HEAT TRANSFERDiah Susanti, PhD

Heat transfer (or heat) is energy in transit due to a temperature difference

Whenever there exists a temperature difference in a medium or between media, heat transfer must occur

There are 3 modes of heat transfers:1. Conduction: heat transfer that will occur across the

medium when a temperature gradient exists in a stationary medium , which may be a solid or a fluid molecular heat transfer

2. Convection: heat transfer that will occur between a surface and a moving fluid when they are at different temperatures.

3. Thermal radiation: all surfaces of finite temperature emit energy in the form of electromagnetic waves. Hence in the absence of an intervening medium, there is net heat transfer by radiation between two surfaces at different temperatures.

CONDUCTIONthrough a solid or stationary fluid

T1 T2

T1 > T2

q”

Moving fluid, T

q”

Ts

CONVECTIONfrom a surface to a moving fluid

Ts > T

NET RADIATIONHeat exchange between two surfaces

surface, T1

surface, T2

q1”

q2”

The three modes of heat transfer

video

Which one is conduction, convection or radiation??

convection

conduction

radiation

1. Conduction is…a. Heat transfer due to a different temperature

across a motionless medium either a solid or a fluid from molecule to molecule.

b. Heat transfer due to a different temperature between a medium and a moving fluid.

c. Heat transfer through electromagnetic waves.

How smart are you??

2. Heat transfer in a vacuum chamber occurs according to …. mode:a. Conductionb. Convectionc. Radiation

3. Whenever you want to eat or drink something hot, you will breathe air from your mouth to cool down the food. This mechanism of heat transfer is classified into..a. Conductionb. Convectionc. Radiation

CONDUCTION

Conduction deals with heat transfer in atomic or molecular level.

Conduction may be viewed as the transfer of energy from the more energetic to the less energetic particles of a substance due to interactions between the particles.

qx”

T1

T2

T1 > T2

x

xo

The energy of a gas related to random translational motion, internal rotation, and vibrational motion of the molecules.

Energy transfer by conduction occur in the direction of decreasing temperature (positive x direction)

The net transfer of energy by random molecular motion is defined as a diffusion of energy.

x

T

qx”

Conduction and particle motion

In kinetic theory,

particles at hot end vibrate a lot

particles at cold end vibrate less

particles in a solid are closely packed,

they vibrate to & from but can't change positions.

Conduction and particle motion

The fast vibrating particles bump into the slower neighbouring particles &

particles at hot end vibrate a lot

particles at cold end vibrate less

make them vibrate more rapidly

energy is transferred(from one particle to

the next & from hot to cold end of rod)

Why are frying-pans and woks usually made of metals but their handles are made of plastic?

Warm-up

IntroductionHow is energy transferred from the cooker to the pan and then to the food?

Energy transfer by conduction

Energy is transferred by conductionfrom the cooker,

through the pan,

to the food.

Studying the heat transferred along a metal rod

What happens to these drawing pins?

Conduction (video)

copper rod

insulating board

wax

drawing pins

What kind of rod conducts heat?Feel the ends of the rods to find out which rod feels hot first.

Conduction (video)

very hot water

glass

wood

iron

copper

Heat the ends of the metal rods and note which drawing pin at the other end falls first.

What kind of rod conducts heat fastest?

Conduction (video)

aluminiumcopper

iron

drawing pins

Does water conduct heat?

Gently heat the top part of the water & find out if the ice melts.

Conduction (video)

water wire gauze

ice

boiling tube

Does air conduct heat?

Leave the cardboard for a while & then take the temperature readings.

Conduction (video)

thermometer

cardboard tube

heater

Leave the cardboard for a while & then take the temperature readings.

Conduction (video)

Does air conduct heat?

Materials conduct heat at different rates.Metals (e.g. copper and iron) are good

conductors of heat.Non-metals (e.g. wood, water and air) are poor conductors (or good insulators).

Energy transfer by conduction

In conduction, heat (energy) is transferred from the hot part to the cold part.

Properties of some conductors and insulators specific for certain material

specific heat capacity (cp), J(gK)-1

ther

mal

con

duct

ivit

y (k

), W

(mK

)-1

Energy transfer by conduction

In conduction, heat is transferred from the hot part to the cold part along an object. Conduction is efficient in conductors but not in insulators.

air water

video

What happen when these two balloons exposed to fire??

Does the orientation of the rod matter?

Energy transfer by conduction

Phoebe heats two metal rods as shown. Which will be heated up first? Why?

Does the orientation of the rod matter?

Both of them are heated up at the same rate.

Energy transferred from the hot end to the cold end by conduction is not affected by the orientation of the rod.

Conduction and particle motion (simulation)

video

How to keep warm?

Examples of conduction

A cotton jacket keeps warm by trapping air next to the body.

How to keep warm?

Examples of conduction

Polar bears keep warm by trapping air in the fur.

How to keep warm?

Examples of conduction (video)

Birds keep warm by trapping air in their feathers.

Hot or cold?

