1. Heat Transfer
DM23815
Chapter 1. Introduction
Eunseop Yeom
esyeom@pusan.ac.kr
School of Mechanical Engineering, Pusan National University

2. 2
1.1 What is heat transfer?
The form of energy that can be transferred from one
system to another as a result of temperature difference.
 Thermodynamics
 Heat
It deals with the amount of energy as a system
undergoes a process from one state to another, and
gives no indication about how long the process will
take. (equilibrium)
 Heat transfer
It deals with the rate of heat transfer to or from a system, and thus determine
the rates of heat transfer and the times of cooling or heating, as well as the
variation of the temperature. (non-equilibrium)
“Heat transfer is energy in transit due to temperature difference.”
E=[J]
q=[W]=[J/s], q'=q/L=[W/m], q''=q/A=[W/m2]
Time
State 1
Temp
State 2

3. 3
Examples of heat transfer mechanisms
Conduction (Heat diffusion) Convection Radiation

4. 4
1.2.1 Conduction
Heat transfer from the more energetic to the adjacent less
energetic particles of a substance due to interactions
between the particles.
Fourier’s law of heat conduction
k : thermal conductivity (열 전도율) [W/m·K]
Two mechanisms
1. The atoms and molecules having energy
will pass those energy with their adjacent atoms
or molecules by means of lattice vibrations.
2. Through the translational motion of free
electrons, heat energy can be transferred in a
conductor like metals having a plenty of free
electrons.
Conductive heat flux
Under steady-state conditions and temperature distribution is linear
L
T
-
T
dx
dT 1
2
 
L
T
k
L
T
T
k
q 2
1
x






x
q


5. 5
1.2.1 Conduction
Thermal conductivity (k) is a measure of material’s ability to conduct heat.
Material k (W/m·K)
Water (liquid) 0.607
Air(gas) 0.026
Human artery 0.476 ± 0.041
Human blood (43%Ht) 0.530
Human plasma 0.572
Human bone 0.373 - 0.496
Human fat 0.23 - 0.27
Human kidney 0.513 - 0.564
Human liver 0.467 - 0.527
Human lung 0.302 - 0.550
Human muscle 0.449 - 0.546
Human skin 0.385 - 3.393
 Thermal conductivities
Duck, Physical properties of tissues: a comprehensive reference
book. (Academic press, 2013).
- If k is high, the material is a good conductor.
- If k is low, the material is a poor conductor or an insulator.
- Thermal conductivity varies with temperature.

6. 6
1.2.1 Convection
Heat transfer due to a superposition of energy transport by the random motion of the
molecules (diffusion), and by the bulk motion of the fluid (advection).
Newton's law of cooling
h : Convection heat transfer coefficient [W/m2·K].
(The term convection refers to heat transfer that will occur between a solid surface and the adjacent fluid
when they are at different temperatures.)
Convective heat flux Ts and T∞ : Temperatures at surface and fluid [K].
conv
q


7. 7
1.2.1 Convection
 Forced convection
 Natural convection
Process h (W/m2·K)
Free convection
Gases 2 - 25
Liquids 50 - 1,000
Forced convection
Gases 25 - 250
Liquids 100 - 20,000
Convection with phase change
Boiling and condensation 2,500 - 100,000
Fluid motion is set up by buoyancy effects resulting
from density difference caused by temperature
difference in the field.
Fluid motion is forced by external means, such as
a fan, a pump, etc.
h depends on conditions in the
boundary layer, which are influenced by
① Surface geometry
② The nature of the fluid motion
③ An assortment of fluid thermodynamic properties
 Convection with phase change
A latent heat exchange is associated with phase
change between liquid and vapor states of the
liquid. Two special cases are boiling and
condensation.
 Convection heat transfer coefficient
Forced convection Free convection
conv
q
 conv
q

Boiling Condensation

8. 8
1.2.3 Radiation
This mode of heat transfer didn’t require any medium to occur. Every matter having a
temperature above absolute zero will emit energy in the form of electromagnetic
waves (or alternatively, photons) and called radiation.
Radiation transfer occurs most efficiently in a vacuum.
Stefan-Boltzmann’s law
4
s
b T
E 
 σ : Stefan-Boltzmann’s constant (5.67×10-8) [W/m2·K4].
T : Absolute temperature of surface [K]
(For black body; ideal radiator)
4
s
T
E 

