Heat Transfer
1
Units of Heat
• Heat is energy in transit, and is measured in energy units.
• The SI unit is the joule (J), or Newton-metre (Nm).
• Historically, heat was measured in terms of the ability to
raise the temperature of water.
• The kilocalorie (kcal), or Calorie (Cal), or “big calorie”:
amount of heat needed to raise the temperature of 1
kilogramme of water by 1 C0 (from 14.50C to 15.50C)
• The calorie, or “little calorie”: amount of heat needed to
raise the temperature of 1 gramme of water by 1 C0 (from
14.50C to 15.50C)
• In industry, the British thermal unit (Btu) is still used:
amount of heat needed to raise the temperature of 1 lb of
water by 1 F0 (from 630F to 640F)
2
Mechanical Equivalent of Heat
Joule demonstrated that water
can be heated by doing
(mechanical) work, and showed
that for every 4186 J of work
done, the temperature of water
rose by 10C per kg.
3
Mechanical Equivalent of Heat
• Conversion between different units of
heat:
1 cal = 10-3 kcal = 3.969 x 10-3 Btu = 4.186 J
1 Cal = 1 kcal=4186 J
4
Heat content
• Change in enthalpy or H is simply called
the heat content or Q
5
DEFINITIONS
• Sensible Heat
– When heat added results in the change in
temperature
• Latent Heat
– When the heat added results in a physical change of
the substance
• Saturation Temperature/Pressure
– Psat/Tsat
– The point at which liquid and vapor may exist in
equilibrium contact with each other
6
DEFINITIONS (cont)
• Saturated Liquid/Vapor
– A liquid/vapor at a specified pressure which is at
Tsat for the pressure
• Subcooled Liquid
– A liquid at that specified pressure which is below
the Tsat
• Superheated Vapor
– A vapor that has been raised above Tsat for a
given pressure
7
DEFINITIONS (cont)
• Latent Heat of Vaporization
– Amount of heat necessary to change a mass of liquid
to vapor without changing the temperature
• Latent Heat of Fusion
– Amount of heat that must be added/removed to a unit
mass to melt/solidify it
8
Change in enthalpy determination
1. Sensible heating at constant pressure
Where
H = mcp(T2-T1)
cp = heat capacity (J/kg.K)
m = mass
2. Heating at constant pressure involving phase
change
•
Heating/cooling processes may occur involving
latent heat, where the temperature remains
constant while the latent heat is added or removed.
9
Latent Heat
10
11
Phase Diagrams
• Visual representation of
phase changes
• Triple point: point at which
all three phases coexist
• Curves branching out from
this point separate phase
regions:
– Fusion curve: solid-liquid
boundary
– Vaporization curve: liquid-gas
boundary
– Sublimation curve: solid-gas
boundary
12
Phase Diagram: Carbon Dioxide
13
Phase Diagram: Water
14
Thermal properties
15
Specific Heat Capacity
• Sensible heat is associated with a temperature change
(can be “sensed”)
• Different
substances
have
different
molecular
configurations and bonding  temperature change not
generally the same for equal amounts of heat
• Specific heat capacity, cp: quantity of heat that is gained
or lost by a unit weight of product to accomplish a
desired change in temperature, without a change in state
(amount of energy needed to raise the temperature of 1
kg of a substance by 1K)
• specific heat in SI unit : kJ/kgC or kJ/kg.K
16
Predicted specific heat
• For meat products with 26-100% moisture content and fruit
juice with moisture content greater than 50% (Dickerson,
1969) :
Cp = 1.675 + 0.025 W
where
W = water content (%)
• For products with known composition:
Cp = 1.424 mc + 1.549 mp + 1.675 mf + 0.873 ma + 4.187 mm
where
m
= mass fraction
subscripts c
= carbohydrate
subscripts p
= protein
subscripts f
= fat
subscripts a
= ash
subscripts m
= moisture
17
Thermal conductivity
• It is the rate of heat that will be conducted
through a unit thickness of the material if a
unit temperature gradient exists across
that thickness
• thermal conductivity (k) in SI units :
J/s.m.C or W/m.C, in English unit :
Btu/h.ft.F
• Strongly temperature-dependent.
18
19
Thermal conductivity
Type of material
Construction materials
Aluminium
Copper
Stainless steel
Other metals
Brick
Concrete
Thermal conductivity
(W m-1 K-1)
220
388
21
45-400
0.69
0.87
Temperature of
measurement (OC)
0
0
20
0
20
20
20
Type of material
Olive oila
Whole milka
Freeze-dried foods
Frozen beefb
Pork (lean) b
Frozen cod
Apple juice
Orange
Green beans
Cauliflower
Egg
Ice
Watera
Thermal conductivity
(W m-1 K-1)
0.17
0.56
0.01-0.04
1.30
0.48
1.66
0.56
0.41
0.80
0.80
0.96
2.25
0.57
Temperature of
measurement (OC)
20
20
0
-10
3.8
-10
20
0.15
-12.1
-6.6
-8
0
21
0
Type of material
Packaging materials
Cardboard
Glass, soda
Polyethylene
Poly (vinyl chloride)
Insulating materials
Polystyrene foam
Polyurethane foam
Other types
Thermal conductivity
(W m-1 K-1)
Temperature of
measurement (OC)
0.07
0.52
0.55
0.29
20
20
20
20
0.036
0.026
0.026-0.052
0
0
30
22
Predicted thermal conductivity
Source : Sweat (1974, 1975)
• For fruit and vegetables with water content > 60%
k
= 0.148 + 0.00493 w
where
k
= thermal conductivity (W/m. OC)
w
= water content (%)
• For meat, temperature 0-60C and water content 60-80
% (wet basis)
k
= 0.080 + 0.0052 w
• thermal conductivity in SI unit : W/m.C or W/m.K
23
Thermal diffusivity, 


