P French handling of alternative cooling techniques: free cooling and ground heat exchanger. [European projects]

Size: px
Start display at page:

Download "P French handling of alternative cooling techniques: free cooling and ground heat exchanger. [European projects]"

Transcription

1 [European projecs] P H. LAHMIDI, CSTB, France More informaion can be found a he ASIEPI projec ebsie:.asiepi.eu Similar Informaion Papers on ASIEPI and/or oher European projecs can be found a he individual projec ebsies and in he publicaions daabase of he BUILD UP Poral:.buildup.eu French handling of alernaive cooling echniques: free cooling and ground hea exchanger There are a lo of alernaive cooling echniques ha improve subsanially he summer comfor ihou (or in a very limied manner) increasing he energy consumpion. For example solar and hermal conrol echniques, hea amorizaion and hea dissipaion echniques. Mos used echniques in France are free cooling in office buildings and ground hea exchanger in dellings. This paper focuses on providing general informaion describing he implemenaion of EN 1541 and EN 154 ino French regulaion o evaluae passive cooling based on venilaion. I conains an explanaion of he calculaion mehod ih deailed informaion on inpu and oupu daa. 1 > Handling of free cooling due o indos opening by implemening EN154 In he pas, buildings ere venilaed naurally. Wih an increased aareness of he cos and environmenal impacs of energy use, naural venilaion is again becoming an increasingly aracive echnique for reducing energy use and cos and for providing comforable indoor climae. During pracically all he summer period, he ouside air can be a source of coolness from evening o morning. So, in he case of a building ih an imporan ineria, a nigh over-venilaion enables he evacuaion of hea sored up in dayime. Figure 1 presens he effec of ineria for differen ypes of buildings in France. The EN 154 sandard describes he mehods o calculae venilaion airflos raes for buildings o be used in applicaions such as energy calculaions, heaing and cooling load calculaions, summer comfor and indoor air qualiy evaluaions. This sandard is implemened ino French regulaion for ne buildings called RT005. The mehod is mean o be applied o: Figure 1: Effec of ineria. all ypes of buildings; no direcly applicable o buildings ih a heigh greaer han 100 m or for rooms here he verical air emperaure difference is greaer han 15K; no applicable o ichens preparing food ha is no for immediae consumpion; no applicable o indusry process venilaion; auomaic indos opening are no considered by his sandard.

2 The inpu parameers and he calculaion mehod can be adjused or complemened for hese differen applicaions. Clause 7 of he sandard explains ha mus/can/should be aen ino accoun for each applicaion, and hich mehod should be used in each case. Three mehods are proposed in he sandard: 1 - Direc mehod The calculaion of mechanical airflos, combusion airflos and indo opening airflos, are all based on sysems characerisics, exernal condiions and design airflos. They do no depend on he inernal pressure condiion: he ineracion beeen he venilaion sysems and he leaages is negleced. - Ieraive mehod The ieraive mehod is required hen he ineracion beeen he venilaion sysems and he leaages canno be negleced. I is herefore proposed for passive duc venilaion. 3 - Saisical analysis for energy calculaion This mehod can be specified a he naional level for energy calculaions. The requiremens for he mehods are given in of he presen sandard. As described belo, he mehod proposed in he sandard, and folloed by French building regulaion o calculae air flo hrough opening indos area and boom hung indos are obained hrough he direc calculaion mehod (see: 6.5 of he presen sandard). I aes ino accoun: he ind urbulence; he ind speed; sac effec; he inside and ouside emperaure; user behaviour. For a single side impac, he airflo is calculaed by: V 0.5 q = vairing 1800* Ao * V = C + C.( V ) + C. H. abs( θ θ ) me s indo i e Wih: q v (m³/h): air flo; A (m²): indo opening area; C o = 0.01 aes ino accoun ind urbulence; C = aes ino accoun sac effec; s C = aes ino accoun ind speed; H V me indo (m): is he free area heigh of he indo; ( m / s) : meeorological ind speed a 10 m heigh; θ i : room air emperaure; θ : oudoor air emperaure. e ASIEPI > P185_French_Handling_of_Alernaive_Cooling_ASIEPI_WP7.doc

3 For a boom hung indo, he raio of he flo hrough he opened area and he oally opened indo is assumed o be depending only on he opening angle α and independen of he raio of he heigh o he idh of he indo. A = C (α ). A Where A is he indo area oally opened. o For C (α ), a polynomial approximaion is proposed in he sandard (see Figure ). In France, he opening area evolves linearly agains operaive emperaure inside he inerval θ op min =0 C andθ op max =4 C, ih: For θ θ, A 0 op < op min = For θ op > θ, A = op max A indo Cross venilaion is aen ino accoun hough consan values forc V ) (see Table 1)..( me Figure : A polynomial approximaion for C (α ) Table 1: Consan values. Cross venilaion 0.01 Venilaion C (α) depends on building ype, maximal opening, noise and ime. The values used in he French regulaion RT 005 are idenical for residenial and saniary buildings and are summarized in he able belo. Table : C (α ) values for residenial and saniary buildings. Noise s caegory From 8 p.m o 7 a.m From 7 p.m o 9 a.m From 9 a.m o 8 p.m BR BR For all oher building ypes, values are presened belo. Table 3: C (α ) values for oher building ypes. Noise s caegory Inoccupaion Occupaion BR BR To presen he effec of indos opening using his model, e performed a calculaion for a ypical French delling in Carpenras (See Figure 3). The useful surface of his building is 100 m² and he surface of indos is m². Resuls obained are summarized in Table 4. Figure 3: Sudied house. Table 4: Resuls of simulaions in Carpenras. Ineria C (α ) Maximum indoor emperaure ligh medium heavy ligh medium heavy ASIEPI > P185_French_Handling_of_Alernaive_Cooling_ASIEPI_WP7.doc 3