Examples of conduction

Under the same condition, a metal block feels colder than a wooden block even the 2 objects are at the same temperature. metal easily conducts energy away

from your hand you feel cold

A From high-temperature area to low-temperature area.

B From low-temperature area to high-temperature area.

C The direction of heat transferred is different in metals and non-metals.

In conduction, heat is transferred...

In conduction, heat is transferred in which of the following direction?

A The temperature of the tile floor is lower.

B Tile is a better conductor of heat than wood.

C Wood is a better conductor of heat than tile.

D Tile is smoother than wood.

Which of the following can explain why a tile floor feels colder than a wooden floor?

Frying-pans are made of...

conductorsFrying-pans are made of metals because they are good _________ of heat, while handles of frying-pans are made of plastic because they are good _________ of heat.

insulators

One-dimensional heat transfer by conduction (diffusion of energy)

T1

T2

L

T

x

qx”

Tx

Fourier’s Law of heat conduction: qx” = - k (dT/dx) (1.1) qx” = - k (T/x) (1.2)

where: qx” = heat flux (Wm-2 or Js-1m-2)k = thermal conductivity (WK-1m-1)T = temperature (K)x = distance (m)

Heat rate = heat flux•area qx = qx”• A

Example 1.1The wall of an industrial furnace is constructed from 0.15 m thick fireclay brick having a thermal conductivity of 1.7 Wm-1K-1. Measurements made during steady state operation reveal temperatures of 1400 and 1150 K at the inner and outer surfaces respectively. What is the rate of heat loss through the wall that is 0.5 m by 3 m on a side?

T1 T2

L = 0.15 mW = 3 m

H = 0.5 mqx”

Assumptions:1. Steady state conditions2. One-dimensional conduction through the wall3. Constant thermal conductivity

How much did you get??

The right answer is…

qx” = 2833 Wm-2

qx = 4250 W

Another form of Fourier’s Law equation:

Fourier’s Law of heat conduction:qx“ = qx/A = - k (dT/dx)

qx = - kA (dT/dx)where: qx” = heat flux (Wm-2 or Js-1m-2)qx = heat rate (W or Js-1)k = thermal conductivity (WK-1m-1)T = temperature (K)x = distance (m)A = area (m2)

1. A heat rate of 3 kW is conducted through a section of an insulating material of cross-sectional area 10 m2 and thickness 2.5 cm. If the inner (hot) surface temperature is 415 oC and the thermal conductivity of the material is 0.2 W/mK, what is the outer surface temperature?

2. The heat flux through a wood slab 50 mm thick, whose inner and outer surface temperatures are 40 and 20 oC respectively, has been determined to be 40 W/m2. what is the thermal conductivity of the wood?

3. What is the thickness required a masonry wall having thermal conductivity 0.75 W/mK if the heat rate is to be 80% of the heat rate through a composite structural wall having thermal conductivity of 0.25 W/mK and a thickness of 100 mm? Both walls are subjected to the same surface temperature difference.

CONVECTION

• Convection heat transfer mode is comprised of two mechanism: the random molecular motion (diffusion) and bulk or macroscopic motion of the fluid.

• Advection: transport due to bulk fluid motion.• Convection: diffusion + advection.

The Boundary Layer Development in Convection Heat Transfer

Heated surface

y u

Velocity distribution, u(y)

y

Temperature distribution, T(y)

q”

T

u0 Ts

uy Ty

fluid

Hydrodynamic (velocity) boundary layer

Thermal boundary layer

if Ts >T convection happens

• The convection heat transfer mode is sustained both by random molecular motion and by the bulk motion of the fluid within the boundary layer.

• The contribution due to random molecular motion (diffusion) dominates near the surface where the fluid velocity is low. In fact, at the interface between the surface and the fluid (y=0), the fluid velocity is zero and heat is transferred by this mechanism only.

• The contribution due to bulk fluid motion originates from the fact that the boundary layer grows as the flow progress in the x direction.

• In effect, the heat that is conducted into this layer is swept downstream and is eventually transferred to the fluid outside the boundary layer.

According to the nature of the flow, convection is classified into two modes:1. Forced convection: when the flow is caused by the external

means, such as a fan, a pump, or atmospheric wind.2. Free or natural convection: when the flow is induced by

buoyancy forces, which arise from the density differences caused by temperature variations in the fluid.

The mixed or combined forced and natural convection may exist in reality.

Typical energy being transferred in convection is sensible heat or internal thermal, energy of the fluid. In addition, there may latent heat exchange due to phase transformation.

Regardless the nature of the convection process, the rate equation is (Newton’s law of cooling):

q” = h(Ts – T) (1.3)q” is the convective heat flux (Wm-2)h is the convection heat transfer coefficient (Wm-2K-1)

Heat flux is positive when heat is transferred from the surface, while negative when heat is transferred to the surface.