k
C
p
• k measures the rate at which heat passes through a
material. The larger it is, the faster the material heats
up.
• Cp measures the heat needed to raise a unit mass
by 1C
• Cp measures the heat needed to raise a unit volume
by 1C. The larger it is, the slower the materials
heats up.
•  is the ratio of k to Cp and therefore indicates the
relative rate at which a material heats up
24
Methods of Heat Transfer
25
Fundamentals
• Heat transfer is thermal energy in transit due
to a temperature difference.
• Whenever there exits a temperature difference
in a medium or between media, heat transfer
must occur.
• Heat transfers are classified with respect to the
physical mechanism which underlies them:
There are 3 heat transfer processes.
26
Mode of heat transfer
• There are three ways that heat may be
transferred between substances at
different temperatures - conduction,
convection, and radiation. We consider
each of these in turn.
»Conduction
»Convection
»Radiation
27
Conduction, Convection
& Thermal Radiation
• Conduction refers to the
transport of energy in a
medium due to a
temperature gradient.
28
Conduction, Convection
& Thermal Radiation
• the convection refers to
heat
transfer
that
occurs
between
a
surface and a fluid (at
rest or in motion) when
they are at different
temperatures.
29
Conduction, Convection
& Thermal Radiation
• Thermal radiation refers
to the heat transfer that
occurs between two
surfaces at different
temperatures. It results
from the energy emitted
by any surface in the
form of electromagnetic
waves.
30
Heat Conduction
• The flow of thermal energy through a substance from a
higher- to a lower-temperature region. Heat conduction
occurs by atomic or molecular interactions.
• The flow of heat by conduction occurs via collisions
between atoms and molecules in the substance and the
subsequent transfer of kinetic energy. Let us consider
two substances at different temperatures separated by a
barrier which is subsequently removed, as in the
following figure.
31
Heat transfer by conduction
When the barrier is removed,
the fast (``hot'') atoms collide
with the slow (``cold'') ones.
In such collisions the faster
atoms lose some speed and
the slower ones gain speed;
thus, the fast ones transfer
some of their kinetic energy
to the slow ones. This
transfer of kinetic energy from
the hot to the cold side is
called a flow of heat through
conduction.
32
Physical Mechanism in
Conduction
The conduction heat transfer results from
diffusion of energy due to random
molecular activity
33
• It is important to note that in conductive
heat transfer, there is no physical
movement of the material.
• Conduction is common mode of heat
transfer in heating/cooling of opaque solid
media.
34
Steady state conduction
• Steady-state conduction is said to exist when the
temperature at all locations in a substance is
constant with time, as in the case of heat flow
through a uniform wall. Examples of essentially
pure transient or periodic heat conduction and
simple or complex combinations of the two are
encountered in the heat-treating of metals, air
conditioning, food processing, and the pouring
and curing of large concrete structures.
35
Different materials transfer heat by conduction at different
rates - this is measured by the material's thermal
conductivity. Suppose we place a material in between
two reservoirs at different temperatures, as in the following
figure.
Measurement of thermal conductivity
36
• Heat conduction is the transmission of
heat across matter.
• Heat transfer is always directed from a
higher to a lower temperature. Denser
substances are usually better conductors;
metals are excellent conductors.
37
Fourier’s Law – Thermal
Conductivity
• For a plane wall having a temperature
distribution T(x), and a cross section area
A (perpendicular to the x-direction), the
heat transfer rate by conduction
through the wall in the x-direction is given
by:
dT ( x )
q x  kA
dx
k is the thermal conductivity (W.m-1.oK-1). It is a transport
property of the wall material.
38
Sign convention
for conductive heat flow
39

