INTRODUCTION TO HEAT TRANSFER

1
INTRODUCTION TO HEAT TRANSFER (ME 411) Summer
2003 Lecture Number II Ali R. Mazaheri Course
webpage www.clarkson.edu/mazahear/MAIN/ME411 De
partment of Mechanical and Aeronautical
Engineering Clarkson University
2
Steady State 1-D Conduction Heat Transfer
The plane wall
q
Fouriers Law
q
T1
T2
3
Electrical Analogy
R
I
v2
v1
T2
q
T1
Thermal resistance
4
Example
Eliminating T2 and T3
T1
T3
T2
T4
RA
RB
RC
5
Another Example
6
Radial Systems
q
dr
r
ri
ro
L
To
q
Ti
Rth
7
Spheres
q
dr
r
ri
ro
To
q
Ti
Rth
8
Electrical Analogy for Convection Boundary
Conditions
Free stream
wall
q
9
q
Example
Assumption T1 gt T2
Fluid B TB
Fluid A TA
T1
T2
h1
h2
q
T2
TB
TA
T1
10
Overall Heat Transfer Coefficient
Fluid B
Fluid A
U?
TAgtTB
q
TA, hA
TA , hA
ri
ro
11
Overall heat transfer coefficient based on inside
area of the tube.
If AAi
UUi
Overall heat transfer coefficient based
on outside area of the tube.
If AAo
UUo
Note Generally, the overall heat transfer
coefficient is being calculate based on the
outside area.
12
Critical Insulation Thickness
The heat transfer always decreases by increasing
the insulation thickness when we are dealing
with plane wall.
However, it is NOT true when a cylindrical
geometry, e.g. tube, is insulated!
example
h, To
q
Ti
ri
ro
where
13
In order to find the maximum of ro we should use
the Maximization condition
q
Insulation Thickness
14
Example
k0.17 W/m oC
Find qcritical per unit length and qcritical /q .
h3 W/m2 oC To20 oC
q
Ti200 oC
Critical thickness
ri
ro
ri2.5 cm
qcritical105.7 W/m
Without insulation
q84.8 W/m
What does it mean?
15
Critical Insulation Thickness for Sphere