The University of Nottingham Malaysia Campus MM3CMT, Computer Modelling Techniques, spring 2013 Assignment: on a Finite Difference and Finite Volume Method A fluid enters a very long pipe by TA temperature and leaves the pipe by TB temperature. The length of pipe is L m with D mm diameter. Assume the thermal conductivity is constant and equal to κ W/mK, ρ=1 kg/m3, specific heat equal 1 and mass flow rate is 0.2 kg/s. calculate temperature distribution along the pipe.

TA

X=0

u Figure Q1.

TB X=L

Pre-processing: 1. Apply a suitable assumption for simplification to reduce the dimension of the problem. 2. Derive the governing equation by using general transport equation. ( ) .( U ) .( grad ) S . t 3. Generate uniform grids (Mesh) with 10 equal cells, find the cell size and draw schematic of computational domain and assign nodal points when the length of domain is L m. Solving: 4. Applied the finite difference method, FDM, to discretise the governing equation. Apply backward difference for the convection term and central difference for the diffusion term. Calculate the temperature distribution along the pipe. you may need to develop a code for this purpose using any software (Matlab®, Excell®, …) 5. FVM 5.1 Applied the finite volume method, FVM, to discretise the governing equation. 5.2 Write the neighbouring coefficient and their value for each nodal point; write the resulting set of equations as a matrix. You can use the Table Q1. 5.3 Develop a code using any language or software (Matlab®, Excell®, …) to solve the above matrix set by using iteration method to calculate temperature distribution. For the results, assume one digit after point as an acceptable accuracy (convergence criteria).

5.4 Now consider a uniform heat generation q kW/m3 , along the pipe. Repeat part 5.3 and show the results.

Node 1 2, 3, 4, … 10

aW

aE

Sp

SU

ap

Table Q1. Post processing: 6. Write a temperature distribution for each node. You...

...The Islamic University of Gaza Faculty of Engineering Civil Engineering Department
NumericalAnalysis ECIV 3306
Chapter 1
Mathematical Modeling
10:51:09 PM
Part one : Approximation and Errors
Specific Study Objectives
• Recognize the difference between analytical and numerical solutions. • Recognize the distinction between truncation and round-off errors. • Understand the concepts of significant figures, accuracy, and precision. • Recognize the difference between true relative error t, approximate relative error a, and acceptable s error
10:51:09 PM
Chapter 1: Mathematical Modeling
Mathematical Model
• A formulation or equation that expresses the essential features of a physical system or process in mathematical terms. • Generally, it can be represented as a functional relationship of the form
10:51:09 PM
Mathematical Modeling
10:51:09 PM
Simple Mathematical Model
Example: Newton’s Second Law (The time rate of change of momentum of a body is equal to the resultant force acting on it)
a = acceleration (m/s2) ….the dependent variable m = mass of the object (kg) ….the parameter representing a property of the system. f = force acting on the body (N)
10:51:09 PM
Complex Mathematical Model
Example: Newton’s Second Law
10:51:09 PM
Where: c = drag coefficient (kg/s), v = falling velocity (m/s)
Complex Mathematical Model
At rest: (v = 0 at t = 0), Calculus can be used...

...TERM PAPER OF 5TH SEMESTER 2010
NUMERICALANALYSIS
MTH204
TOPIC: Using trapezoidal rule and simpson’s rule, evaluate the integral [pic]
DOA:
DOS: 12th November, 2010
Submitted to: Submitted by:
Ms.Nitika Chugh Mr. William Anthony
Deptt. Of Mathematics Regd no:10805460
Rollno:RD1803B30
ACKNOWLEDGEMENT
I would like to express my gratitude for the many helpful comment and suggestions .I have received over the last few days regarding the expository and critical expects of my term work and especially for those comments which bear directly or may various argument for the center thesis of term work.
Most importantly I would like to thank my HOD (head of department) and my teacher Ms. Nitika Chugh for her days of supervision. Her critical commentary on my work has played a major role in both the content and presentation of our discussion and arguments.
I have extend my appreciation to the several sources which provided various kinds of knowledge base support for me during this period.
Last and not the least my God and my parent helped me to overcome the problem while preparing this project....

...Preparation Guide NumericalAnalysis
This preparation guide helps you to prepare for numerical aptitude assessments. It provides guidance on how best to approach the assessment, allowing you to give your best possible performance.
Why are Aptitude Assessments used?
Employers often use aptitude assessments as part of their assessment procedures for the selection and development of staff. Research has shown that they are powerful predictors of performance at work.
Assessments help you to:
- demonstrate your strengths - be assessed fairly on job relevant criteria - find out more about your strengths and development needs - make future career decisions based on your abilities
Assessments help employers to:
- select people best suited to the demands of the job - identify areas where individuals might benefit from further development - obtain objective information about people’s abilities
Instructions
On the following pages are some practice questions which are similar to those you will be asked in the assessment. Completing these will help you understand the types of questions used and gain experience in taking ability tests. These questions are designed to assess your ability to understand numerical information. You will be presented with a series of tables and graphs, each followed by several questions. Your task is to choose the best answer to each question from the options given. Have a pen and paper...