Thermal Conduction
T ( x)
q x  kA
x
40
The law of heat conduction, also known as Fourier's
law, states that the time rate of heat flow Q through a
slab (or a portion of a perfectly insulated wire, as
shown in the figure) is proportional to the gradient of
temperature difference:
T ( x)
q x  kA
x
q is the time rate of heat flow through a slab,
k is a conductivity constant (dependent on the nature of
the material and its temperature),
A is the transversal surface area,
ΔT is the temperature difference through which the heat
is being transferred,
Δx is the thickness of the body of matter through which
the heat is passing.
41
• This law forms the basis for the derivation of
the heat equation. R-value is the unit for heat
resistance, the reciprocal of the conductance.
Ohm's law (I = V/R) is the electrical analogue
of Fourier's law.
rate of
flow
of
electron
driving force
a transfer process 
resistance
α
voltage
resistance of conductor

driving force
resistance
42
• For a given temperature difference between the reservoirs,
materials with a large thermal conductivity will transfer large
amounts of heat over time - such materials, like copper, are
good thermal conductors.
• Conversely, materials with low thermal conductivities will
transfer small amounts of heat over time - these materials,
like concrete, are poor thermal conductors. It is also why
fiberglass insulation, and also feathers and fur, have air
pockets - dead air is a poor thermal conductor, and so the
air pockets aid in cutting back on the heat loss through the
material.
• Home insulation is thus a poor thermal conductor, which
keeps as much heat in as possible. Instead of being rated
in terms of thermal conductivity, insulation is therefore
usually rated in terms of its thermal resistance, which is
defined as
43
• Materials which have a high thermal conductivity
have, by definition, a low thermal resistance they are poor heat insulators. On the other hand,
materials with a low thermal conductivity have a
high thermal resistance - they are good heat
insulators. Good insulating materials therefore
should have a high thermal resistance. In fact,
the ``R'' value quoted for insulation is the
thermal resistance (in British units).
44
Conductance
•
Fourier's law can also be stated as:
where U is the conductance. The reciprocal of
conductance is resistance, equal to:
45
Thermal Resistance: Analogy between the
conduction of heat and electric charge
• Just as an electrical
charge is associated
with the conduction of
electricity,
• a thermal resistance
may be associated
with the conduction
of heat:
v1  v2
R
i
T1  T2
R
q
•
oK.W-1
46
Conduction Heat Transfer Rate
versus Thermal Resistance
• By definition:
T1  T2
R
q
• Therefore:

1
q  T1  T2 
R
47
Relationship between Rconv and k
• By definition, the heat
conduction is:
dT
T1  T2
q x  kA
 q  kA
dx
L
T1  T2
R
q
• Therefore:
1 kA

R L
48
Example
Steel: k = 14 J/s-m-C
How much energy is
conducted in 40 seconds?
-----------------------------------------------q = kA (T2 - T1)/L
q = 14 (2)(475)/10
= 1330 J/s
Q= qt = 1330 (40)
= 5.32 x 104 J
49