALCULATION OF SOUND RADIATION FROM FACILITIES WITH GAS FLOWED PIPES INTRODUCTION

THE MODELING AND CALCULATION OF SOUND RADIATION FROM FACILITIES WITH GAS FLOWED PIPES INTRODUCTION THE MODELING AND CALCULATION OF SOUND ADIATION FOM FACILITIES WITH GAS FLOWED PIPES INTODUCTION Analysis o the emission caused by industrial acilities like chemical plants, reineries or other production

More information

THE PSEUDO SINGLE ROW RADIATOR DESIGN

THE PSEUDO SINGLE ROW RADIATOR DESIGN International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 146-153, Article ID: IJMET_07_01_015 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1

More information

HEAVY OIL FLOW MEASUREMENT CHALLENGES

HEAVY OIL FLOW MEASUREMENT CHALLENGES HEAVY OIL FLOW MEASUREMENT CHALLENGES 1 INTRODUCTION The vast majority of the world s remaining oil reserves are categorised as heavy / unconventional oils (high viscosity). Due to diminishing conventional

More information

Physics 111. Exam #1. January 24, 2014

Physics 111. Exam #1. January 24, 2014 Phyic 111 Exam #1 January 24, 2014 Name Pleae read and follow thee intruction carefully: Read all problem carefully before attempting to olve them. Your work mut be legible, and the organization clear.

More information

Fundamentals of THERMAL-FLUID SCIENCES

Fundamentals of THERMAL-FLUID SCIENCES Fundamentals of THERMAL-FLUID SCIENCES THIRD EDITION YUNUS A. CENGEL ROBERT H. TURNER Department of Mechanical JOHN M. CIMBALA Me Graw Hill Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl

More information

Name: SID: Instructions

Name: SID: Instructions CS168 Fall 2014 Homework 1 Aigned: Wedneday, 10 September 2014 Due: Monday, 22 September 2014 Name: SID: Dicuion Section (Day/Time): Intruction - Submit thi homework uing Pandagrader/GradeScope(http://www.gradecope.com/

More information

8. ENERGY PERFORMANCE ASSESSMENT OF COMPRESSORS 8.1 Introduction

8. ENERGY PERFORMANCE ASSESSMENT OF COMPRESSORS 8.1 Introduction 8. ENERGY PERFORMANCE ASSESSMENT OF COMPRESSORS 8.1 Introduction The compressed air system is not only an energy intensive utility but also one o the least energy eicient. Over a period o time, both perormance

More information

Engine Heat Transfer. Engine Heat Transfer

Engine Heat Transfer. Engine Heat Transfer Engine Heat Transfer 1. Impact of heat transfer on engine operation 2. Heat transfer environment 3. Energy flow in an engine 4. Engine heat transfer Fundamentals Spark-ignition engine heat transfer Diesel

More information

Ideal Rankine Cycle T 1 2

Ideal Rankine Cycle T 1 2 Vapor Poer Cycle We kno that the Carnot cycle i mot efficient cycle operatg beteen to pecified temperature limit. Hoever; the Carnot cycle i not a uitable model for team poer cycle ce: he turbe ha to handle

More information

FREE CONVECTION FROM OPTIMUM SINUSOIDAL SURFACE EXPOSED TO VERTICAL VIBRATIONS

FREE CONVECTION FROM OPTIMUM SINUSOIDAL SURFACE EXPOSED TO VERTICAL VIBRATIONS International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 214-224, Article ID: IJMET_07_01_022 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1

More information

OUTPUT STREAM OF BINDING NEURON WITH DELAYED FEEDBACK

OUTPUT STREAM OF BINDING NEURON WITH DELAYED FEEDBACK binding neuron, biological and medical cybernetic, interpike interval ditribution, complex ytem, cognition and ytem Alexander VIDYBIDA OUTPUT STREAM OF BINDING NEURON WITH DELAYED FEEDBACK A binding neuron

More information

Notes on Polymer Rheology Outline

Notes on Polymer Rheology Outline 1 Why is rheology important? Examples of its importance Summary of important variables Description of the flow equations Flow regimes - laminar vs. turbulent - Reynolds number - definition of viscosity

More information

HEAT AND MASS TRANSFER

HEAT AND MASS TRANSFER MEL242 HEAT AND MASS TRANSFER Prabal Talukdar Associate Professor Department of Mechanical Engineering g IIT Delhi prabal@mech.iitd.ac.in MECH/IITD Course Coordinator: Dr. Prabal Talukdar Room No: III,

More information

ME 24-221 THERMODYNAMICS I

ME 24-221 THERMODYNAMICS I Solution to extra problem in chapter 8 Noember 9, 000 Fall 000 J. Murthy ME 4- HERMODYNAMICS I 8.5 Water i ued a the working fluid in a Carnot cycle heat engine, where it change from aturated liquid to