4 As expeced, o ensure comforable condiions, he maximal opening and a heavy ineria are he mos efficien combinaion. Figure 4: Principle of ground hea exchanger > Handling of ground hea exchanger by implemening EN1541 The earh remains much more cooler han he air in summer. This coolness can be used by means of earh cooling ubes (see Figure 4). These are underground ubes hrough hich venilaion air is circulaed. The venilaion air is hereby reheaed in iner and cooled don in summer. An earh cooling ube mus be correcly designed for beer efficiency and for easier mainenance in order o avoid any healh ris relaed o he qualiy of air. Annex A of his sandard describes a simplified model o calculae air precooling due o supplying air hrough ducs lying in he ground. The model calculaes: Figure 5: round emperaures for several duc dephs (X: annual hour, Y: Temperaures) leaving air emperaure of he hea exchanger; hea flux beeen ground and air in duc. The model aes ino consideraion he specific duc parameers and he ineria of he ground, depending on he deph of he ducs in he ground. Also he ground maerial is aen ino accoun by a correcion facor for he ground emperaure. This model ill be implemened ino he nex French regulaion scheduled for 01. In his model he ground emperaure depends on o parameers: he annual mean ouside emperaure; air emperaure and he deph of he ducs. The ground emperaure is modelled as a sinus curve based on he annual mean ouside air emperaure. The deph of ducs correcs he sinus curve in o ays: he ampliude decreases in funcion of he deph; he ground emperaure is rearded in funcion of he deph. I means he ineria of he ground increases in funcion of he deph. The ground emperaure depends on he annual mean and he ampliude of he annual sing of he ouside air emperaure a he building locaion, and on he deph of he duc in he ground (see Figure 5). To ae ino consideraion he ineria of he ground, he ouside air emperaure is correced by AH, VS and gm. AH correcs he ampliude, depending on he deph of he ducs lying in he ground. AH 3 = deph deph deph + 1 VS correcs he ground emperaure by a ime shif, depending on he deph of he ducs lying in he ground. VS = 4.( deph deph deph deph 4 ) ASIEPI > P185_French_Handling_of_Alernaive_Cooling_ASIEPI_WP7.doc 4

5 Table 5: gm values.. maerial gm Mois soil 1 Dray sand 0.9 Mois sand 0.98 Mois clay 1.04 We clay 1.05 Finally, he air ground emperaure is calculaed as follo: ih Δ sing. T TA π = gm. T AM AH. ΔTA.sin. VS [ JH + 4. ] being he ampliude of he annual ouside air emperaure Some gm values for soil maerials are proposed in his sandard (see Table 5). The leaving air emperaure is calculaed ih he formula: Figure 6: Poenial of hea ground exchanger in Nice during Augus ASIEPI parners: BBRI (BE; echnical co-ordinaor), NKUA (R; financial & adminisraive co-ordinaor), TNO (NL), IBP (DE), SINTEF (NO), CSTB (FR), Cee de Lyon (FR), REHVA (BE), ENEA (IT), AICIA (ES), NAPE (PL), VTT (FI), E-U-Z (DE), Enviros (CZ), SBi (DK) Associaed parners: Eurima (BE), PCE (BE), ES-SO (BE), EuroAce (BE), FIEC (BE), Acciona I (ES) Subconracors: Kaunas Universiy (LT), Universiy of Budapes (HU), Universiy of Buchares (RO), BRE (UK), UCD (IE) Lin:.asiepi.eu Wih: T AirOu = T ( T T U e : Transfer coefficien of he air duc Cp air : specific hea capaciy of air M air : Dry air mass flo rae AirIn U e. AS ). e M air. Cp Finally, he air ground emperaure and leaving air emperaure can be calculaed. Figure 6 presens an example of poenial of his echnique in he souh of France during Augus. The air oule from he duc is much cooler han exernal emperaure. 3 > Acnoledgemens Differen naional conribuions ere made by many of he projec parners. The parners are all lised on.asiepi.eu. 4 > References 1. EN 1541: Calculaion mehods for energy losses due o venilaion and infilraion in commercial buildings.. EN154 Calculaion mehods for he deerminaion of air flo raes in buildings including infilraion. air Original ex language: English Disclaimer: ASIEPI has received funding from he Communiy s Inelligen Energy Europe programme under he conrac EIE/07/169/SI The sole responsibiliy for he conen of his publicaion lies ih he auhors. I does no necessarily reflec he opinion of he European Communiies. Neiher he European Commission nor he auhors are responsible for any use ha may be made of he informaion conained herein. European Communiies, 009 Reproducion is auhorised provided he source is acnoledged ASIEPI > P185_French_Handling_of_Alernaive_Cooling_ASIEPI_WP7.doc 5

Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture

Scientific Herald of the Voronezh State University of Architecture and Civil Engineering. Construction and Architecture Scienific Herald of he Voronezh Sae Universiy of Archiecure and Civil Engineering. Consrucion and Archiecure UDC 625.863.6:551.328 Voronezh Sae Universiy of Archiecure and Civil Engineering Ph. D. applican

More information

Errata (1 st Edition)

Errata (1 st Edition) P Sandborn, os Analysis of Elecronic Sysems, s Ediion, orld Scienific, Singapore, 03 Erraa ( s Ediion) S K 05D Page 8 Equaion (7) should be, E 05D E Nu e S K he L appearing in he equaion in he book does

More information

Example: Parametric fire curve for a fire compartment

Example: Parametric fire curve for a fire compartment Documen Ref: SX04a-EN-EU Shee 1 of 5 Tile Eurocode Ref EN 1991-1-:00 Made by Z Sokol Dae Jan 006 Checked by F Wald Dae Jan 006 Example: Parameric fire curve for a fire comparmen This example shows he deerminaion

More information

Simplified Indices Assessing Building Envelope's Dynamic Thermal Performance: A Survey

Simplified Indices Assessing Building Envelope's Dynamic Thermal Performance: A Survey Simplified Indices Assessing Building Envelope's Dynamic Thermal Performance: A Survey Ferrari, S. Building Environmen Science and Technology Deparmen, Poliecnico di Milano (email: simone.ferrari@polimi.i)

More information

Application Note AN Software release of SemiSel version 3.1. New semiconductor available. Temperature ripple at low inverter output frequencies

Application Note AN Software release of SemiSel version 3.1. New semiconductor available. Temperature ripple at low inverter output frequencies Applicaion Noe AN-8004 Revision: Issue Dae: Prepared by: 00 2008-05-21 Dr. Arend Winrich Ke y Words: SemiSel, Semiconducor Selecion, Loss Calculaion Sofware release of SemiSel version 3.1 New semiconducor

