INTRODUCTION TO HEAT TRANSFER

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INTRODUCTION TO HEAT TRANSFER (ME 411) Summer
2003 Lecture Number IV Ali R. Mazaheri Course
webpage www.clarkson.edu/mazahear/MAIN/ME411 De
partment of Mechanical and Aeronautical
Engineering Clarkson University
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Two-Dimensional Heat Conduction
Isotherm line
Tconstant
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1. Analytical Analysis
T2
H
T1
T1
B.Cs.
W
T1
Let
NEW B.Cs.
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Separation of Variables
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Last B.C.
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or
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Superposition
Temperature Distribution
T2
T2
T1
H
H
H


T3
T1
T3
T1
T1
T1
W
W
W
T1
T1
T1
Heat Transfer Evaluation
q1
T2
H
T1
T1
q1 q2 q3 q4
q3
q2
W
T1
q4
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2. Graphical Analysis
Heat-Flow line
Isotherm line
For each element
where N is the number of isotherm lines.
Conduction Shape factor
So for each element
If there are M heat-flow lanes then
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Numerical Analysis(Conduction)
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If
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Example
q1
Node 1
Node 2
Node 3
q3
q2
Node 4
q4
q1 q2 q3 q4
To examine the superposition
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Numerical Analysis(Convection)
If
If the boundary is insulated, h0 and
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Numerical Analysis (Convection at an exterior
corner)
If
Biot number (Bi)
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N-Nodes Problem
For n nodes
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Gauss Method
Making a upper triangle matrix
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Gauss-Seidel Method
Make an initial guess for temperatures
until