Chapter11 Thermal conduction - Weebly · A metal rod heated at one end will transfer thermal energy to the other end by conduction. In this method, some of the electrons in the metal

11. Heat Transfer

By Liew Sau Poh

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Outline

11.1 Conduction 11.2 Convection 11.3 Radiation 11.4 Global warming

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Objectives

a) explain the mechanism of heat conduction through solids, and hence, distinguish between conduction through metals and non-metals

b)define thermal conductivity c) use the equation

for heat conduction in one dimension

xkA

tQ 12

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Objectives

d)describe and calculate heat conduction through a cross-sectional area of layers of different materials

e) compare heat conduction through insulated and non-insulated rods

f) describe heat transfer by convection g)distinguish between natural and forced

convection 4

Objectives

h) describe heat transfer by radiation i) use Stefan-Boltzmann equation dQ/dt =

e AT4 j) define a black body k) explain the greenhouse effect and

thermal pollution l) suggest ways to reduce global warming

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11 Heat Transfer

Internal energy may be transferred from one body to another. These occur in 3 modes:

(http://docushare.harford.edu/dsweb/Get/Document-239986/Physical%20Science%20105%20Chapter%2007.ppt)

Conduction Convection Radiation

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11.1 Conduction

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11.1 Conduction

The type of energy transfer that is due to atoms transferring vibrations to neighboring atoms is called thermal conduction. The rate of thermal conduction depends on the substance.

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11.1 Conduction

A metal rod heated at one end will transfer thermal energy to the other end by conduction. In this method, some of the electrons in the metal (called conduction electrons) are free to roam and collide with other electrons. Metals like copper are good conductors. Water is not a good conductor, rather it is considered to be an insulator, a poor conductor.

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11.1 Conduction

Ions in the lattice structure of a solid can also vibrate, causing their neighbors to vibrate. The neighbors then cause their neighbors to shake, and the process spreads until the solid approaches thermal equilibrium. This spreads more slowly then electron collisions so that materials that do not have many free electrons are not good thermal conductors.

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11.1 Conduction

Copper Cookware Copper has a high thermal conductivity. When you heat from below, the flame or element concentrates heat. A good copper bottom will conduct heat evenly across the bottom for better heat distribution in the pot.

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11.1 Conduction

Good insulators are poor conductors Double Pane Windows with Air Insulation

The superior insulating properties of air (poor thermal conductivity) provide insulation for windows. The air is sandwiched between two panes of glass and sealed.

Down is a good insulator. 12

Relative Thermal Conductivities

Silver 1.01 Copper 0.99

Aluminum 0.50 Ice 0.005

Water 0.0014 Snow 0.00026

Fiberglass 0.00015 Cork 0.00011 Wool 0.0001 Wood 0.0001

Air 0.000057 13

11.1 Conduction The process of heat conduction is visualized as resulting from molecular interactions (interactions/collisions between electrons and molecules):

Molecules in one part of a body at higher temperature vibrate faster. They collide with and transfer some of their energy to less energetic molecules located toward the cooler part of the body. In this way energy is conductively transferred from a higher-temperature region to a lower-temperature region - transfer as a result of a temperature difference.

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11.1 Conduction Thermal conductors are materials that are good conductors of heat. Metals (a type of solid) are thermal conductors. Why?

A metal has a large number of electrons that are free to move around (conduction electrons), and are not permanently bound to any particular atom or molecule. The free electrons are believed to be primarily responsible for the heat conduction of metals.

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11.1 Conduction

Thermal insulators are materials that are poor conductors of heat. Non-metals such as wood or cloth are thermal insulators. Why?

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11.1 Conduction

In general, the ability of a substance to conduct heat depends on its phase.

Gases are poor thermal conductors because their molecules are relatively far apart, and collisions are therefore infrequent. Liquids are better thermal conductors than gases because their molecules are closer together and can interact more readily. Non-metals have relatively few free electrons.

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11.1 Conduction

Can we describe heat conduction quantitatively? Heat conduction is the time rate of heat flow (Q/ t) in a material for a given temperature difference ( t). Experiments have established that the rate of heat flow through a substance depends on the temperature difference between its boundaries. Heat conduction also depends on the size and shape of the object.

