Thermodynamics
deals with the amount of
heat transfer as a system undergoes from one
equilibrium state to another.
• Driving force - difference of temperature
Heat transfer
deals with the
rate
of heat
transfer as well as
the temperature distribution
within the system at a specified time.
HEAT TRANSFER
Heat transfer in daily life
The human
body
Air-conditioning
systems
water-in
water-out
Car
radiators
Power
plants
Refrigerator
system
Circuit boards
The
experimental approach
(testing and taking measurements)
• advantages
-
dealing with the actual physical system
-
getting a physical value within the limits of
experimental uncertainty
• disadvantages
-
expensive, time consuming, and often
impractical.
The
analytical approach
(analysis or calculations)
• advantage - fast and inexpensive
• disadvantages - assumptions and idealisations made in the
analysis →
→
→
→ impact on the results.
Modelling
- prediction of the course of an event before it
actually occurs
- studying of various aspects of an event
mathematically without actually running expensive and
time-consuming experiments.
THERMODYNAMICS of nonequilibrium processes
Conservation of energy principle - 1st thermodynamic law
Total energy
entering
the system
Total energy
leaving
the system
Change in the
total energy
of the system
out
in
E
E
•
•
=
Energy balance for steady process in the rate form:
dt
dE
E
=
•
- e
nergy transfer
rate
- time derivative (overdot)
(J/s)
Energy balance for closed stationary system
(fixed mass)
T
mc
U
E
E
V
out
in
∆
=
∆
=
−
where:
U -
internal energy
m -
mass of thermodynamic system
c
V
-
specific heat at constant volume
∆
∆
∆
∆
T -
temperature change of the system
)
(
2
1
T
T
mc
Q
V
−
=
Energy balance for steady - flow systems (mass flow)
→
→
→
→
engineering devices (e.g. water heaters, car radiators)
Steady flow
- no change in
time at a specified location
Unsteady flow -
transient
one
Uniform
flow - no change
with position thorough the
surface or region at a
specified time (1D case)
The change in the total
energy of the control
volume during a process
∆
∆
∆
∆E
CV
= 0
ρ
m
V
•
•
=
⋅
=
C
A
v
Volume flow rate:
(m
3
/s)
C
vA
ρ
=
•
m
v
(kg/s)
The mass flow rate through a
differential cross-sectional area
dA
C
of a pipe or duct :
dm = ρ
ρ
ρ
ρv
n
dA
C
(kg/s)
m
m
m
out
in
•
•
•
=
=
Steady-flow system with one inlet and one exit
• Assumption: changes in kinetic and potential energy are
negligible
The rate of net heat transfer into or out of the control volume
:
E
Q
•
•
=
(J/s)
c
p
• Conduction
• Convection
• Radiation
The mechanisms of HEAT TRANSFER
Conduction
– energy transfer from
the more energetic particles of a
substance to the adjacent less
energetic ones →
→
→
→
a result of
interactions between the particles.
Convection
- energy transfer between
a solid surface and the adjacent liquid
or gas which is in motion →
→
→
→ it
involves
combined
effects
of
conduction and fluid motion.
Radiation
- energy emitted by matter
in the form of electromagnetic waves
(or photons) →
→
→
→ a result of the changes
in the electronic configurations of the
atoms or molecules.
CONDUCTION
In
solids
:
- vibrations of the molecules
in a lattice
- energy transport by free
electrons.
In
gases
and
liquids
-
collisions
of
the
molecules during their
random motion.
SURFACE ENERGY BALANCE
A surface contains no volume
or mass, thus no energy →
→
→
→ a
fictitious system with
E = const
during the process (steady-
state system)
Surface energy balance both
for steady and transient
conditions:
out
in
E
E
•
•
=
Energy interactions at
the outer wall surface of a house
Energy balance for the outer
surface of the wall:
3
2
1
Q
Q
Q
•
•
•
+
=
The
rating
problems deal with the determination of
the
heat transfer rate
for an existing system at a
specified temperature difference.
CONDUCTION
The
sizing
problems deal with the determination of
the size of a system in order to transfer heat at a
specified rate
for a
specified temperature difference
.
dt
dQ
Q
=
•
Heat transfer rate
(J/s = W)
The
parameters
that effect the
rate of heat
conduction
through a
windowless wall
:
- geometry (surface area and thickness) of the wall
- material of the wall
- temperature difference across the wall.