More information

Mechanical Fatigue and Load-Induced Aging of Loudspeaker Suspension. Wolfgang Klippel,

Mechanical Fatigue and Load-Induced Aging of Loudspeaker Suspension. Wolfgang Klippel, Mechanical Faigue and Load-Induced Aging of Loudspeaker Suspension Wolfgang Klippel, Insiue of Acousics and Speech Communicaion Dresden Universiy of Technology presened a he ALMA Symposium 2012, Las Vegas

More information

Vehicle Arrival Models : Headway

Vehicle Arrival Models : Headway Chaper 12 Vehicle Arrival Models : Headway 12.1 Inroducion Modelling arrival of vehicle a secion of road is an imporan sep in raffic flow modelling. I has imporan applicaion in raffic flow simulaion where

More information

1. Calibration factor

1. Calibration factor Annex_C_MUBDandP_eng_.doc, p. of pages Annex C: Measureen uncerainy of he oal heigh of profile of a deph-seing sandard ih he sandard deviaion of he groove deph as opography er In his exaple, he uncerainy

More information

Exponential Weighted Moving Average (EWMA) Chart Under The Assumption of Moderateness And Its 3 Control Limits

Exponential Weighted Moving Average (EWMA) Chart Under The Assumption of Moderateness And Its 3 Control Limits DOI: 0.545/mjis.07.5009 Exponenial Weighed Moving Average (EWMA) Char Under The Assumpion of Moderaeness And Is 3 Conrol Limis KALPESH S TAILOR Assisan Professor, Deparmen of Saisics, M. K. Bhavnagar Universiy,

More information

MATHEMATICAL DESCRIPTION OF THEORETICAL METHODS OF RESERVE ECONOMY OF CONSIGNMENT STORES

MATHEMATICAL DESCRIPTION OF THEORETICAL METHODS OF RESERVE ECONOMY OF CONSIGNMENT STORES MAHEMAICAL DESCIPION OF HEOEICAL MEHODS OF ESEVE ECONOMY OF CONSIGNMEN SOES Péer elek, József Cselényi, György Demeer Universiy of Miskolc, Deparmen of Maerials Handling and Logisics Absrac: Opimizaion

More information

LINEAR SLOT DIFFUSERS

LINEAR SLOT DIFFUSERS Supply, Reurn, Dummy Linear Slo Diffusers A OSLD OTIMA model OSLD is a supply linear slo diffuser wih inegral volume conrol damper and hi and miss air sraighening deflecors. h Hi and miss air sraigheners

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION DOI: 0.038/NCLIMATE893 Temporal resoluion and DICE * Supplemenal Informaion Alex L. Maren and Sephen C. Newbold Naional Cener for Environmenal Economics, US Environmenal Proecion

More information

Sub Module 2.6. Measurement of transient temperature

Sub Module 2.6. Measurement of transient temperature Mechanical Measuremens Prof. S.P.Venkaeshan Sub Module 2.6 Measuremen of ransien emperaure Many processes of engineering relevance involve variaions wih respec o ime. The sysem properies like emperaure,

More information

d 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3

d 1 = c 1 b 2 - b 1 c 2 d 2 = c 1 b 3 - b 1 c 3 and d = c b - b c c d = c b - b c c This process is coninued unil he nh row has been compleed. The complee array of coefficiens is riangular. Noe ha in developing he array an enire row may be divided or

More information

Navneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi

Navneet Saini, Mayank Goyal, Vishal Bansal (2013); Term Project AML310; Indian Institute of Technology Delhi Creep in Viscoelasic Subsances Numerical mehods o calculae he coefficiens of he Prony equaion using creep es daa and Herediary Inegrals Mehod Navnee Saini, Mayank Goyal, Vishal Bansal (23); Term Projec

More information

Q.1 Define work and its unit?

Q.1 Define work and its unit? CHP # 6 ORK AND ENERGY Q.1 Define work and is uni? A. ORK I can be define as when we applied a force on a body and he body covers a disance in he direcion of force, hen we say ha work is done. I is a scalar

More information

MEASUREMENTS AND THEORETICAL CALCULATIONS OF DIFFUSED RADIATION AND ATMOSPHERE LUCIDITY

MEASUREMENTS AND THEORETICAL CALCULATIONS OF DIFFUSED RADIATION AND ATMOSPHERE LUCIDITY ENGINEERING FOR RURAL DEVELOPMENT Jelgava, 8.-9.5.9. MEASUREMENTS AND THEORETICAL CALCULATIONS OF DIFFUSED RADIATION AND ATMOSPHERE LUCIDITY Ilze Pelēce, Uldis Iljins, Imans Ziemelis Lavia Universiy of

More information

Bias in Conditional and Unconditional Fixed Effects Logit Estimation: a Correction * Tom Coupé

Bias in Conditional and Unconditional Fixed Effects Logit Estimation: a Correction * Tom Coupé Bias in Condiional and Uncondiional Fixed Effecs Logi Esimaion: a Correcion * Tom Coupé Economics Educaion and Research Consorium, Naional Universiy of Kyiv Mohyla Academy Address: Vul Voloska 10, 04070

More information

Electrical and current self-induction

Electrical and current self-induction Elecrical and curren self-inducion F. F. Mende hp://fmnauka.narod.ru/works.hml mende_fedor@mail.ru Absrac The aricle considers he self-inducance of reacive elemens. Elecrical self-inducion To he laws of

More information

The Potential Effectiveness of the Detection of Pulsed Signals in the Non-Uniform Sampling

The Potential Effectiveness of the Detection of Pulsed Signals in the Non-Uniform Sampling The Poenial Effeciveness of he Deecion of Pulsed Signals in he Non-Uniform Sampling Arhur Smirnov, Sanislav Vorobiev and Ajih Abraham 3, 4 Deparmen of Compuer Science, Universiy of Illinois a Chicago,

More information

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle

Physics 235 Chapter 2. Chapter 2 Newtonian Mechanics Single Particle Chaper 2 Newonian Mechanics Single Paricle In his Chaper we will review wha Newon s laws of mechanics ell us abou he moion of a single paricle. Newon s laws are only valid in suiable reference frames,

More information

Load Calculations Heat Balance Method - Theory. Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering, Oklahoma State University