(For real body)
ε : Emissivity(방사율). (0 ≤ ε ≤ 1)
A measure of how efficiently a surface emits energy relative to a blackbody.
It depends strongly on the surface material and finish.
rad
q


9. 9
1.2.3 Radiation
G
Gabs 

αG
εE
q b
rad 



 
sur
s
r
rad T
T
A
h
q 

  
2
2
sur
s
sur
s
r T
T
T
T
h 

  hr : Radiation heat transfer coefficient
Radiation may also be incident (입사) on a surface from its surroundings. Irradiation
G (조사) is all radiation on a unit area of the surface. A portion or all of irradiation may be
absorbed by the surface.
α : Absorptivity (흡수율) (0 ≤ α ≤ 1)
When the surface is opaque (α < 1), portions of the irradiation are reflected.
4
sur
T
G 

(For black body; ideal absorber)
σ : Stefan-Boltzmann’s constant (5.67×10-8) [W/m2·K4].
T : Absolute temperature of surrounding black body [K]
abs
G
E When the surface is assumed to be α = ε.
 Net rate of radiation heat transfer from surface
 
4
surr
4
s
rad T
T
ε
q 


 

10. 10
1.3 Relationship to thermodynamic
 First law of thermodynamics
The increase in the amount of energy stored in a control volume must equal the amount of energy
that enters the control volume, minus the amount of energy that leaves the control volume.
g
out
in
st
st E
E
-
E
dt
dE
E 


 


Energy transported by the medium into the control volume. → surface phenomena
Energy transported by the medium out of the control volume → surface phenomena
Energy generated in the control volume → volumetric phenomena
(e.g., chemical, electrical, electromagnetic, or nuclear)
V
q
Eg

  : heat generation rate per unit volume
: volume
q

V
Energy stored in the control volume → volumetric phenomena
in
E

out
E

g
E

st
E

 
CVT
t
Est 



 ρ: density volume, V : volume, C : specific heat,
t : time, T : temperature
For steady-state conditions → 0

st
E


11. 11
1.3 Relationship to thermodynamic
rad
q

conv
q

cond
q

 The surface energy balance
In the special case, the control surface of a medium contains no mass or volume.
Accordingly, the generation and storage terms of the conservation equation are no longer relevant.
out
in E
E 
 
0








 rad
conv
cond q
q
q

12. 12
1.3 Relationship to thermodynamic
 Second law of thermodynamics
It is impossible for any system to operate in a thermodynamic cycle and deliver a net amount of
work to its surroundings while receiving energy by heat transfer from a single thermal reservoir.
Kelvin-Plank statement
The second law states that if the physical process is irreversible, the combined entropy of the
system and the environment must increase. The final entropy must be greater than the initial
entropy for an irreversible process:
in
out
in
out
in
in Q
Q
-
1
Q
Q
Q
Q
W
η 



Efficiency of a heat engine
h
c
c
T
T
-
η 1

Carnot efficiency
The Carnot efficiency is the maximum possible efficient that
any engine can achieve operating between low and high
temperature reservoirs.
i
h,
i
c,
in
out
in
out
m
T
T
-
q
q
-
Q
Q
-
η 1
1
1 


Modified efficiency for realistic heat transfer process
tot
in
h
c
R
q
T
T
-

1
m
in
q
W 










tot
in
h
c
in
R
q
T
T
-
q 1
Power output of heat engine
  h
t,
/R
i
h,
h
in T
T
q 

  c
t,
/R
c
i
c,
out T
T
q 


13. 13
1.4 Units and Dimensions
 SI base units
 Multiplying prefixes
Basic dimensions
Length (L), Mass (M), Time (t), and Temperature (T)
All physical quantities of heat transfer may be related
to these four basic dimensions.
Celsius temperature scale remains widespread. Zero on
the Celsius scale (0°C) is equivalent to 273.15 K