1. INTRODUCTION What is Heat Transfer ? Continuum Hypothesis
Local Thermodynamic Equilibrium
Conduction
Radiation
Convection
Energy Conservation

2. WHAT IS HEAT ? In a solid body
Crystal : a three-dimensional periodic array of atoms
Oscillation of atoms about their various positions of equilibrium (lattice vibration): The body possesses heat.
Conductors: free electrons ↔ Dielectics

3. Vibration of crystals with an atom
Longitudinal polarization vs. Transverse polarization
us-1 us
us+1
us+2 s
s+1
s+2
s+3
s-1
us-1 us
us+1
us+2
us+3
The energy of the oscillatory motions:
the heat-energy of the body
More vigorous oscillations:
the increase in temperature of the body

4. Internuclear separation distance
In a gas
The storage of thermal energy:
molecular translation, vibration and rotation
change in the electronic state
intermolecular bond energy
average kinetic energy
kB = × J/K
Internuclear separation distance
(diatomic molecule)
Energy
dissociation energy for state 1
dissociation energy for state 2
electronic state 2
vibrational state
rotational state
electronic state 1
at T = 300 K,
air M = kg/kmol
= m/s

5. HEAT TRANSFER
Heat transfer is the study of thermal energy transport within a medium or among neighboring media by
Molecular interaction: conduction
Fluid motion: convection
Electromagnetic wave: radiation
resulting from a spatial variation in temperature.
Energy carriers: molecule, atom, electron, ion, phonon (lattice vibration), photon (electro-magnetic wave)

6. CONTINUUM HYPOTHESIS Ex) density microscopic uncertainty
macroscopic uncertainty
local value of density
(3×107 molecules at sea level, 15°C, 1atm)

7. microscopic uncertainty
due to molecular random motion
macroscopic uncertainty
due to the variation associated with spatial distribution of density
In continuum, velocity and temperature vary smoothly. → differentiable
Mean free path of air at STP (20°C, 1atm)
lm = 66 nm,
bulk motion vs molecular random motion

8. LOCAL THERMODYNAMIC EQUILIBRIUM
hot wall at Th
adibatic wall L
adibatic wall
gas
cold wall at Tc
a) lm << L : normal pressure
b) lm ~ L : rarefied pressure
c) lm >> L

9. CONDUCTION Gases and Liquids Due to interactions of
atomic or molecular
activities
Net transfer of energy by random
molecular motion
Molecular random motion→ diffusion
Transfer by collision of random
molecular motion

10. Solids
Due to lattice waves induced by
atomic motion
In non-conductors (dielectrics):
exclusively by lattice waves
In conductors:
translational motion of free electrons
as well

11. Fourier’s Law heat flux [J/(m2s) = W/m2]
k: thermal conductivity [W/m·K]
As Dx → 0,

12. Notation Q : amount of heat transfer [J] q : heat transfer rate [W],
: heat transfer rate per unit area [W/m2]
: heat transfer rate per unit length [W/m]

13. Heat Flux
vector quantity

14. Ex)
T = constant line or surface: isothermal lines or surfaces (isotherms)

15. temperature : driving potential of
heat flow
heat flux : normal to isotherms
along the surface of T(x, y, z) = constant
T(x, y, z) = constant

16. Steady-State One Dimensional Conduction
T = T(x) only
steady-state

17. or
As Dx → 0,
When k = const.,

18. RADIATION Thermal Radiation
visible
0.4
0.7
ultra violet
infrared
thermal radiation

19. Characteristics of Thermal Radiation
Independence of existence and temperature of medium
Ex) ice lens
black carbon paper
ice lens

20. 2. Acting at a distance
Ex) sky radiation
electromagnetic wave or photon
photon mean free path
ballistic transport
diffusion
volume or integral phenomena
conduction
fluid: molecular random motion
free electron
solid: lattice vibration (phonon)
diffusion or differential phenomena as long as continuum holds

21. Blackbody spectral emissive power
3. Spectral and Directional Dependence
quanta
history of path
Blackbody spectral emissive power
surface emission

22. Two Points of View Electromagnetic wave
Maxwell’s electromagnetic theory
Useful for interaction between radiation and matter
2. Photons
Planck’s quantum theory
Useful for the prediction of spectral properties of absorbing, emitting medium

23. Radiating Medium Transparent medium ex: air Participating medium
emitting, absorbing and scattering
ex: CO2, H2O
Opaque material