Load Calculations Heat Balance Method - Theory. Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering, Oklahoma State University Load Calculaions Hea Balance Mehod - Theory Prof. Jeffrey D. Spiler School of Mechanical and Aerospace Engineering, Oklahoma Sae Universiy Tonigh The hea balance mehod heory The hea balance mehod applicaion

More information

Development of a new metrological model for measuring of the water surface evaporation Tovmach L. Tovmach Yr. Abstract Introduction

Development of a new metrological model for measuring of the water surface evaporation Tovmach L. Tovmach Yr. Abstract Introduction Developmen of a new merological model for measuring of he waer surface evaporaion Tovmach L. Tovmach Yr. Sae Hydrological Insiue 23 Second Line, 199053 S. Peersburg, Russian Federaion Telephone (812) 323

More information

Modal identification of structures from roving input data by means of maximum likelihood estimation of the state space model

Modal identification of structures from roving input data by means of maximum likelihood estimation of the state space model Modal idenificaion of srucures from roving inpu daa by means of maximum likelihood esimaion of he sae space model J. Cara, J. Juan, E. Alarcón Absrac The usual way o perform a forced vibraion es is o fix

More information

Kriging Models Predicting Atrazine Concentrations in Surface Water Draining Agricultural Watersheds

Kriging Models Predicting Atrazine Concentrations in Surface Water Draining Agricultural Watersheds 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Kriging Models Predicing Arazine Concenraions in Surface Waer Draining Agriculural Waersheds Paul L. Mosquin, Jeremy Aldworh, Wenlin Chen Supplemenal Maerial Number

More information

Transverse and Longitudinal Damped Vibrations of Hydraulic Cylinder in a Mining Prop

Transverse and Longitudinal Damped Vibrations of Hydraulic Cylinder in a Mining Prop Vibraions in Physical Sysems Vol. 7 (06) Transverse and Longiudinal Damped Vibraions of Hydraulic Cylinder in a Mining Prop Wojciech SOCHACK nsiue of Mechanics and Fundamenals of Machinery Design Universiy

More information

CONFIDENCE INTERVAL FOR THE DIFFERENCE IN BINOMIAL PROPORTIONS FROM STRATIFIED 2X2 SAMPLES

CONFIDENCE INTERVAL FOR THE DIFFERENCE IN BINOMIAL PROPORTIONS FROM STRATIFIED 2X2 SAMPLES Proceedings of he Annual Meeing of he American Saisical Associaion Augus 5-9 00 CONFIDENCE INTERVAL FOR TE DIFFERENCE IN BINOMIAL PROPORTIONS FROM STRATIFIED X SAMPLES Peng-Liang Zhao John. Troxell ui

More information

Easy evaluation of establishment treatments

Easy evaluation of establishment treatments Easy evaluaion of esablishmen reamens Oscar García Insiuo Foresal, Chile Absrac The obvious approaches o comparing profiabiliy of compeing ree esablishmen echniques or reamens would require much daa on

More information

On Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature

On Measuring Pro-Poor Growth. 1. On Various Ways of Measuring Pro-Poor Growth: A Short Review of the Literature On Measuring Pro-Poor Growh 1. On Various Ways of Measuring Pro-Poor Growh: A Shor eview of he Lieraure During he pas en years or so here have been various suggesions concerning he way one should check

More information

Lecture 4 Notes (Little s Theorem)

Lecture 4 Notes (Little s Theorem) Lecure 4 Noes (Lile s Theorem) This lecure concerns one of he mos imporan (and simples) heorems in Queuing Theory, Lile s Theorem. More informaion can be found in he course book, Bersekas & Gallagher,

More information

Exponentially Weighted Moving Average (EWMA) Chart Based on Six Delta Initiatives

Exponentially Weighted Moving Average (EWMA) Chart Based on Six Delta Initiatives hps://doi.org/0.545/mjis.08.600 Exponenially Weighed Moving Average (EWMA) Char Based on Six Dela Iniiaives KALPESH S. TAILOR Deparmen of Saisics, M. K. Bhavnagar Universiy, Bhavnagar-36400 E-mail: kalpesh_lr@yahoo.co.in

More information

1. VELOCITY AND ACCELERATION

1. VELOCITY AND ACCELERATION 1. VELOCITY AND ACCELERATION 1.1 Kinemaics Equaions s = u + 1 a and s = v 1 a s = 1 (u + v) v = u + as 1. Displacemen-Time Graph Gradien = speed 1.3 Velociy-Time Graph Gradien = acceleraion Area under

More information

Two Coupled Oscillators / Normal Modes

Two Coupled Oscillators / Normal Modes Lecure 3 Phys 3750 Two Coupled Oscillaors / Normal Modes Overview and Moivaion: Today we ake a small, bu significan, sep owards wave moion. We will no ye observe waves, bu his sep is imporan in is own

More information

Stability and Bifurcation in a Neural Network Model with Two Delays

Stability and Bifurcation in a Neural Network Model with Two Delays Inernaional Mahemaical Forum, Vol. 6, 11, no. 35, 175-1731 Sabiliy and Bifurcaion in a Neural Nework Model wih Two Delays GuangPing Hu and XiaoLing Li School of Mahemaics and Physics, Nanjing Universiy

More information

Shiva Akhtarian MSc Student, Department of Computer Engineering and Information Technology, Payame Noor University, Iran

Shiva Akhtarian MSc Student, Department of Computer Engineering and Information Technology, Payame Noor University, Iran Curren Trends in Technology and Science ISSN : 79-055 8hSASTech 04 Symposium on Advances in Science & Technology-Commission-IV Mashhad, Iran A New for Sofware Reliabiliy Evaluaion Based on NHPP wih Imperfec

More information

Turbulent Flows. Computational Modelling of Turbulent Flows. Overview. Turbulent Eddies and Scales

Turbulent Flows. Computational Modelling of Turbulent Flows. Overview. Turbulent Eddies and Scales School of Mechanical Aerospace and Civil Engineering Turbulen Flows As noed above, using he mehods described in earlier lecures, he Navier-Sokes equaions can be discreized and solved numerically on complex

