The resistance to flow in a pipe is parameterized by a dimensionless number
called the friction factor f: For turbulent flow, the Colebrook equation
provides a means to calculate the friction factor:
1
2.51
2 log
f
3.7 D Re f
where = the roughness (m)
Goals of this lecture is to learn:
How to use Gauss-Seidel and Jacobi methods
What the diagonal dominance is
How relaxation can improve the convergence of
the iterative scheme
How to solve systems of nonlinear equation
using Newton-Raphson method
Gaus
Goals of this lecture is to learn:
Understanding what roots problems are and
where they occur in engineering
Learning how to determine a root graphically
Knowing how to solve a root problem with
bisection method
A paratrooper leaps from a
stationary ho
Goals of this lecture is to learn:
How to use Cramers rule
How to implement forward elimination and
backward substitution as in Gauss elimination
The concepts of singularity and ill-conditioning
How to implement partial pivoting
How to obtain efficie
3/26/2013
Goals of this lecture is to learn:
The difference between the initial value
problem and boundary value problem
How to implement Shooting method to
solve the boundary value problem
How to implement finite difference method
1
3/26/2013
A thin l
Goals of this lecture is to learn:
How to implement the following single
application Newton-Cotes formulas
Trapezoidal rule, Simpsons 1/3 rule, Simpsons 3/8
rule
How to implement the following composite
Newton-Cotes formulas
Trapezoidal rule, Simpsons
Goals of this lecture is to learn:
How to determine a root using NewtonRaphson method
How to solve a root problem with secant and
modified secant method
How to use MATLAB fzero function to estimate
roots
How to determine the roots of polynomials with
3/21/2013
Goals of this lecture is to learn:
How to implement the following RungeKutta(RK) methods for a single ODE
Euler
Heun
Midpoint
Fourth-Order RK
How to implement the following RungeKutta(RK) methods for systems of ODE
Euler
Fourth-Order RK
1
3/
2/14/2013
Goals of this lecture is to learn:
How to compute the slop and intercept of a
best fit straight line with linear regression
How to linearize nonlinear equation so that they
can be fit with linear regression
How to implement linear regression
Goals of this lecture is to learn:
Perform matrix operations and being able
assess when it is feasible
How to represent a system of linear algebraic
equations in matrix form
How to solve linear algebraic equations with left
division and matrix inversio
85-220
Numerical Analysis for Engineering
Vesselin Stoilov
Department of Mechanical Automotive and Materials Engineering
University of Windsor
Winter 2015
Dr. Vesselin Stoilov, Associate Professor
responsable for lectures, tutorials, examinassions, and
fi
2/6/2013
A coating on a panel surface is cured by radiant energy from the
heater as shown in Figure 1. The temperature of the coating is
determined by radiative and convective heat transfer processes. If
the radiation is treated as diffuse and gray, the f
Goals of this lecture is to learn:
How to implement polynomial interpolation
How to implement inverse polynomial
interpolation
How to implement spline interpolation
Waters dynamic viscosity (10-3Ns/m2) is
related to temperature T(C) in the following
ma
3/13/2013
Goals of this lecture is to learn:
How to implement finite differences
formulas for numerical differentiation
How to implement the Richardson
extrapolation to increase the accuracy of
numerical differenciation
How to use diff, gradient MALAB
3/21/2013
A model of the atmospheric fluid dynamics is the described by
the Lorenz equations(Edward Lorenz (1917-2008) meteorologist,
MIT professor)
dx
ax ay
dt
dy
rx y xz
dt
dz
bz xy
dt
x= intensity of the atmospheric motion
y, z = temperature variati
Goals of this lecture is to learn:
How to implement Romberg Integration
How to implement the Gauss Quadratures
How to use quad, quadl MALAB functions to
calculate define integrals
Pipeline oil flow in circular pipe.
The experimentally measured velocity
2/13/2013
Goals of this lecture is to learn:
How to implement polynomial regression
How to use General Linear Least-Squares
approach
How to implement nonlinear regression
1
2/13/2013
Assume that the following sequence of distances
traveled at different
Goals of this lecture are to learn:
How to implement piecewise interpolation in
MATLAB.
How to implement multidimensional
interpolation with MATLAB.
The time for which an automobile accelerates to
a steady velocity without decelerating are
shown below
t
4/2/2013
An n-order diffusion model of a single pollutant
is
dc
Dcn
dx
x, cm
0
5
15
30
45
c, mole
6.750
5.594
4.420
3.291
2.223
Use linear regression to determine D and n. Use
first order forward difference to compute the
derivative.
1
4/2/2013
Given a s
4/4/2013
A U-tube manometer is initially filled with water, but is exposed to a pressure
difference such that the water level on the left side of the U-tube is 0.05 m
higher that the water level on the right. At t = 0, the pressure difference is
suddenly
Fundamentals of Convection
Chapter 6
Objectives
Understand the physical mechanism of convection and its
classification
Physical
Mechanism of Convection
Development of velocity and thermal boundary layers over surfaces
Gain a working knowledge of the dimen
Transient Heat Conduction
Objectives
Assess when the temperature of an object varies
nearly uniformly with time, making the simplified
lumped system analysis applicable.
92-328 Heat Transfer S2015
1
Chapter 4: Transient Heat Conduction
Lumped System Anal
Convection
The mode of energy transfer between a
solid surface and the liquid or gas that is in
motion.
It involves the combined effects of
conduction and fluid motion.
The faster the fluid motion, the greater the
convection heat transfer.
92-328 Heat
Steady Heat Conduction
Objectives
Understand the concept of thermal resistance and its
limitations, and develop thermal resistance networks for
practical heat conduction problems
Solve steady conduction problems that involve multilayer
rectangular, cylind
Simultaneous Heat Transfer Mechanisms
When radiation and convection occur simultaneously
between a surface and a gas,
Qtotal
hcombined As (Ts T )
(W )
Combined heat transfer coefficient hcombined includes
the effects of both convection and radiation
A sol
06-92-328
Heat Transfer
Summer 2015
Vesselina Roussinova, PhD, PEng
Assistant Professor
Mechanical Engineering
Office: CEI room 2180
Contact via email
vtr@uwindsor.ca
92-328 Heat Transfer S2015
2
Chapter 1: Introduction and Basic Concepts
Textbook
Heat an
Internal Forced Convection
Chapter 8
Learning Objectives
Obtain average velocity and average temperature from a knowledge
of the velocity and temperature profiles in internal flow
Understand different flow regions in internal flow, such as the entry
and t
Heat Transfer-S15
Final Exam
August 15, 2015 (Saturday)
Start: 8:30 AM
Location: ED room 1101
Final Exam
Closed book exam
Exam duration: 2 hours
Problem solving: 4 problems
Material covered after the midterm
Chapter 6: Fundamentals of convection
Chapter 7
Heat Exchangers
Chapter 11
Objectives
At the end of this chapter, you should be able to:
Recognize numerous types of heat exchangers, and classify
them,
Develop an awareness of fouling on surfaces, and determine
the overall heat transfer coefficient for a
External Forced Convection
Chapter 7
Learning Objectives
Internal vs. External Flows
Understanding friction drag and pressure drag,
and evaluate the average drag and convection
coefficients in external flow
Calculate the drag force and heat transfer for
f