1. Heat Transfer I, 4th Lecture
Thursday, January 23, 2014:
Insulation and R values (Section 2-3);
Radial Systems (Section 2-4);
Overall Heat Transfer Coefficient
(Section 2-5)

2. 1-D heat flow cylindrical sections
q
C
B
A
r1
r2
r3
r4
T1
T2
T3
T4

3. Electrical Analog
T4T2
T3
T1
ln(r2/r1)/(2πkAL) ln(r3/r2)/(2πkBL) ln(r4/r3)/(2πkCL)
q
RA RB
RC

4. 1-D Heat Flow Multiple Cylindrical
Sections
q=2πL(T1-T4)/
ln(r2/r1)/kA + ln(r3/r2)/kB + ln(r4/r3)/kC

5. Example Problem 2-2
A thick-walled tube of stainless steel [18% Cr, 8%
Ni, k= 19 W/m•°C] with a 2-cm diameter (ID)
and 4-cm outer diameter (OD) is covered with a
3-cm layer of asbestos insulation [k= 19
W/m•°C]. If the inside wall temperature of the
pipe is maintained at 600 °C, calculate the heat
loss per unit length.

6. Example Problem Solution
• q=2πL(T1-T2)/[ln(r2/r1)/kS+ ln(r3/r2)/kasb]
• q/L=2π(600⁰C-100⁰C)/[ln(4/2)/19+ln(5/2)/0.2]
• q/L = 680 W/m

7. Overall Heat Transfer Coefficient
Fluid A
Fluid B
q
TA
TB
T2
T1
h2
h1

8. Electrical Analog
TBT1
T2
TA
1/(h1A) delta x/(kA) 1/(h2A)
q
RA Rwall
RB

9. Overall Heat Transfer Coefficient U
• q=(TA – TB ) / (1/h1A + ∆x/kA + 1/h2A )
• q=UAToverall
• U= (1/h1 + ∆x/k + 1/h2 )

10. Questions?
• Please read Sections 2-6, 2-7, 2-8, and 2-9