More information

h[n] is the impulse response of the discrete-time system:

h[n] is the impulse response of the discrete-time system: Definiion Examples Properies Memory Inveribiliy Causaliy Sabiliy Time Invariance Lineariy Sysems Fundamenals Overview Definiion of a Sysem x() h() y() x[n] h[n] Sysem: a process in which inpu signals are

More information

Curling Stress Equation for Transverse Joint Edge of a Concrete Pavement Slab Based on Finite-Element Method Analysis

Curling Stress Equation for Transverse Joint Edge of a Concrete Pavement Slab Based on Finite-Element Method Analysis TRANSPORTATION RESEARCH RECORD 155 35 Curling Sress Equaion for Transverse Join Edge of a Concree Pavemen Slab Based on Finie-Elemen Mehod Analysis TATSUO NISHIZAWA, TADASHI FUKUDA, SABURO MATSUNO, AND

More information

Keywords: thermal stress; thermal fatigue; inverse analysis; heat conduction; regularization

Keywords: thermal stress; thermal fatigue; inverse analysis; heat conduction; regularization Proceedings Inverse Analysis for Esimaing Temperaure and Residual Sress Disribuions in a Pipe from Ouer Surface Temperaure Measuremen and Is Regularizaion Shiro Kubo * and Shoki Taguwa Deparmen of Mechanical

More information

INDEX. Transient analysis 1 Initial Conditions 1

INDEX. Transient analysis 1 Initial Conditions 1 INDEX Secion Page Transien analysis 1 Iniial Condiions 1 Please inform me of your opinion of he relaive emphasis of he review maerial by simply making commens on his page and sending i o me a: Frank Mera

More information

SIMULATION ON HYDRAULIC HEATING SYSTEM OF BUILDING UNDER THE CONTROL OF THERMOSTAT RADIATOR VALVES. Xu Baoping, Fu Lin, and Di Hongfa

SIMULATION ON HYDRAULIC HEATING SYSTEM OF BUILDING UNDER THE CONTROL OF THERMOSTAT RADIATOR VALVES. Xu Baoping, Fu Lin, and Di Hongfa SIMULAION ON HYDRAULIC HEAING SYSEM OF BUILDING UNDER HE CONROL OF HERMOSA RADIAOR VALVES Xu Baoping Fu Lin and Di Hongfa Deparmen of Building Science and echnology singhua Universiy Beiing 100084 China

More information

RC, RL and RLC circuits

RC, RL and RLC circuits Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.

More information

Sterilization D Values

Sterilization D Values Seriliaion D Values Seriliaion by seam consis of he simple observaion ha baceria die over ime during exposure o hea. They do no all live for a finie period of hea exposure and hen suddenly die a once,

More information

STUDY ON THE AIR MOVEMENT CHARACTER IN SOLAR WALL SYSTEM. Y Li, X Duanmu, Y Sun, J Li and H Jia

STUDY ON THE AIR MOVEMENT CHARACTER IN SOLAR WALL SYSTEM. Y Li, X Duanmu, Y Sun, J Li and H Jia Proceedings: Building Simulaion 007 SUDY ON HE AIR MOVEMEN CHARACER IN SOLAR WALL SYSEM Y Li, X Duanmu, Y Sun, J Li and H Jia College of Archiecure and Civil Engineering, Beijing Universiy of echnology,

More information

Final Spring 2007

Final Spring 2007 .615 Final Spring 7 Overview The purpose of he final exam is o calculae he MHD β limi in a high-bea oroidal okamak agains he dangerous n = 1 exernal ballooning-kink mode. Effecively, his corresponds o

More information

θ with respect to time is

θ with respect to time is From MEC '05 Inergraing Prosheics and Medicine, Proceedings of he 005 MyoElecric Conrols/Powered Prosheics Symposium, held in Fredericon, New Brunswick, Canada, Augus 17-19, 005. A MINIMAL JERK PROSTHESIS

More information

Advances in Engineering Research (AER), volume Global Conference on Mechanics and Civil Engineering (GCMCE 2017)

Advances in Engineering Research (AER), volume Global Conference on Mechanics and Civil Engineering (GCMCE 2017) Advances in Engineering Research (AER), volume 2017 Global Conference on Mechanics and Civil Engineering (GCMCE 2017) Comparaive Analysis of Esimaion Formula of Acid Dew Poin for Differen Flue Gas Jinhui

More information

Decomposing Value Added Growth Over Sectors into Explanatory Factors

Decomposing Value Added Growth Over Sectors into Explanatory Factors Business School Decomposing Value Added Growh Over Secors ino Explanaory Facors W. Erwin Diewer (UBC and UNSW Ausralia) and Kevin J. Fox (UNSW Ausralia) EMG Workshop UNSW 2 December 2016 Summary Decompose

More information

0.1 MAXIMUM LIKELIHOOD ESTIMATION EXPLAINED

0.1 MAXIMUM LIKELIHOOD ESTIMATION EXPLAINED 0.1 MAXIMUM LIKELIHOOD ESTIMATIO EXPLAIED Maximum likelihood esimaion is a bes-fi saisical mehod for he esimaion of he values of he parameers of a sysem, based on a se of observaions of a random variable

More information

Basic Circuit Elements Professor J R Lucas November 2001

Basic Circuit Elements Professor J R Lucas November 2001 Basic Circui Elemens - J ucas An elecrical circui is an inerconnecion of circui elemens. These circui elemens can be caegorised ino wo ypes, namely acive and passive elemens. Some Definiions/explanaions

More information

Christos Papadimitriou & Luca Trevisan November 22, 2016

Christos Papadimitriou & Luca Trevisan November 22, 2016 U.C. Bereley CS170: Algorihms Handou LN-11-22 Chrisos Papadimiriou & Luca Trevisan November 22, 2016 Sreaming algorihms In his lecure and he nex one we sudy memory-efficien algorihms ha process a sream

More information

Simulation-Solving Dynamic Models ABE 5646 Week 2, Spring 2010

Simulation-Solving Dynamic Models ABE 5646 Week 2, Spring 2010 Simulaion-Solving Dynamic Models ABE 5646 Week 2, Spring 2010 Week Descripion Reading Maerial 2 Compuer Simulaion of Dynamic Models Finie Difference, coninuous saes, discree ime Simple Mehods Euler Trapezoid

