Heat transfer methods

TEMPERATURE & HEAT

Lecture 12

When there is a temperature difference

between two objects, heat transfer can occur.

Heat transfer methods

Three methods of heat transfer :

• Conduction

• Convection

• Radiation

In general all three processes occur

simultaneously.

One method normally dominates

Direct physical contact

results in collisions between molecules

Hot Cold Conduction

Same ideas applies to heat conduction within a

single object containing regions at different

temperatures.

Conduction is the transfer of heat by direct

physical contact.

Conduction

Molecules in object at higher temperature have

higher average kinetic energy and vice versa;

Result

energy transfer

hot cold

•Temperature difference DT (T1-T2)

•Area of contact A

•Thickness of the object d

•coefficient of thermal conductivity k

of the substance

Rate of heat conduction

The rate of heat transfer (Q/t) by

conduction depends on:

Consider an object of area A, thickness d,

opposite faces at temperatures T1 and T2

T1 T2

Q

A

d

Large k value: good thermal conductor

Small k value: poor thermal conductor

→ insulator

(Q/t) =rate of heat flow (Watts, W)

k = coefficient of thermal conductivity (Wm-1K-1)

A = area of object m2

DT = temperature difference (K or oC)

d= thickness of object (m)

T1-T2 = DT

Q kA T

t d

D

Rate of heat conduction

T1 T2

Q

A

d

Steady state:

constant heat flow

Equilibrium condition

Rate of heat conduction

Thermal conduction occurs at different

rates in different materials

Wooden stick burning at one end remains

relatively cold at the other end.

Metal spoon transmits heat rapidly from

one end to the other.

In metals there are electrons that can move

freely→carry thermal energy. Metals are good

thermal conductors.

Thermal conductivity of an object determines

how hot or cold it feels to the touch.

Example:

Tiles and carpet at

the same temperature

Material k (Wm-1K-1)

Copper 400

Glass 0.8

Brick 0.6

Floor tile 0.7

Wood 0.08

Muscle 0.042

Air 0.02

Carpet 0.04

Fat 0.021

Thermal Conductivities

Thermal Conductivities

Thermal conductivity of Dental Materials

Enamel 0.93 Wm-1K-1

Dentine 0.58 Wm-1K-1

Zinc phosphate cement 1.17 Wm-1K-1

Amalgam ≈ 55 Wm-1K-1

Composite 2 Wm-1K-1

Gold 290 Wm-1K-1

Low Thermal Conductivity layer

(e.g. zinc phosphate cement) needed underneath

amalgam filling to protect pulp from a temperature

rise.

Enamel and dentine are effective

thermal insulators

•reduces thermal shock to pulp (hot or cold foods)

Amalgam : High Thermal Conductivity.

If layer of dentine between bottom of cavity floor

and pulp is thin » »» thermal shock

Transfer of thermal energy depends on

Thermal conductivity

Thermal diffusivity

Thermal Diffusivity

Time

Tem

pera

ture

Thermal Diffusivity

kh

c

k (thermal conductivity)

(density)

c (specific heat) units m2s-1

Thermal diffusivity (h):

measures how rapidly a material can change

its temperature to reach a steady state

Measures transient thermal response of material

More important thermal characteristic in dentistry

than thermal conductivity

Since temperature changes rapidly in oral cavity;

thermal stimuli are transient

Thermal Diffusivity (10-6 m2s-1)

Enamel 0.41

Dentine 0.24

Zinc phosphate

cement

0.88

Amalgam 9.6

Gold 116

Thermal Diffusivity

Thermal diffusivity value

usually more appropriate in deciding dental

materials suitability

Examples

Ability of restorative base material

to protect pulp from thermal damage

Denture base material: should have high

thermal diffusivity so that wearers are

“immediately” aware of hot/cold food

Diffusivity value: recognises heat is absorbed in

raising temp of material, thus reducing the heat

available to pass through material kh

c

How much thermal energy is lost in a period

of 24hours by conduction through a window

of area 1.0m² and thickness 0.4cm if the

temperatures at the outer and inner surfaces

are 5.0°C and 15°C respectively?

kglass = 0.84 W.m-1.°C-1

Q/t = [(0.84*1.0*10)/0.004]W = 2100W

In 24hours:

Q=2100 x 24 x 3600 J = 181.44MJ

Rate of heat conduction

Example.

Q kA T

t d

D

(2100W = 2100 Joules per second)

In general, hot fluids

have a lower density

than cold fluids

(thermal expansion),

Convection is the transfer of heat by mass

movement of fluid (liquid or gas).