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11.1 Conduction

Heat flow through a uniform slab of material is directly proportional to its surface area, , and inversely proportional to its thickness, (Fourier's law of conduction): where is called the thermal gradient (the change in temperature per unit length), and the constant, k is called the thermal conductivity

,Q TkAt dT

d

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11.1 Conduction

The thermal conductivity characterizes the heat-conducting ability of a material: the greater the value of k for a material, the more rapidly it will conduct heat. The SI units of thermal conductivity k are: J/(m s K). The thermal conductivity varies slightly over different temperature ranges, but can be considered constant over the usual temperature ranges and differences

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11.1 Conduction

Thermal Resistance to Conduction: R- Value: If you are interested in insulating your house or in keeping coke cans cold on a picnic, you are more concerned with poor heat conductors than with good ones. For this reason, the concept of thermal resistance has been introduced into engineering practice. The value of a slab of thickness is defined as .dR

k 21

11.1 Conduction

Thus, the lower the thermal conductivity of the material of which a slab is made, the higher the R-value of the slab. Note that is a property attributed to a slab of a specified thickness, not to a material.

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11.1 Conduction

Heat: Q = C T (internal energy transferred) Q = amount of heat that must be supplied to raise the temperature by an amount T . [Q] = Joules or calories. (1 Cal = 4.186 J, 1 kcal = 1 Cal = 4186 J) Energy to raise 1 g of water from 14.5 to 15.5 °C (James Prescott Joule found the mechanical equivalent of heat.) C Heat capacity (in J/ K) 23

11.1 Conduction

Q = c m T c: specific heat (heat capacity per units of mass) amount of heat to raise T of 1 kg by 1 °C [c] = J/(kg °C) Sign convention: +Q : heat gained, - Q : heat lost

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Latent Heat

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Latent Heat

Latent heat: amount of internal energy needed to add or to remove from a substance to change the state of that substance. Phase change: T remains constant but internal energy changes Heat does not result in change in T

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Latent Heat e.g. : solid liquid or liquid gas (heat goes to breaking chemical bonds) L = Q / m Heat per unit mass [L] = J/kg Q = m L + if heat needed (boiling) - if heat given up (freezing) Lf : Latent heat of fusion: solid liquid Lv : Latent heat of vaporization: liquid gas

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Energy transfer mechanisms

Thermal conduction (or conduction):

Energy transferred by direct contact. e.g.: energy enters the water through the bottom of the pan by thermal conduction. Important: home insulation, etc.

x

Th Tc

A

Energy flow

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Energy transfer mechanisms

Rate of energy transfer ( J / s or W)

Through a slab of area A and thickness Dx, with opposite faces at different temperatures, Tc and Th P = Q / t = k A (Th - Tc ) / x k :Thermal conductivity (J/s m °C)

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Thermal Conductivity

Matter J/s m C

Matter J/s m C

Matter J/s m C

Aluminum 238 Air 0.0234 Asbestos 0.25 Copper 397 Helium 0.138 Concrete 1.3 Gold 314 Hydrogen 0.172 Glass 0.84 Iron 79.5 Nitrogen 0.0234 Ice 1.6 Lead 34.7 Oxygen 0.0238 Water 0.60 Silver 427 Rubber 0.2 Wood 0.10

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11.1 Conduction

Two identically shaped bars (one blue and one green) are placed between two different thermal reservoirs . The thermal conductivity coefficient k is twice as large for the blue as the green.

100 CTjoint

300 C

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11.1 Conduction

P = Q / t = k A (Th - Tc ) / x Top: Pgreen = Pblue = Q / t = 2 k A (Thigh - Tj ) / x= k A (Tj - Tlow ) / x 2 (Thigh - Tj ) = (Tj - Tlow ) 3 Tj(top) = 2 Thigh + Tlow By analogy for the bottom (comparing eq.1):

3 Tj(bottom) = 2 Tlow + Thigh 32

11.1 Conduction

3 Tj(top) = 2 Thigh + Tlow 3 Tj(bottom) = 2 Tlow + Thigh Eq.1 Eq.2:

3 (Tj(top) - Tj(bottom) )= Thigh Tlow = 300-100 > 0 (positive)

The joint at upper bar has highier Temp then lower bar.

100 CTjoint

300 C

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11.1 Conduction

Conduction through a composite slab The energy transferred through one material in a certain time must be equal to that transferred through the other material in the same time. i.e. P1,cond = P2,cond

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11.1 Conduction

solve for TX then

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11.1 Conduction

For n layers (Equation for heat flow) -

your body in the winter. 36

Temperature Distribution for a Rod

Insulated rod No heat escapes from the sides of the rod. Same quantity of heat flux flows passed a cross-section in every second. Since dQ/dt is constant where dQ/dt = -

/dx, then the temperature gradient /dx must be also constant, (same at any point along the length of the rod). Hence the line in the temperature distribution graph is a straight line that slants downwards.

