Module 2: Conduction
Section 3 – Transient Conduction
Instructor: Dr. Sukwon Choi
Associate Professor
Department of Mechanical Engineering
The Pennsylvania State University
Lecture #14
Summary
Announcements:
- HW#3 is due next Monday (2/19).
- HW#2 grade appeal is due next Monday.
- Exam#1 will held on next Friday (2/23) in class: Chapters 1-5 (general lumped
capacitance analysis)
Previously, we learned:
• The lumped capacitance method (LCM) is the simplest method used to determine the
thermal time response of a system.
• The main assumption of the LCM is that there is no spatial temperature variation within
the solid during the transient process.
• The applicability of the LCM can be determined by:
BiLCM 
Rcond ULc

Rsurface
k
Conduction resistance of the system
Surface thermal resistance of the system
U: Overall heat transfer coefficient
Lc: Characteristic length, volume/area
In our class (and for may practical applications), if BiLCM < 0.1, we can use the LCM
Example 5.1: Baseplate of an iron
Aluminum alloy
ρ
2800 kg/m3
c
900 J/kg K
k
180 W/m K
ε
0.8
q”
12,500 W/m2K
L
0.007 m
As
0.04 m2
Tsur = Tinf
25°C
h
10 W/m2 K
Example 5.1: Ironing out the LCM concept, cont’d
Example 5.1: Ironing out the LCM concept, cont’d
Example 5.2: Coated furnace surface during start-up
Example 5.2: Coated furnace surface during start-up
[m2K/W]
R=R”/A [K/W]
Example 5.2: Coated furnace surface during start-up
Data Center Cooling
https://youtu.be/WNOyBdWZNwE?si=eUKbpjUIUMo0p-jq