Convection

Natural convection.

heated fluid naturally

rises and the cold fluid

moves downward,

complex patterns (such

as convections rolls in

a pot of water or hot air

rising above a fire).

Water in pot

Air in room

Convection occurs when fluid is unevenly heated.

Convection can also be forced

Convection

Examples:

•Blood circulation.

•Engine cooled by pumped air or water.

Gases and liquids are not good thermal

conductors

however they can transfer heat rapidly by

convection.

Natural convection in atmosphere

plays major role in determining the

daily weather conditions

Natural convection in oceans

Important global heat transfer mechanism

Convection

Body temp ≈ 37ºC

Blood circulation:

Blood flow regulated according to need.

Overheated person, blood vessels to

surface dilate and so carry more blood to

the surface for cooling.

Layers of fat beneath the skin

help to maintain body temperature

Fat

Poor thermal conductor:

few blood vessels to carry blood to surface

where energy losses by convection can occur

Radiation

The sun is our major source of heat.

It warms the earth: How?

Heat transfer by conduction and convection

not possible.

Very little material (relatively few molecules)

between us and the sun

Heat transfer from sun is by radiation

Energy in the form of electromagnetic waves

All objects emit electromagnetic radiation.

At ordinary temperatures this radiation

is mainly at infrared wavelengths.

Travel and carry energy through empty space

10-13m 10-10 10-7 10-6 10-5 10-2 10m

Electromagnetic Spectrum

Radiation

Infrared radiation is strongly absorbed by

water molecules including those in our body cells.

Infrared radiation is converted to heat

as it is absorbed by our bodies.

energy

Wavelength

Radiation is a property of a

single object: it does not

depend on a temperature

difference.

Radiation

Hot Cold

Given 2 objects, the higher temperature one

radiates more than the lower temperature

one so there is a net transfer from the former to

the latter.

Radiation

Fundamentally different from conduction and

convection which involve molecular collisions;

------ non-contact!

Does not require a material substance for its

transmission. Can transmit in vacuum.

The rate of heat radiation (Q/t) from a single

object is proportional to:

•Temperature (T) K

•Surface area of the object (A)

•emissivity of the substance at the

surface (e)

= Stefan-Boltzmann constant

= 5.67 x 10-8 W m-2 K-4

e =emissivity (0 ≤ e ≤ 1) (depends on surface)

Q/t = rate of heat radiation (W)

Q/t increases very strongly with temperature!!

Rate of heat radiation

Any object with a temperature greater than

absolute zero (0K) emits radiant heat.

Hence a fire will radiate heat into a room but

the room will also transfer heat to the fire by

radiation

4QeAT

t

Rate of heat radiation

emissivity (0 ≤ e ≤ 1) (depends on surface)

Black, rough surface e→1

Bright Shiny surface e→0

Bright shiny surfaces reflect most of the

radiation falling of them and so are poor

absorbers and poor emitters

Black surfaces

are good emitters and absorbers.

The net rate of radiation by a object at T1 in

surroundings T2 is:

Net rate of heat transfer depends only on the

properties of the object and the temperature

of the surroundings

If temperature of the object and surrounding

are equal there is no net heat transfer.

4 4

1 2( )Q

eA T Tt

What is the rate of heat loss by radiation from

a black roof of area 250m², if its temperature

is 25°C and that of the surroundings is 0°C?

Assume the emissivity of the roof is 0.95.

Q/t =

5.67x10-8 Wm-2 K-4* 0.95 * 250m2 * [(298 K) 4-(273 K)4]

Q/t =1346.6x10-8*23.3x108 W = 31,376 W

T1=(273+25)K=298K

T2=(273+0)K=273K

4 4

1 2( )Q

eA T Tt

Rate of heat radiation:

Example.

Compare the rate of heat loss by conduction

and by radiation through a window of area

2m² and thickness 5mm, if the inside

temperature is 20°C and the outside 5°C.

The emissivity of the room is 0.5;

kglass = 0.84 W.m-1.°C-1 .

Example

Rate of heat loss by conduction:

Q/t = 0.84*2.0*15/0.005 W = 5,040W

Rate of heat loss by radiation:

Q/t = 5.67.10-8 * 0.5 * 2 * (2934-2784)

Q/t = 79W

T1=273+20K=293K

T2=273+5K=278K

Heat lost by conduction is much greater

than that lost by radiation.