More information

International Journal of Heat and Mass Transfer

International Journal of Heat and Mass Transfer International Journal of Heat and Ma Tranfer 5 (9) 14 144 Content lit available at ScienceDirect International Journal of Heat and Ma Tranfer journal homepage: www.elevier.com/locate/ijhmt Technical Note

More information

Prediction of Pressure Drop in Chilled Water Piping System Using Theoretical and CFD Analysis

Prediction of Pressure Drop in Chilled Water Piping System Using Theoretical and CFD Analysis Shirish P. Patil et.al / International Journal o Engineering and Technology (IJET) Prediction o Pressure Drop in Chilled Water Piping System Using Theoretical and CFD Analysis Shirish P. Patil #1, Abhijeet

More information

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati

Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation

More information

Trace Layer Import for Printed Circuit Boards Under Icepak

Trace Layer Import for Printed Circuit Boards Under Icepak Tutorial 13. Trace Layer Import for Printed Circuit Boards Under Icepak Introduction: A printed circuit board (PCB) is generally a multi-layered board made of dielectric material and several layers of

More information

A) When two objects slide against one another, the magnitude of the frictional force is always equal to μ

A) When two objects slide against one another, the magnitude of the frictional force is always equal to μ Phyic 100 Homewor 5 Chapter 6 Contact Force Introduced ) When two object lide againt one another, the magnitude of the frictional force i alway equal to μ B) When two object are in contact with no relative

More information

Numerical Simulation and Experimental Verification of Air Flow through a Heated Pipe

Numerical Simulation and Experimental Verification of Air Flow through a Heated Pipe International Journal of Mechanical & Mechatronic Engineering IJMME-IJENS Vol:0 No:02 7 Numerical Simulation and Exerimental Verification of Air Flow through a Heated Pie Qaier Abba, M. Mahabat Khan, Rizwan

More information

Chapter 10 Velocity, Acceleration, and Calculus

Chapter 10 Velocity, Acceleration, and Calculus Chapter 10 Velocity, Acceleration, and Calculu The firt derivative of poition i velocity, and the econd derivative i acceleration. Thee derivative can be viewed in four way: phyically, numerically, ymbolically,

More information

Combining Statistics and Semantics via Ensemble Model for Document Clustering

Combining Statistics and Semantics via Ensemble Model for Document Clustering ombining tatitic and emantic via Enemble Model or Document lutering amah Jamal Fodeh Michigan tate Univerity Eat Laning, MI, 48824 odeham@mu.edu William F Punch Michigan tate Univerity Eat Laning, MI,

More information

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22 BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

More information

4.What is the appropriate dimensionless parameter to use in comparing flow types? YOUR ANSWER: The Reynolds Number, Re.

4.What is the appropriate dimensionless parameter to use in comparing flow types? YOUR ANSWER: The Reynolds Number, Re. CHAPTER 08 1. What is most likely to be the main driving force in pipe flow? A. Gravity B. A pressure gradient C. Vacuum 2.What is a general description of the flow rate in laminar flow? A. Small B. Large

More information

Large Generators and High Power Drives

Large Generators and High Power Drives Large Generator and High Power Drive Content of lecture 1. Manufacturing of Large Electrical Machine 2. Heating and cooling of electrical machine 3. Eddy current loe in winding ytem 4. Excitation of ynchronou

More information

MSc Financial Economics: International Finance. Bubbles in the Foreign Exchange Market. Anne Sibert. Revised Spring 2013. Contents

MSc Financial Economics: International Finance. Bubbles in the Foreign Exchange Market. Anne Sibert. Revised Spring 2013. Contents MSc Financial Economic: International Finance Bubble in the Foreign Exchange Market Anne Sibert Revied Spring 203 Content Introduction................................................. 2 The Mone Market.............................................

More information

SOLUTIONS TO CONCEPTS CHAPTER 16

SOLUTIONS TO CONCEPTS CHAPTER 16 . air = 30 m/. = 500 m/. Here S = 7 m So, t = t t = 330 500 SOLUIONS O CONCEPS CHPER 6 =.75 0 3 ec =.75 m.. Here gien S = 80 m = 60 m. = 30 m/ So the maximum time interal will be t = 5/ = 60/30 = 0.5 econd.

More information

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,

More information

Lecture 5 Hemodynamics. Description of fluid flow. The equation of continuity

Lecture 5 Hemodynamics. Description of fluid flow. The equation of continuity 1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood

More information

Modelling and Simulation of a Single Particle in Laminar Flow Regime of a Newtonian Liquid

Modelling and Simulation of a Single Particle in Laminar Flow Regime of a Newtonian Liquid Excerpt rom the Proceedings o the OMSOL onerence 009 Bangalore Modelling and Simulation o a Single Particle in Laminar low Regime o a Newtonian Liquid Jamnani inesh, 1 1 Alpha Project Services, Vadodara,

More information

Bob York. Simple FET DC Bias Circuits

Bob York. Simple FET DC Bias Circuits Bob York Simple FET DC Bia Circuit Loa-Line an Q-point Conier the effect of a rain reitor in the comnon-ource configuration: Smaller + g D out KL: Thi i the equation of a line that can be uperimpoe on

More information

Define conversion and space time. Write the mole balances in terms of conversion for a batch reactor, CSTR, PFR, and PBR.