More information

Section 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients

Section 3.5 Nonhomogeneous Equations; Method of Undetermined Coefficients Secion 3.5 Nonhomogeneous Equaions; Mehod of Undeermined Coefficiens Key Terms/Ideas: Linear Differenial operaor Nonlinear operaor Second order homogeneous DE Second order nonhomogeneous DE Soluion o homogeneous

More information

Estimation of Kinetic Friction Coefficient for Sliding Rigid Block Nonstructural Components

Estimation of Kinetic Friction Coefficient for Sliding Rigid Block Nonstructural Components 7 Esimaion of Kineic Fricion Coefficien for Sliding Rigid Block Nonsrucural Componens Cagdas Kafali Ph.D. Candidae, School of Civil and Environmenal Engineering, Cornell Universiy Research Supervisor:

More information

Analogue amplifier card

Analogue amplifier card Analogue amplifier card RE 30110/06.05 replaces: 10.04 1/10 Type VT-VSPA-1-X/ H/A/D 6641/00 Table of conens Conens Page Feaures 1 Ordering deails, accessories Funcion 3 Block circui diagram and connecion

More information

Rapid Termination Evaluation for Recursive Subdivision of Bezier Curves

Rapid Termination Evaluation for Recursive Subdivision of Bezier Curves Rapid Terminaion Evaluaion for Recursive Subdivision of Bezier Curves Thomas F. Hain School of Compuer and Informaion Sciences, Universiy of Souh Alabama, Mobile, AL, U.S.A. Absrac Bézier curve flaening

More information

ME425/525: Advanced Topics in Building Science

ME425/525: Advanced Topics in Building Science ME425/525: Advanced Topics in Building Science Indoor environmenal qualiy for susainable buildings: Lecure 6 Dr. Ellio T. Gall, Ph.D. Lecure 6 Today s objecives o Error propagaion Apply o SS soluion (venilaion,

More information

Expected Severity Model for FMEA under Weibull Failure and Detection Time Distributions with a Common Shape Parameter

Expected Severity Model for FMEA under Weibull Failure and Detection Time Distributions with a Common Shape Parameter Expeced Severiy Model for FMEA under Weibull and Deecion Time Disribuions wih a Common Shape Parameer Hyuck Moo Kwon Division of Sysems Managemen and Engineering Pukyong Naional Universiy, Busan 4853,

More information

Chapter 2. Models, Censoring, and Likelihood for Failure-Time Data

Chapter 2. Models, Censoring, and Likelihood for Failure-Time Data Chaper 2 Models, Censoring, and Likelihood for Failure-Time Daa William Q. Meeker and Luis A. Escobar Iowa Sae Universiy and Louisiana Sae Universiy Copyrigh 1998-2008 W. Q. Meeker and L. A. Escobar. Based

More information

Dam Flooding Simulation Using Advanced CFD Methods

Dam Flooding Simulation Using Advanced CFD Methods WCCM V Fifh World Congress on Compuaional Mechanics July 7-12, 2002, Vienna, Ausria Dam Flooding Simulaion Using Advanced CFD Mehods Mohamed Gouda*, Dr. Konrad Karner VRVis Zenrum für Virual Realiy und

More information

CHAPTER 2 Signals And Spectra

CHAPTER 2 Signals And Spectra CHAPER Signals And Specra Properies of Signals and Noise In communicaion sysems he received waveform is usually caegorized ino he desired par conaining he informaion, and he undesired par. he desired par

More information

Content-Based Shape Retrieval Using Different Shape Descriptors: A Comparative Study Dengsheng Zhang and Guojun Lu

Content-Based Shape Retrieval Using Different Shape Descriptors: A Comparative Study Dengsheng Zhang and Guojun Lu Conen-Based Shape Rerieval Using Differen Shape Descripors: A Comparaive Sudy Dengsheng Zhang and Guojun Lu Gippsland School of Compuing and Informaion Technology Monash Universiy Churchill, Vicoria 3842

More information

UNIVERSITY OF TRENTO MEASUREMENTS OF TRANSIENT PHENOMENA WITH DIGITAL OSCILLOSCOPES. Antonio Moschitta, Fabrizio Stefani, Dario Petri.

UNIVERSITY OF TRENTO MEASUREMENTS OF TRANSIENT PHENOMENA WITH DIGITAL OSCILLOSCOPES. Antonio Moschitta, Fabrizio Stefani, Dario Petri. UNIVERSIY OF RENO DEPARMEN OF INFORMAION AND COMMUNICAION ECHNOLOGY 385 Povo reno Ialy Via Sommarive 4 hp://www.di.unin.i MEASUREMENS OF RANSIEN PHENOMENA WIH DIGIAL OSCILLOSCOPES Anonio Moschia Fabrizio

More information

Dead-time Induced Oscillations in Inverter-fed Induction Motor Drives

Dead-time Induced Oscillations in Inverter-fed Induction Motor Drives Dead-ime Induced Oscillaions in Inverer-fed Inducion Moor Drives Anirudh Guha Advisor: Prof G. Narayanan Power Elecronics Group Dep of Elecrical Engineering, Indian Insiue of Science, Bangalore, India

More information

Nature Neuroscience: doi: /nn Supplementary Figure 1. Spike-count autocorrelations in time.

Nature Neuroscience: doi: /nn Supplementary Figure 1. Spike-count autocorrelations in time. Supplemenary Figure 1 Spike-coun auocorrelaions in ime. Normalized auocorrelaion marices are shown for each area in a daase. The marix shows he mean correlaion of he spike coun in each ime bin wih he spike

More information

APPM 2360 Homework Solutions, Due June 10

APPM 2360 Homework Solutions, Due June 10 2.2.2: Find general soluions for he equaion APPM 2360 Homework Soluions, Due June 10 Soluion: Finding he inegraing facor, dy + 2y = 3e µ) = e 2) = e 2 Muliplying he differenial equaion by he inegraing

More information

Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro. Category: Isotropic Linear Elasticity, Dynamics, Member

Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro. Category: Isotropic Linear Elasticity, Dynamics, Member Verificaion Example Program: RFEM 5, RSTAB 8, RF-DYNAM Pro, DYNAM Pro Caegory: Isoropic Linear Elasiciy, Dynamics, Member Verificaion Example: 0104 Canilever Beam wih Periodic Exciaion 0104 Canilever Beam