Rate of heat radiation:

4 4

1 2( )Q

eA T Tt

Q kA T

t d

D

= 5.67 x 10-8 W m-2 K-4

Regulation of body temperature

Body temperature

Maintain at nearly constant value ≈ 37oC

Basic metabolic action

Most of consumed energy → heat inside body

Efficiency of muscles (external work) ≈ 20%

Physical activity

80% of consumed energy → heat inside body

Heat must be removed to maintain temp ≈ 37oC

Example: cycling for one hour

energy consumption 360kcal 80% =288kcal

Q = c.m. TD QT =

c.mD

288 4186T = 4.6

3500 75

oC

D

Q=288x4186 Joules

Mass=75kg

Specific heat c ≈3500 J.kg-1.°C-1

Temperature rise

Regulation of Body Temperature

Removal of heat from body (conduction)

Heat flow from inside body to skin surface

Temperature difference required

Skin temperature lower

Warm environment 35 oC

Cold environment 28 oC

Body tissue:

poor conductor without blood flow

Thermal Conductivity

k ≈ 0.2 Wm-1 oC-1

Q kA T

t d

D

1 1 21.2( ) 1.5 2

200.03

oQ Wm C m CJs

t m

17 /Q

kcal hrt

without blood flow Insufficient conduction rate

to remove excess heat from body

Regulation of Body Temperature

Heat transported

inside body to skin

by blood movement (circulatory system)

capillaries leading to the skin dilate

Skin to outer skin surface by conduction

Thermal Conductivity ( k) of air ≈ 0.02 Wm-1C-1

(confined by clothing) low

Heat must be quickly removed from skin

Heat removed from skin by

Convection (air colder than skin)≈(10kcal/hour)

Radiation ( environment colder than skin)

evaporation

4 4

1 2( )Q

eA T Tt

The net rate of radiation from skin at T1 = 32oC

to surroundings at T2 = 25oC is:

8 2 4 2 4 45.67 10 1 1.5 305 298Q

Wm K mt

165 56 /Q

Js kcal hrt

Perspiration

Principally cooling off when surrounding

temperature is greater than skin temperature.

Perspiration leads to cooling of the body by

evaporation of water:

Preferential evaporation of high energy

molecules reduces the average temperature of

the remaining molecules.

So 2.26x106 J (540 kcal ) of heat is lost for every

Kg (litre) of sweat that evaporates from skin

Latent heat of vaporisation of water

(Lv)=2.26x106 J.kg-1

(Lv)=540 kcal.kg-1

Large value of latent heat of vaporisation

QT =

c.mD

6

o -1

2.26 10 JT = 9.2

3500 J(kg. C) 70 kg

oC

D

Evaporation of 1kg(1litre) water from70kg person

(body mainly composed of water) lowers body

temperature by

Example.

The temperature of the sun is approximately

6x103K at its surface. Assuming it is spherical

with a radius of 6.95x108 m and an emissivity

of 0.92, calculate the total power radiated from

its surface. = 5.67 x 10-8 W m-2 K-4

4QeAT

t

Stefan’s law

Power is the rate at which energy is used

P= Q/t

Surface area A of sphere (sun) = 4pr2

A = 4p*(6.95x108 m)2 ≈ 6 x1018 m2

Total power radiated from sun

= 5.67x10-8 Wm-2K-4 *(0.92)* 6 x1018m2 *6x103K)4

=4.06x1026 W

Perspiration

Efficient cooling by evaporation may employ a

liquid other than water, e.g. alcohol rub in

hospitals.

When relative humidity is high, this process

is inefficient and body overheats; water

gathers on skin surface because it is not

removed by evaporation.

Relative humidity is concerned with the saturation

of air with water vapour and hence does not

affect the evaporation of alcohol

Evaporation rate also depends on

Environmental temperature

Wind speed

On hot day fan circulating air at ambient

temperature feels cool because air from it is drier

compared to sweaty body and therefore enables

increased evaporation

Heat loss in real situations

Thermos flask

Hot or cold

liquid

Rubber support

Vacuum

Container

Spring

centering

device

Glass walls

with silvered

surfaces

Vacuum minimises heat lost (or gained) by

conduction & Convection

Silvered surfaces minimise heat lost

(or gained) by radiation

Heat loss in real situations

Room

Conduction

Convection around

windows & doors

(cold air)

Co

nve

ctio

n (

ho

t a

ir)

Convection

•complex

•system-dependent.

•no simple mathematics

Wind chill:

Forced air convection around the body

increases the rate of heat transfer.

Trapped air is used as insulator:

Feathers

Hair

Fibre glass

Sweaters

Jackets

coats

Convection