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Insulated rod

Temperature

2

1 x

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Non-insulated rod Heat escapes from the sides of the rod. Heat flux passing through one cross-section nearer at the cold end of the rod is less then passing through another cross-section slightly further apart from the cold end. The quantity of heat flowing from the hot wnd through a cross-section per second gets lesser and lesser as moving along the rod towards the cold end.

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Non-insulated rod dQ/dt become smaller and smaller as the heat moving towards the cold end, as same as the /dt. A curve is observed in the temperature distribution graph whose gradient decreases towards the cold end.

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Non-insulated rod Temperature

2

1 x

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Temperature Distribution for Composite Rod Insulated composite rod

No heat escapes from the sides of the rods. Therefore dQ/dt = -k1A( /dx)1 = -k2A( If k1 > k2, then ( /dx)1 < ( /dx)2 and get line (i) in the temperature distribution graph shown in figure (a). If k1 > k2, then we get line (ii).

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Temperature Distribution for Composite Rod

Insulated composite rod Temperature

3

1 x

2 k1 k2 3 1

(i) (ii)

(a) 43

Temperature Distribution for Composite Rod Non-insulated composite rods

If the rods are not insulated, the graph of temperature distribution gives a curve as shown in figure (b).

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Temperature Distribution for Composite Rod

Non-insulated composite rods Temperature

3

1

x

2 k1 k2 3 1 (b) 45

Determination of thermal conductivity

Thermal conductivity, k = dQ/dt, where A = 1 m2

2 1 = 1 K and x = 1 m. The unit of k is W m-1 K-1. Thermal conductivity of a solid is defined as the rate at which heat flows perpendicularly through unit cross-sectional area of a solid under steady condition, per unit temperature gradient along the direction of heat flow.

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Determination of Thermal Conductivity of Good Conductors (Searle's Method)

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Figure above shows the apparatus used in Searle's method which is used to determine the thermal conductivity of a good conductor, such as a metal. The special feature of the apparatus is that the sample is in the form of a thick, long insulated rod. Although the rod is insulated, a little heat is lost from the sides of the rod. The rod is of large cross-sectional area, so that the rate of heat lost from the sides is negligible compared to the rate of heat flow along the rod.

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A long rod is used, so that the larger temperature dropped across the long length of the rod can be measured accurately. A bigger temperature differences reduces the percentage error in the measurement of the temperature difference. Since the rod is insulated, the rate of heat flow and the temperature gradient are constant along the rod. Hence, the temperature gradient can be measured along one section of the rod, and the rate of heat flow along another section.

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The end M of the rod is heated in a steam chest. Water from a constant pressure apparatus flows in a coil around the end N of the rod. When the steady state is attained, the

thermometers T1, T1, T1 and T4 resoectivelv are nolec.

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The temperature gradient, where l = distance between the thermometers T1, and T2. lf m = mass of water collected in time

interval l, then rate of heat flow

, where c = specific heat capacity of water

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Using is

, d = diameter of rod measured using a venire calipers

Thermal conductivity

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Determination of Thermal Conductivity of a Poor Conductor (Lees' Method)

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A thick brass disc B with a hole holding a thermometer Z, is hung using thin suspension wires. The sample, in the form of a thin circular disc with the same diameter as the disc B, is placed on B. No lagging is required because the rate of heat loss from the sides of the thin sample is negligible. The surface area of the sides of the sample is small compared to the large cross-sectional area of the sample.

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Since the sample is a poor conductor, for the steady state to be achieved in a short time, the sample must be thin. Heat will require a very long time to flow through a thick sample. On top of the sample is placed a steam chest which has a thick brass base with a hole holding a thermometer T1.

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Steam is allowed into the steam chest. When the readings of the thermometers T1 and T2 do not increase further but stay constant, steady state has been achieved. Heat flows from the steam in the steam chest through the brass base C the sample, the thick brass disc B and out from the base of disc B.

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Brass is a good conductor of heat. Hence, the temperature 0, at the upper surface of the circular sample is recorded by the thermometer T1. Thermometer T, records the temperature 0, of the lower surface of the sample. The thickness, x of the sample is measured using a micrometer screw gauge. Hence, temperature gradient across the sample =

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The second part of the experiment is to measure the rate of heat flow achieved The steam chest and sample are removed. The brass disc B is slowly heated using a Bunsen burner until its temperature is a

the experiment.