...INTERNATIONAL JOURNAL SYSTEMATIC OF BACTERIOLOGY, 1976, p. 146-157 Apr. Copyright 0 1976 International Association of Microbiological Societies
Vol. 26, No. 2 Printed in U . S A .
Phenotypic Description, NumericalAnalysis, and Proposal for an Improved Taxonomy and Nomenclature of the Genus Zymomonas Kluyver and van Niel 1936
J. DE LEY
Laboratory
of
AND
J. SWINGS
Microbiology and Microbial Genetics, Faculty of Sciences, State University, K . L . Ledeganckstraat 35, B-9000 Gent, Belgium
One hundred thirty-eight phenotypic features were determined in 38 Zymomonas strains from diverse origin (Zairese fermenting palm saps, Mexican pulque, British spoiled beer, and sick cider). The similarity between all the strains was very high: 27 features were present, and 74 features were absent in all of them; 37 features were variable. By numericalanalysis all strains formed one cluster above the simple matching coefficient of 0.88. There were no significant differences between motile and nonmotile strains or between sucrosefermenting and non-sucrose-fermenting strains. A strain from sick cider in Bristol, United Kingdom, was a border case in its phenotypic features, deoxyribonucleic acid relatedness, and protein electropherograms. We propose: (i) to discontinue the use of the species name of Zymomonas anaerobia and its subspecies Z. anaerobia subsp. anaerobia and 2. anaerobia subsp. irnmobilis, and to include...

...CHAPTER I
INTRODUCTION
On the global scale, mean annual surface temperature has increased over the past century by 0.6 0
C (IPCC 2001). Various models have been developed to assess climate change impact at the
global and regional level. Temperature and precipitation trends differ at the local level and have
differing impact. Also, various studies have been done in different parts of the world for
detecting climate trends and changes. Some of these have shown significant trends (Capodici et
al., 2008; Feidas et al., 2007; Gemmer et al. 2004). However, very limited work has been
conducted at the national level especially on time series analysis. (Dankers , Hiederer, 2008)
Based on the available information it was reported that the surface average temperature in Nepal
is rising by 0.5 degrees Celsius per decade (Dhakal, 2003). However, the country lacks
comprehensive report on temperature rise and climate changes.
However, there is more general information available on climate change and its impacts. The
information lacks at local and specific level regarding the extent and pattern of change in
precipitation and temperature, the locations of high or low trend, and pattern of climate variables.
These pieces of information are essential for implementing effective measures to help the poor
communities to cope and adapt to impacts of climate change.
Nepal is a highly...

...
Sydney TemperatureAnalysis Report
Student name: Crystal
Assessment: GAC013
Table of Contents
Sections of a Scientific Report
Abstract
1.0 Introduction
With the development of human activities, climate changes over time all around the world. As we known Australia has a staggering tourist landscapes, the climate in Sydney, however, changes quickly due to human activities in many different ways.
Therefore, purpose of this report is to commend the suit season for four people who need the climate information about Sydney.
2.0 Methods and Materials
In order to do this we use these the following data were collected: temperature data, humidity data and rainfall data. First, an excel document was created. And then relevant data and information ware input to four different worksheets. Next, the data was recorded into tables, and then placed into charts for easy analysis.
3.0 Results
3.1 Quarterly Temperature
The following bar chart demonstrates Sydney mean maximum temperature in quarterly over 10 years. Year 2004, Year 2006 and Year 2011 were the hottest years as 27.3. Year 2008 was the coldest 25.3.
Figure1.1
The following line chart illustrates over 10 years Quarter2 has the least fluctuation in temperature and Quarter 4 has the most fluctuation....

...EE 4225 Project
Distribution Feeder Analysis
11/29/2010
Kris Bartell
Matt Drzewiecki
Evan Zaborski
1.0 Abstract
This project offered the opportunity to simulate the voltage profile of an IEEE sample distribution feeder. Through an iterative process, this can be accomplished using a series of calculations. To achieve this goal, the simulation package Matlab was used as the driving force behind the programming and calculating.
Discussion
2.1 Individual Segment Modeling
To simulate the feeder, the first thing needed is a model of each line segment. To construct this model, code can be written that computes the distances between conductors by using the configurations and conductor values given for each line segment. These results provide the information needed to create the primitive impedance matrix, Zprim. Using the matrix operation known as Kron reduction, shown in Equation (1) below, these primitive matrices can be converted into Zabc impedance matrices.
Z=A-BC^(-1) D (1)
Each matrix can then be multiplied by its respective segment length to convert to actual ohmic values of line resistance. These matrices represent the main part of the line model.
2.2 Load Modeling
Each load connected to the feeder can now be modeled. To accurately simulate the voltage profile, three types of loads will be modeled. These include a constant current load, a constant impedance load, and a load with constant real and...

...(
) Let y*=1,000,000 and y=999,996; then the error is Ey =|y*-y|=|1000000-999996|=4
Chapter 1:
(
and the relative error is
RE y
y* y y
4 1000000
0.000004
) Let z*=0.000012 and z=0.000009; then the error is Ez =|z*-z|=|0.000012-0.000009|=0.000003 and the relative error is
Error Analysis
1
REz
z* z z
0.000003 0.000012
4
0.25
In the practice of numericalanalysis it is important to be aware that computed solutions are not exact mathematical solutions. The precision of a numerical solution can be diminished in several subtle ways. Understanding these difficulties can often guide the practitioner in the proper implementation and/or development of numerical algorithms. Definition 1.1 Suppose x is an approximation to x*. The absolute error is Ex = |x* -x|.
And the relative error is REx that x*≠0 .
2
In case ( ), there is not too much difference between Ex and REx, and either could be used to determine the accuracy of x. In case ( ), the value of y is of magnitude 106, the error Ey is large, and the relative error REx is small. In this case, y would probably be considered a good approximation to y*. In case ( ), z is of magnitude 10-6 and the error Ez is the smallest of all three cases, but the relative error REz is the largest. In terms of percentage, it amounts to 25%, and thus z is a bad approximation to z*.
5
x* x , provided x
The absolute error...

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