Define conversion and space time. Write the mole balances in terms of conversion for a batch reactor, CSTR, PFR, and PBR. CONERSION ND RECTOR SIZING Objectives: Deine conversion and space time. Write the mole balances in terms o conversion or a batch reactor, CSTR, PR, and PBR. Size reactors either alone or in series once

More information

Chapter H - Problems

Chapter H - Problems Chapter H - Problem Blinn College - Phyic 45 - Terry Honan Problem H.1 A wheel rotate from ret to 1 ê in 3. Aume the angular acceleration i contant. (a) What i the magnitude of the wheel' angular acceleration?

More information

VISUAL PHYSICS School of Physics University of Sydney Australia. Why do cars need different oils in hot and cold countries?

VISUAL PHYSICS School of Physics University of Sydney Australia. Why do cars need different oils in hot and cold countries? VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW VISCOSITY POISEUILLE'S LAW? Why do cars need different oils in hot and cold countries? Why does the engine runs more freely as

More information

Equalizer tap length requirement for mode group delay-compensated fiber link with weakly random mode coupling

Equalizer tap length requirement for mode group delay-compensated fiber link with weakly random mode coupling Equalizer tap length requirement or mode group delay-compenated iber link with weakly random mode coupling eng Bai,2,* and Guiang Li,3,4 CREOL, The College o Optic & Photonic, Univerity o Central Florida

More information

Module 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur

Module 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur Module 8 Three-phae Induction Motor Verion EE IIT, Kharagpur Leon 33 Different Type of Starter for Induction Motor (IM Verion EE IIT, Kharagpur Inructional Objective Need of uing arter for Induction motor

More information

Fluid Mechanics: Static s Kinematics Dynamics Fluid

Fluid Mechanics: Static s Kinematics Dynamics Fluid Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three

More information

CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY

CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY Annale Univeritati Apuleni Serie Oeconomica, 2(2), 200 CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY Sidonia Otilia Cernea Mihaela Jaradat 2 Mohammad

More information

HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi

HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi 2 Rajesh Dudi 1 Scholar and 2 Assistant Professor,Department of Mechanical Engineering, OITM, Hisar (Haryana)

More information

International Journal of Latest Research in Science and Technology Volume 4, Issue 2: Page No.161-166, March-April 2015

International Journal of Latest Research in Science and Technology Volume 4, Issue 2: Page No.161-166, March-April 2015 International Journal of Latest Research in Science and Technology Volume 4, Issue 2: Page No.161-166, March-April 2015 http://www.mnkjournals.com/ijlrst.htm ISSN (Online):2278-5299 EXPERIMENTAL STUDY

More information

ESCI 340 Physical Meteorology Cloud Physics Lesson 2 Formation of Cloud Droplets

ESCI 340 Physical Meteorology Cloud Physics Lesson 2 Formation of Cloud Droplets ESCI 40 Phyical Meteorology Cloud Phyic Leon 2 Formation of Cloud Droplet Reference: A Short Coure in Cloud Phyic, Roger and Yau Reading: Roger and Yau, Chapter 6 The objective of thi leon are: 1) Undertand

More information

Solution of the Heat Equation for transient conduction by LaPlace Transform

Solution of the Heat Equation for transient conduction by LaPlace Transform Solution of the Heat Equation for tranient conduction by LaPlace Tranform Thi notebook ha been written in Mathematica by Mark J. McCready Profeor and Chair of Chemical Engineering Univerity of Notre Dame

More information

Work, Energy & Power. AP Physics B

Work, Energy & Power. AP Physics B ork, Energy & Power AP Physics B There are many dierent TYPES o Energy. Energy is expressed in JOULES (J) 4.19 J = 1 calorie Energy can be expressed more speciically by using the term ORK() ork = The Scalar

More information

Heat Transfer From A Heated Vertical Plate

Heat Transfer From A Heated Vertical Plate Heat Transfer From A Heated Vertical Plate Mechanical and Environmental Engineering Laboratory Department of Mechanical and Aerospace Engineering University of California at San Diego La Jolla, California

More information

Assessing the Discriminatory Power of Credit Scores

Assessing the Discriminatory Power of Credit Scores Aeing the Dicriminatory Power of Credit Score Holger Kraft 1, Gerald Kroiandt 1, Marlene Müller 1,2 1 Fraunhofer Intitut für Techno- und Wirtchaftmathematik (ITWM) Gottlieb-Daimler-Str. 49, 67663 Kaierlautern,

