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