Steady-state conduction through a plane wall
The temperature difference
across the wall:
∆
∆
∆
∆T = T
2
- T
1
Fourier's law of conduction
where:
dT/dx
- temperature gradient
Λ
Λ
Λ
Λ
-
thermal conductivity;
unit:
W/(m · K) = W/(m·
0
C)
A
- area normal to the direction of heat transfer
dx
dT
A
cond
Q
Λ
−
=
•
(J/s) = (W)
The
thermal conductivity
Λ
Λ
Λ
Λ
of a material
is the rate of heat transfer through a unit thickness of
the material per unit area and per unit temperature
difference.
A
dx
dT
Q
|
|
•
=
Λ
Λ
Λ
Λ
Λ
is a measure of how fast heat will be conducted in
a material.
unit:
W/(m · K)
Λ
Λ
Λ
Λ
Λ
Λ
Λ
Λ
Experimental setup to
determine the thermal
conductivity of a
material
• Steady - flow
conditions
Λ
Λ
Λ
Λ
W/(m
0
C)
Λ
Λ
Λ
Λ
W/(m
o
C)
T
∝
Λ
For
gases:
For liquids
(except water)
Λ
Λ
Λ
Λ decreases
versus T
HEAT FLUX
- the rate of heat transfer per unit
surface area
&q
Adt
dQ
q
=
•
where
A
is the area of the
surface perpendicular to the
direction of heat flow
∫
=
A
dA
q
Q
&
&
Thus:
Unit: J/(m
2
s) = W/m
2
Copper
Λ = 401 W/(m·
o
C)
Silicon
Λ = 148 W/(m·
o
C)
The flux of heat flow through a solid is directly proportional to
its thermal conductivity
v
CONVECTION
- conduction with fluid motion
Heat transfer from a hot surface to air by convection
• In
forced convection
the fluid is forced to move by
external means such as a fan, pump, or the wind.
• The fluid motion in
natural convection
is due to
buoyancy effects only
Convection
Newton's law of cooling
where:
h
- convection heat transfer coefficient;
unit: W/(m
2
K)
A
S
- surface area through which convection heat transfer
takes place
T
S
- surface temperature
T
∞
∞
∞
∞
- temperature of the fluid sufficiently far from
the surface.
)
(
∞
−
=
T
T
hA
Q
s
s
conv
&
Coefficient h
is not a property of a fulid;
it depends on the variables influencing convection
(surface geometry, nature of fluid motion, bulk fluid
velocity)
RADIATION
)
(
4
4
surr
s
s
rad
T
T
A
Q
−
=
εσ
&
σ
=
×
−
5 67 10
8
.
W / m . K
2
4
Stefan-Boltzmann constant
Stefan-Boltzmann law for a
black - body
Emissivity
is the ratio of the radiation (energy flux) emitted by a
surface to the radiation emitted by a blackbody at the same
temperature.
where:
-
emissivity of the surface; 0 ≤
≤
≤
≤ εεεε ≤
≤
≤
≤ 1
A
S
-
surface area
-
surface temperature
-
average surrounding surface temperature
ε
T
surr
s
T
Black-body radiation represents the maximum
amount of radiation that can be emitted from a
surface at a specified temperature
Real bodies emit and absorb less radiation than a
blackbody at the same temperature
Absorptivity of a surface
α
α
α
α
;
0 ≤
≤
≤
≤ α
α
α
α ≤
≤
≤
≤ 1
- the fraction of the radiation energy incident on a
surface that is absorbed by the surface
The rate of radiation
absorption by the surface
The Kirchhoff's law of radiation:
The emissivity and the
absorptivity of a surface are equal at the same temperature and
wavelength.
A surface at T
s
is completely enclosed by a much larger (or black)
surface at T
surr
Net rate of radiation
heat transfer
No effect of surrounding
surface area and
emissivity
where
h
c
is the combined heat transfer
coefficient
)
(
∞
•
−
=
T
T
A
h
S
S
c
total
Q
Combined
convection
and
radiation
The total heat transfer rate to or from a surface:
Comfort conditions for living →
→
→
→ studies of heat
transfer, convection and radiation