More information

Rotation of an Object About a Fixed Axis

Rotation of an Object About a Fixed Axis Chapter 1 Rotation of an Object About a Fixed Axi 1.1 The Important Stuff 1.1.1 Rigid Bodie; Rotation So far in our tudy of phyic we have (with few exception) dealt with particle, object whoe patial dimenion

More information

HEAT TRANSFER IM0245 3 LECTURE HOURS PER WEEK THERMODYNAMICS - IM0237 2014_1

HEAT TRANSFER IM0245 3 LECTURE HOURS PER WEEK THERMODYNAMICS - IM0237 2014_1 COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE HEAT TRANSFER IM05 LECTURE HOURS PER WEEK 8 HOURS CLASSROOM ON 6 WEEKS, HOURS LABORATORY, HOURS OF INDEPENDENT WORK THERMODYNAMICS

More information

A limit equilibrium method for the assessment of the tunnel face stability taking into account seepage forces

A limit equilibrium method for the assessment of the tunnel face stability taking into account seepage forces A limit equilibrium method for the aement of the tunnel face tability taking into account eepage force P. Perazzelli (1), T. Leone (1), G. Anagnotou (1) (1) ETH Zurich, Switzerland World Tunnel Congre

More information

A note on profit maximization and monotonicity for inbound call centers

A note on profit maximization and monotonicity for inbound call centers A note on profit maximization and monotonicity for inbound call center Ger Koole & Aue Pot Department of Mathematic, Vrije Univeriteit Amterdam, The Netherland 23rd December 2005 Abtract We conider an

More information

Design Capacities for Structural Plywood

Design Capacities for Structural Plywood Deign Capacitie for Structural Plyood Alloale Stre Deign (ASD) The deign value in thi document correpond ith thoe pulihed in the 005 edition of the AF&PA American Wood Council Alloale Stre Deign (ASD)/RFD

More information

Heat and Mass Correlations

Heat and Mass Correlations Heat and Mass Correlations Alexander Rattner, Jonathan Bohren November 13, 008 Contents 1 Dimensionless Parameters Boundary ayer Analogies - Require Geometric Similarity 3 External Flow 3 3.1 External

More information

The Viscosity of Fluids

The Viscosity of Fluids Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

More information

Exposure Metering Relating Subject Lighting to Film Exposure

Exposure Metering Relating Subject Lighting to Film Exposure Expoure Metering Relating Subject Lighting to Film Expoure By Jeff Conrad A photographic expoure meter meaure ubject lighting and indicate camera etting that nominally reult in the bet expoure of the film.

More information

Optimization of Heat Sink Design and Fan Selection in Portable Electronics Environment

Optimization of Heat Sink Design and Fan Selection in Portable Electronics Environment Optimization o Heat Sink Desin and Fan Selection in Portable Electronics Environment Abstract Modern portable electronics have seen component heat loads increasin, while the space available or heat dissipation

More information

Mobility Improves Coverage of Sensor Networks

Mobility Improves Coverage of Sensor Networks Mobility Improve Coverage of Senor Networ Benyuan Liu Dept. of Computer Science Univerity of Maachuett-Lowell Lowell, MA 1854 Peter Bra Dept. of Computer Science City College of New Yor New Yor, NY 131

More information

Viscous flow in pipe

Viscous flow in pipe Viscous flow in pipe Henryk Kudela Contents 1 Laminar or turbulent flow 1 2 Balance of Momentum - Navier-Stokes Equation 2 3 Laminar flow in pipe 2 3.1 Friction factor for laminar flow...........................

More information

TEACHER BACKGROUND INFORMATION THERMAL ENERGY

TEACHER BACKGROUND INFORMATION THERMAL ENERGY TEACHER BACKGROUND INFORMATION THERMAL ENERGY In general, when an object performs work on another object, it does not transfer all of its energy to that object. Some of the energy is lost as heat due to

More information

Pipe flow with friction losses solutions using HP and TI calculators By Gilberto E. Urroz, October 2005

Pipe flow with friction losses solutions using HP and TI calculators By Gilberto E. Urroz, October 2005 Pipe low with riction losses solutions using HP and TI calculators By Gilberto E. Urroz, October 005 1. arcy-weisbach Equation and riction actor The basic equation governing riction losses in a pipeline

More information

Radial-axial Radial mixing is based on the premise that the fluids to be mixed enter the mixer in the correct proportions simultaneously

Radial-axial Radial mixing is based on the premise that the fluids to be mixed enter the mixer in the correct proportions simultaneously Brochure E-0501 1 Introduction. Static mixers are used for a wide range of applications including mixing, heat exchange and dispersion, due to numerous unique innovations our products are especially suitable

More information