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The sample is placed on top of disc B and

recorded every 20 seconds until the

plotted. The gradient of the graph when

is calculated 61


Using the equation Q = mcQ

When the lower surface of the temperature is 0r, the rate of heat flow through the sample is

where D = diameter of sample

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Thermal conductivity,

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11.2 Convection

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11.2 Convection

Convection is heat flow by the movement of a fluid Convection involves the movement of cold and hot matter, such as hot air rising upward over a flame. This effect is the combined effects of pressure differences, conduction, and buoyancy.

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11.2 Convection

The air is heated through conduction (particle collision), causing the air to expand, and its density to decrease. The warm air is displaced by denser colder air.

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11.2 Convection

When the movement results from differences in density, it is called natural convection (fluid currents are due to gravity)

Air currents at the beach Water currents in a saucepan while heating

Hot water is lighter and flow upward

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11.2 Convection

When the movement is forced by a fan or a pump, it is called forced convection (fluid is pushed around by mechanical means fan or pump)

Forced-air heating systems Hot-water baseboard heating Blood circulation in the body

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11.3 Radiation

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11.3 Radiation

Thermal radiation transfers energy through emission of electromagnetic waves does not require physical contact Electromagnetic radiation does not involve the transfer of matter. Objects reduce their internal energy by giving off electromagnetic radiation of particular wavelengths or are heated by electromagnetic radiation.

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11.3 Radiation

Example, a car in the winter is hot inside because electromagnetic radiation, sunlight, gets trapped inside as heat. All objects radiate energy continuously in the form of electromagnetic waves due to thermal vibrations of the molecules

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11.3 Radiation All objects radiate energy continuously in the form of electromagnetic waves due to thermal vibrations of the molecules

At ordinary temperatures (~20 C) nearly all the radiation is in the infrared (wavelengths longer than visible light) At 800 C a body emits enough visible radiation to be self-luminous and appears

- At 3000 C (incandescent lamp filament) the radiation contains enough visible light so the

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11.3 Radiation

An ideal emitter and absorber of radiation is called a blackbody. An ideal black body will absorb totally all radiation of any wavelength which fall on it (would appear black). The radiation emitted by a black-body is known as black body radiation.

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Black body: intensity vs wavelength at different temperature

As temperature decreases, the peak of the black body radiation curve move to the lower intensities and longer wavelength

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Black-body Spectrum

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11.3 Radiation

The Stefan Boltzmann law (or Stefan's law), states that the total energy radiated per unit surface area of a black body per unit time (or the black-body irradiance or emissive power), is directly proportional to the fourth power of the black body's thermodynamic temperature T (or absolute temperature). E (m-2 s-1) = T4

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4AeTdtdQP

11.3 Radiation

The rate at which energy is radiated is given by Stefan-Boltzmann Law:

P is the rate of energy transfer (power), in Watts

= Stefan-Boltzmann constant = 5.67 x 10 8 W/m2 K4 A is the surface area of the object e is a constant called the emissivity, and ranges from 0 to 1 surface; e = 1 for a black-body T is the temperature in Kelvin

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11.3 Radiation

Object absorb radiation as well. Thus, a body that is not in thermodynamic equilibrium, the net power radiated is the different between the power emitted and the power absorbed.

Pnet = Pemit - Pabsorb

Net rate of energy gained or lost given by:

T0 = temperature of environment

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4net TTAeP

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Applications of Thermal Radiation

Choice of clothing Black fabric acts as a good absorber, so about half of the emitted energy radiates toward the body White fabric reflects thermal radiation well

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Applications

Thermography as medical diagnostic tool

Measurement of emitted thermal energy using infrared detectors, producing a visual display Areas of high temperature are indicated, showing regions of abnormal cellular activity

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Applications

Measuring body temperature Radiation thermometer measures the intensity of the infrared radiation from the eardrum Eardrum is good location to measure temperature since it

temperature control center)

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11.4 Global Warming

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Greenhouse Effects

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11.4 Global Warming Greenhouse Effects

Visible light and short-wavelength infrared radiation are absorbed by contents of greenhouse, resulting in the emission of longer-wavelength infrared radiation (IR) Longer-wavelength IR absorbed by glass Glass emits IR, half of which is emitted back inside the greenhouse Convection currents are inhibited by the

atmosphere) 85

11.4 Global Warming

in greenhouse 2 are

particularly good absorbers of IR More greenhouse gasses in the atmosphere means more IR is absorbed

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GREENHOUSE GASES

CARBON DIOXIDE AND METHANE

THE BURNING OF FOSSIL FUELS 87

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Causes Of Global Warming

Gas: Source: Use: Way It Increases Global Warming:

Water Vapour (Steam)

Oceans, lakes, rivers, reservoirs. Humans have little impact upon levels.

Absorbs limited outgoing radiation.