Typical values of the convection heat transfer coefficient

Process h (Wm-2K-1)

Free convection: Gases LiquidsForced convection: Gases LiquidsConvection with phase change: Boiling or condensation

2 – 2550 – 1000

25 – 25050 – 20,000

2500 – 100,000

1.11. An electric heater is embedded in a long cylinder of diameter 30 mm. When water with a temperature of 25 oC and velocity of 1 m/s flows crosswise over the cylinder, the power per unit length required to maintain the surface at a uniform temperature of 90 oC is 28 kW/m. When air, also at 25 oC, but with velocity of 10 m/s is flowing, the power per unit length required to maintain the same temperature is 400 W/m. Calculate and compare the convection coefficients for the flows of water and air.1.13. A square isothermal chip is of width w = 5 mm on a side and is mounted in a substrate such that its side and back surfaces are well insulated, while the front surface is exposed to the flow of a coolant at T = 15 oC. From a reliability considerations, the chip temperature must not exceed T = 85 oC. If the coolant is air and the corresponding convection coefficient is h = 200 W/m2K, what is the maximum allowable chip power? If the coolant is a dielectric liquid for which h = 3000 W/m2K, what is the maximum allowable chip power?

RADIATION

• Radiation may occur from solid, liquid, or gas surfaces.• Regardless of the form of the matter, the emission may be

attributed to changes in the electron configurations of the constituent atoms or molecules.

• The energy of the radiation field is transported by electromagnetic waves (or alternatively photons)

Surface of emissivity , absorptivity , and temperature Ts

Gas T, hG E

q”conv

Surface of emissivity , absorptivity , and temperature Ts

Gas T, h

q”convq”rad

Surroundings at Tsur

(a) (b)

Radiation exchange (a) at a surface (b) between a surface and large surroundings

• Radiation that is emitted by the surface (Fig. a) originates from the thermal energy of matter bounded by the surface, and the rate at which energy is released per unit area (Wm-2) is termed the surface emissive power E.

• There is an upper limit to the emissive power, which is prescribed by the Stefan-Boltzmann law

Eb = Ts4 (1.4)

s is Stefan-Boltzmann constant = 5.67x10-8 Wm-2K-4

Such a surface is called an ideal radiator or blackbody.• The heat flux emitted by a real surface is less than that of a

blackbody at the same temperature and is given byE = Ts

4 (1.5)Where is a radiative property of the surface termed the emissivity. With values in the range 0≤≤1, this property provides a measure of how efficiently a surface emits energy relative to a blackbody.

• Radiation may also be incident on a surface from its surroundings. It may originate from a special source such as the sun. Irrespective of the source(s), the rate at which all such radiation is incident on a unit area of the surface as the irradiation G.

• A portion or all of the irradiation may be absorbed by the surface, thereby increasing the thermal energy of the material. The rate of irradiation absorptivity:

Gabs = G (1.6)Where 0≤≤1. If <1 and the surface is opaque, portions of the irradiation are reflected. If the surface is semitransparent, portions of the irradiation may also be transmitted. The value depends on the nature of irradiation and the surface itself.• Absorbed and emitted radiation increase and reduce the thermal

energy of matter, respectively, while reflected and transmitted radiation have no effect on this energy.

• A special case that occurs frequently involves radiation exchange between a small surface Ts and a much larger, isothermal surface that completely surrounds the smaller one (Fig. b). The surroundings could, for example, be the walls of a room or a furnace whose temperature Tsur differs from that of an enclosed surface (TsurTs). For such condition, the irradiation may be approximated by emission from a blackbody at Tsur in which case G = Tsur

4

• If the surface is assumed to be one for which = (a gray surface), the net rate of radiation heat transfer from the surface, expressed per unit area of the surface is (thermal energy difference between radiation emission and adsorption):

q”rad = q/A = Eb(Ts) - G = (Ts4 – Tsur

4) (1.7)

Another expression for net radiation heat exchange: qrad = hrA(Ts – Tsur), (1.8)

Where the radiation heat transfer coefficient, hr is from (1.7)hr = (Ts + Tsur)(Ts

2 +Tsur2) (1.9)

The total rate of heat transfer from the surface is then q = qconv + qrad = hA(Ts-T) + A (Ts

4 –Tsur4) (1.10)

Example 1.2. An uninsulated steam pipe passes through a room in which air and walls are at 25 oC. The outside diameter of the pipe is 70 mm and its surface temperature and emissivity are 200 oC and 0.8, respectively. What are the surface emissive power and irradiation? If the coefficient associated with free convection heat transfer from the surface to the air is 15 Wm-2K-1,what is the rate of heat loss from the surface per unit length of pipe?

airT = 25 oC h = 15 Wm-2K-1

L E

G

Ts = 200 oC = 0.8

Tsur = 25 oCD = 70 mm

q’

The Surface Energy BalanceEx. 1.5. The hot combustion gases of a furnace are separated from the ambient air and its surroundings, which are 25 oC, by a brick wall 0.15 m thick. The brick has thermal conductivity of 1.2 W/m K and a surface emissivity of 0.8. Under steady state conditions an outer surface temperature of 100 oC is measured. Free convection heat transfer to the air adjoining the surface is characterized by convection coefficient of h = 20 W/m2K. What is the brick inner surface temperature?