More information

Validation of Micro-Perforated Panels Models

Validation of Micro-Perforated Panels Models Purue Universiy Purue e-pubs Publicaions of he Ray W. Herrick Laboraories School of Mechanical Engineering 10-008 Valiaion of Micro-Perforae Panels Moels J Suar Bolon Purue Universiy, bolon@purue.eu Kang

More information

Learning Objectives: Practice designing and simulating digital circuits including flip flops Experience state machine design procedure

Learning Objectives: Practice designing and simulating digital circuits including flip flops Experience state machine design procedure Lab 4: Synchronous Sae Machine Design Summary: Design and implemen synchronous sae machine circuis and es hem wih simulaions in Cadence Viruoso. Learning Objecives: Pracice designing and simulaing digial

More information

EE 435. Lecture 31. Absolute and Relative Accuracy DAC Design. The String DAC

EE 435. Lecture 31. Absolute and Relative Accuracy DAC Design. The String DAC EE 435 Lecure 3 Absolue and Relaive Accuracy DAC Design The Sring DAC . Review from las lecure. DFT Simulaion from Malab Quanizaion Noise DACs and ADCs generally quanize boh ampliude and ime If convering

More information

Lab 10: RC, RL, and RLC Circuits

Lab 10: RC, RL, and RLC Circuits Lab 10: RC, RL, and RLC Circuis In his experimen, we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors. We will sudy he way volages and currens change in

More information

Module 2 F c i k c s la l w a s o s f dif di fusi s o i n

Module 2 F c i k c s la l w a s o s f dif di fusi s o i n Module Fick s laws of diffusion Fick s laws of diffusion and hin film soluion Adolf Fick (1855) proposed: d J α d d d J (mole/m s) flu (m /s) diffusion coefficien and (mole/m 3 ) concenraion of ions, aoms

More information

ACE 564 Spring Lecture 7. Extensions of The Multiple Regression Model: Dummy Independent Variables. by Professor Scott H.

ACE 564 Spring Lecture 7. Extensions of The Multiple Regression Model: Dummy Independent Variables. by Professor Scott H. ACE 564 Spring 2006 Lecure 7 Exensions of The Muliple Regression Model: Dumm Independen Variables b Professor Sco H. Irwin Readings: Griffihs, Hill and Judge. "Dumm Variables and Varing Coefficien Models

More information

GMM - Generalized Method of Moments

GMM - Generalized Method of Moments GMM - Generalized Mehod of Momens Conens GMM esimaion, shor inroducion 2 GMM inuiion: Maching momens 2 3 General overview of GMM esimaion. 3 3. Weighing marix...........................................

More information

ACE 562 Fall Lecture 5: The Simple Linear Regression Model: Sampling Properties of the Least Squares Estimators. by Professor Scott H.

ACE 562 Fall Lecture 5: The Simple Linear Regression Model: Sampling Properties of the Least Squares Estimators. by Professor Scott H. ACE 56 Fall 005 Lecure 5: he Simple Linear Regression Model: Sampling Properies of he Leas Squares Esimaors by Professor Sco H. Irwin Required Reading: Griffihs, Hill and Judge. "Inference in he Simple

More information

LAPLACE TRANSFORM AND TRANSFER FUNCTION

LAPLACE TRANSFORM AND TRANSFER FUNCTION CHBE320 LECTURE V LAPLACE TRANSFORM AND TRANSFER FUNCTION Professor Dae Ryook Yang Spring 2018 Dep. of Chemical and Biological Engineering 5-1 Road Map of he Lecure V Laplace Transform and Transfer funcions

More information

Dynamic Effects of Feedback Control!

Dynamic Effects of Feedback Control! Dynamic Effecs of Feedback Conrol! Rober Sengel! Roboics and Inelligen Sysems MAE 345, Princeon Universiy, 2017 Inner, Middle, and Ouer Feedback Conrol Loops Sep Response of Linear, Time- Invarian (LTI)

More information

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should

In this chapter the model of free motion under gravity is extended to objects projected at an angle. When you have completed it, you should Cambridge Universiy Press 978--36-60033-7 Cambridge Inernaional AS and A Level Mahemaics: Mechanics Coursebook Excerp More Informaion Chaper The moion of projeciles In his chaper he model of free moion

More information

Appendix to Creating Work Breaks From Available Idleness

Appendix to Creating Work Breaks From Available Idleness Appendix o Creaing Work Breaks From Available Idleness Xu Sun and Ward Whi Deparmen of Indusrial Engineering and Operaions Research, Columbia Universiy, New York, NY, 127; {xs2235,ww24}@columbia.edu Sepember

More information

Mathcad Lecture #8 In-class Worksheet Curve Fitting and Interpolation

Mathcad Lecture #8 In-class Worksheet Curve Fitting and Interpolation Mahcad Lecure #8 In-class Workshee Curve Fiing and Inerpolaion A he end of his lecure, you will be able o: explain he difference beween curve fiing and inerpolaion decide wheher curve fiing or inerpolaion

More information

Polymer Engineering (MM3POE)

Polymer Engineering (MM3POE) Polymer Engineering (MM3POE) VISCOELASTICITY hp://www.noingham.ac.uk/~eazacl/mm3poe Viscoelasiciy 1 Conens Wha is viscoelasiciy? Fundamenals Creep & creep recovery Sress relaxaion Modelling viscoelasic

More information

INVERSE RESPONSE COMPENSATION BY ESTIMATING PARAMETERS OF A PROCESS COMPRISING OF TWO FIRST ORDER SYSTEMS

INVERSE RESPONSE COMPENSATION BY ESTIMATING PARAMETERS OF A PROCESS COMPRISING OF TWO FIRST ORDER SYSTEMS Inernaional Journal of Informaion Technology and nowledge Managemen July-December 0, Volume 5, No., pp. 433-438 INVERSE RESPONSE COMPENSATION BY ESTIMATING PARAMETERS OF A PROCESS COMPRISING OF TWO FIRST

More information

Lecture -14: Chopper fed DC Drives

Lecture -14: Chopper fed DC Drives Lecure -14: Chopper fed DC Drives Chopper fed DC drives o A chopper is a saic device ha convers fixed DC inpu volage o a variable dc oupu volage direcly o A chopper is a high speed on/off semiconducor