24. Stefan-Boltzmann’s law
Blackbody:
a perfect absorber
Blackbody emissive power
Stefan by experiment (1879):
Boltzmann by theory (1884):

25. Planck’s law spectral distribution of hemispherical
(The Theory of Heat Radiation, Max Planck, 1901)
spectral distribution of hemispherical
emissive power of a blackbody in vacuum
h: Planck constant: ×10-34 J•s
C0: speed of light in vacuum: ×108 m/s
k: Boltzmann constant: ×10-23 J/K

26. Blackbody spectral emissive power
El,b (W/m2.mm)
For a real surface,
Wavelength, l (mm)
e : emissivity
Blackbody spectral emissive power

27. Ray-tracing method vs Net-radiation method
Surface Radiation
Ray-tracing method vs Net-radiation method G J
G: irradiation [W/m2]
J: radiosity [W/m2]
r : reflectivity e
diffuse-gray surface at T
a : absorptivity
Kirchihoff’s law

29. aG
esT4 e
diffuse-gray surface at T

30. Ex) a body in an enclosure
[W]
T2, e2, A2 q1
T1, e1, A1
when
Tsur
Ts, e, a, A q
e = a
Surrounding can be regarded as a blackbody.

31. A1 A2
Why is the irradiation on the small object the same as ?

32. A1 A2
F: view factor
Reciprocity:

33. CONVECTION
energy transfer due to bulk or macro- scopic motion of fluid
bulk motion: large number of molecules moving collectively
convection: random molecular motion
+ bulk motion
advection: bulk motion only

34. solid wall
hydrodynamic (or velocity)
boundary layer
thermal (or temperature)
boundary layer
at y = 0, velocity is zero: heat transfer only by molecular random motion

35. solid wall
When radiation is negligible,
h : convection heat transfer
coefficient [W/m2.K]
Newton’s Law of Cooling

37. Convection Heat Transfer Coefficient
not a property: depends on geometry and fluid dynamics
forced convection
free (natural) convection
external flow
Internal flow
laminar flow
turbulent flow

38. First law of thermodynamics
ENERGY CONSERVATION
First law of thermodynamics
control volume (open system)
material volume (closed system)
control volume
In a time interval Dt:
steady-state:

39. Surface Energy Balance
Ex)
sur.

40. Example 1.2 air Find: Surface emissive power E and irradiation G
Pipe heat loss per unit length,
Assumptions:
Steady-state conditions
Radiation exchange between the pipe and the room is between a small surface in a much larger enclosure.
Surface emissivity = absorptivity

41. air
1. Surface emissive power and irradiation

42. air
2. Heat loss from the pipe

43. Conduction does not take place ?
Example 1.2
air
Q: Why not ?
Conduction does not take place ?

44. T r
air

45. Example 1.4 Hydrogen-air Proton Exchange Membrane (PEM) fuel cell
Three-layer membrane electrode
assembly (MEA)
Anode:
Cathode:
(exothermic)
Role of electrolytic membrane
transfer hydrogen ions
serve as a barrier to electron
transfer
Membrane needs a moist state
to conduct ions.
Liquid water in cathode: block
oxygen from reaching cathode
reaction site → need to control Tc
The convection heat coefficient, h

46. Find: The required cooling air velocity, V, needed to maintain steady state operation at Tc = 56.4ºC.
Assumptions:
Steady-state conditions
Negligible temperature variations within the fuel cell
Large surroundings
Insulated edge of fuel cell
Negligible energy flux by the gas or liquid flows

47. Energy balance on the fuel cell

48. Example 1.5 section A-A A A cubical cavity
ice of mass M at the fusion temperature
Find:
Expression for time needed to melt the ice, tm
Assumptions:
1) Inner surface of wall is at through the process.
2) Constant properties
3) Steady-states, 1-D conduction through each wall
4) Conduction area of one wall =

49. section A-A
: latent heat of fusion

50. Example 1.7 air Coating to be cured Find: 1) Cure temperature T for
2) Effect of air flow on the cure temperature for
Value of h for which the cure temperature is 50°C.
Assumptions:
Steady-state conditions
Negligible heat loss from back surface of plate
Plate is very thin and a small object in large surroundings,
coating absorptivity w.r.t. irradiation from the surroundings

51. air
coating

53. air T y
Coating to be cured

54. Heat Transfer WHY HEAT TRANSFER ? Natural System Bio-System
Environment
Sensors & Actuators
Heat
Transfer
Energy Conversion
Process
Electrical & Electronics
Manufac-turing

55. Natural System / Temperature Distribution in the Earth