Roots of equations
Roots
Open Methods
Open Methods
Open
6.1 Simple Fixed-Point Iteration
s 6.2 Newton-Raphson Method
s 6.3 Secant Method
s 6.4 MATLAB function: fzero
s
Open Methods
Open
What if we don't have two endpoints
bracketing the root?
s There exis
Algebraic Equation Systems
Algebraic
Direct Methods
Gauss Elimination
Gauss
8.1 Solving small numbers of equations
8.2 Naive Gauss Elimination
8.3 Pivoting
8.4 Tridiagonal Systems
MATLAB M-files
GaussNaive, GaussPivot, Tridiag
Small Matrices
Small
a11
Roots of equations
Roots
Bracketing Methods
Bracketing Methods
Bracketing
s
5.1 Introduction and Background
s
5.2 Graphical Methods
s
5.3 Bracketing Methods and Initial Guesses
s
5.4 Bisection
s
5.5 False-Position
Roots of Equations
Roots
s
Our first real
Chapter 7
Chapter
Linear Algebraic Equations
Linear
and Matrices
and
System of Algebraic Equations
Two types of systems that can be modeled using linear algebraic equations:
(a) Lumped variable system that involves coupled finite components
Mass (flow rat
Summary sheet 1 of ChE 312-heat conduction, convection & radiation
Heat transfer: thermal energy in transit due to a spatial temperature difference
1. Conduction:
Applied to solid, liquid, gas; Solid more significant. Metal/ carbon materials are good
cond
ChE 312 Summary 4 -The Plane Wall-with heat generation
Consider 1-D, steady-state, constant k, uniform generation, and asymmetric surface conditions:
Heat diffusion equation:
d dT
k
dx dx
General Solution:
dT q
+q =0 2 + =0
dx
k
2
T ( x ) =q/ 2k x 2 + C
Summarysheetofweek2
T
Rt
ThermalResistances
q
Conductioninaplanewall:
Rt ,cond
2.1
L
kA
2.2
Convection:
Rt ,conv
1
hA
2.3
Conductioninacompositewall:
2.4
Rtot
1
L
1
h1 A kA h 2 A
qx kA
qx
dT kA
Ts,1 Ts,2
dx
L
Rt Rtot
qx
Rtot
TemperatureDistribut
Summary sheet 3- energy balance, heat equation, boundary
A differential equation whose solution provides the temperature distribution in a stationary medium.
Cartesian Coordinates:
T
k
x x
T
k
y y
T
z k z
T
q cp
t
Net transfer of thermal energy i
ChE 390
Course Syllabus
1/5
Department of Chemical Engineering
ChE 390 CHEMICAL ENGINEERING LABORATORY 3 (Winter, 2017)
COURSE INSTRUCTOR
Mingqian (John) Zhang
Office: DWE 2530B
Phone: 519-888-4567 ext. 35815
Email: m78zhang@uwaterloo.ca
Office hour: any