More information

Dual Current-Mode Control for Single-Switch Two-Output Switching Power Converters

Dual Current-Mode Control for Single-Switch Two-Output Switching Power Converters Dual Curren-Mode Conrol for Single-Swich Two-Oupu Swiching Power Converers S. C. Wong, C. K. Tse and K. C. Tang Deparmen of Elecronic and Informaion Engineering Hong Kong Polyechnic Universiy, Hunghom,

More information

Block Diagram of a DCS in 411

Block Diagram of a DCS in 411 Informaion source Forma A/D From oher sources Pulse modu. Muliplex Bandpass modu. X M h: channel impulse response m i g i s i Digial inpu Digial oupu iming and synchronizaion Digial baseband/ bandpass

More information

Th Q Estimation Through Waveform Inversion

Th Q Estimation Through Waveform Inversion Th-10-01 Q Esimaion Through Waveform Inversion J. Bai* (ION) & D. Yings (ION) SUMMARY This paper presens an approach o esimae he qualiy facor Q hrough waveform inversion. In a viscoacousic medium consising

More information

Single and Double Pendulum Models

Single and Double Pendulum Models Single and Double Pendulum Models Mah 596 Projec Summary Spring 2016 Jarod Har 1 Overview Differen ypes of pendulums are used o model many phenomena in various disciplines. In paricular, single and double

More information

A Specification Test for Linear Dynamic Stochastic General Equilibrium Models

A Specification Test for Linear Dynamic Stochastic General Equilibrium Models Journal of Saisical and Economeric Mehods, vol.1, no.2, 2012, 65-70 ISSN: 2241-0384 (prin), 2241-0376 (online) Scienpress Ld, 2012 A Specificaion Tes for Linear Dynamic Sochasic General Equilibrium Models

More information

Effect of Heat Loss on Pressure Falloff Tests

Effect of Heat Loss on Pressure Falloff Tests Inernaional Journal of Engineering Trends and Technology (IJETT) Volume 39 Number 1- Sepember 016 Effec of Hea Loss on Pressure Falloff Tess Ashkan Jahanbani G. #1, Tom A. Jelmer # #1, eparmen of Peroleum

More information

STATE-SPACE MODELLING. A mass balance across the tank gives:

STATE-SPACE MODELLING. A mass balance across the tank gives: B. Lennox and N.F. Thornhill, 9, Sae Space Modelling, IChemE Process Managemen and Conrol Subjec Group Newsleer STE-SPACE MODELLING Inroducion: Over he pas decade or so here has been an ever increasing

More information

CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK

CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 175 CHAPTER 10 VALIDATION OF TEST WITH ARTIFICAL NEURAL NETWORK 10.1 INTRODUCTION Amongs he research work performed, he bes resuls of experimenal work are validaed wih Arificial Neural Nework. From he

More information

Numerical Dispersion

Numerical Dispersion eview of Linear Numerical Sabiliy Numerical Dispersion n he previous lecure, we considered he linear numerical sabiliy of boh advecion and diffusion erms when approimaed wih several spaial and emporal

More information

EFFECT OF OPERATING PARAMETERS ON FORMATION PROCESS OF DEFECTS IN MODERATOR BLOCK IN GRAPHITE REACTORS

EFFECT OF OPERATING PARAMETERS ON FORMATION PROCESS OF DEFECTS IN MODERATOR BLOCK IN GRAPHITE REACTORS Jr of Indusrial Polluion Conrol 32(2)(2016) pp 437-441 wwwiconrolpolluioncom Research EFFECT OF OPERATING PARAMETERS ON FORMATION PROCESS OF A MOCHALOV, A NAYMUSHIN *, V NESTEROV, S SAVANYUK AND I SHAMANIN

More information

Structural Dynamics and Earthquake Engineering

Structural Dynamics and Earthquake Engineering Srucural Dynamics and Earhquae Engineering Course 1 Inroducion. Single degree of freedom sysems: Equaions of moion, problem saemen, soluion mehods. Course noes are available for download a hp://www.c.up.ro/users/aurelsraan/

More information

Analogue amplifier card for 4/3 proportional directional valves of type 4WRE

Analogue amplifier card for 4/3 proportional directional valves of type 4WRE Analogue amplifier card for / proporional direcional valves of ype WRE RE 09/07.05 Replaces: 06.0 /0 Type VT-VRPA-.-X/ Series X H66 Table of conens Conens Page Feaures Ordering code Funcion Block circui

More information

Activity 4 Solutions: Transfer of Thermal Energy

Activity 4 Solutions: Transfer of Thermal Energy Aciviy 4 Soluions: Transfer of Thermal nergy 4.1 How Does Temperaure Differ from Thermal nergy? a) Temperaure Your insrucor will demonsrae molecular moion a differen emperaures. 1) Wha happens o molecular

More information

Module 4: Time Response of discrete time systems Lecture Note 2

Module 4: Time Response of discrete time systems Lecture Note 2 Module 4: Time Response of discree ime sysems Lecure Noe 2 1 Prooype second order sysem The sudy of a second order sysem is imporan because many higher order sysem can be approimaed by a second order model

More information

Air Traffic Forecast Empirical Research Based on the MCMC Method

Air Traffic Forecast Empirical Research Based on the MCMC Method Compuer and Informaion Science; Vol. 5, No. 5; 0 ISSN 93-8989 E-ISSN 93-8997 Published by Canadian Cener of Science and Educaion Air Traffic Forecas Empirical Research Based on he MCMC Mehod Jian-bo Wang,

More information

Authors. Introduction. Introduction

Authors. Introduction. Introduction Auhors Hidden Applied in Agriculural Crops Classificaion Caholic Universiy of Rio de Janeiro (PUC-Rio Paula B. C. Leie Raul Q. Feiosa Gilson A. O. P. Cosa Hidden Applied in Agriculural Crops Classificaion

More information

Heat Transfer. Revision Examples

Heat Transfer. Revision Examples Hea Transfer Revision Examples Hea ransfer: energy ranspor because of a emperaure difference. Thermal energy is ransferred from one region o anoher. Hea ranspor is he same phenomena lie mass ransfer, momenum

More information