Water vapour and clouds are responsible for nearly 98% of the natural greenhouse effect.

Carbon Dioxide

Burning of fossil fuels, and forests, breathing animals, less produced by southern hemisphere (less land).

Absorption of long wave radiation.

Approximately 50%.

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Gas: Source: Use:

Way It Increases

Global Warming:

Methane (CH4)

Much from break down of organic matter by bacteria (rice paddy fields) cows, swamps marshes.


Approximately 18%.

Ozone

Naturally from some oxygen atoms. Ozone in the troposphere is due to chemical reactions between sunlight and agents of pollution.

Filters short wave UV radiation.

Difficult to estimate.

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Gas Source Use: Way It Increases Global Warming

CFCs Fridges and aerosols.

25%, but increasing due to ability to survive within the atmosphere for 100 years.

Nitrous Oxide

Nitrate fertilisers, transport and power stations (combustion).


Approximately 6%.

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Positive And Negative Effects Impact

on: Effect: Consequence (-): Consequence (+):

Health

Malaria and cholera increase, due to temperature increase.

More money needed to fight disease, strain on medical services, rise in death rate.

Vegetation

Shifting flora and fauna to different areas. Extinction of some species.

Spread of pests and disease, alteration in crop yields, may increase food shortages.

Canadian Prairies could become major wheat growing belt. Areas able to grow different crops, for example, citrus fruits in the UK. 93

Positive And Negative Effects Impact

on: Effect: Consequence (-):

Consequence (+):

Weather

More extreme climates in inland locations. More frequent and devastating hurricanes.

Unknown at present.

Unknown at present.

Ocean

Sea temperatures increase, sea levels rise, shift in ocean currents.

Changes in number of fish stocks and their location will impact the fish industry.

Increase in fish stocks in certain areas.

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Positive And Negative Effects

Impact on: Effect: Consequence (-): Consequence (+):

Landscape

Reduced snow cover in some areas. Glaciers melt in Antarctica.

Rise in sea levels.

Extended summer season in some landscapes due to higher temperatures, increasing revenue.

Hydrology

Reduction of wetland areas, as precipitation is reduced. In some places river flooding may increase.

Great pressure on water supplies. Problems for HEP schemes and irrigation.

Increased awareness of water conservation measures, less water wastage.

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Positive And Negative Effects

Impact on: Effect: Consequence (-): Consequence (+):

Population

Reduction of areas suitable for human habitation, for example. lowland Bangladesh.

Increased population densities increase possibility of disease and malnutrition.

Forced movement of population from densely populated coastal areas, to interior locations.

Climate

Location of jet stream may alter. Depressions may shift south, causing them to be more intense.

Better forecasting needed to warn people of approaching storms. Insurance premiums will increase.

More accurate weather forecasting developed

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Action to Reduce Global Warming

Challenge others about global warming. Broaden impact others with more facts to persuade people to make simple yet effective changes in daily behavior. Energy-saving techniques are initially expensive (like solar power) or take extra time (like recycling), so people need to be convinced that their efforts matter via education.

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Vote and influence your government with telephone calls, e-mails, letters, and meetings to government. Choose vegetarian or vegan meals

Livestock emit more greenhouse gas than transportation is. petroleum used in creating ammonium nitrate fertilizer. agricultural water consumption and land use

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Recycle more by using recycling bins, composting, etc.

Encourage neighbors, supervisors, colleagues, and businesses to do likewise (15-25% of people do not recycle). Reuse recycled paper Reduce waste

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Use energy-efficient product. Use compact fluorescent bulbs. Replace three frequently used light bulbs with compact fluorescent bulbs. LED lightbulbs are even more efficient.

Fill the dishwasher. Run the dishwasher only with a full load. Buy locally made and locally grown products, reducing energy for transport. 100


Buy minimally packaged goods. Less packaging could reduce your garbage significantly. Unplug unused electronics. Even when electronic devices are turned off, they use energy. Unplugging them or switching them off. Get into the habit of switching the power off before you go to bed.

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Plant and Grow fast growing plants. Plants like bamboo grow faster and produce 35% more oxygen than trees like oak or birch, and require fewer chemicals and care.

Use public transportation. Taking the bus, the train, the subway or other forms of public transportation lessens the load on the roads and reduces one's individual greenhouse gas emissions

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Ride a bicycle. Taking the bike instead of the car is a very simple solution. Use refills. Try using refills instead of buying new jars or bottles each time. This reduces your consumption and is usually cheaper, too.

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Summary: Heat transfer Mechanism of thermal conduction Thermal conductivity dQ/dt = -kA d /dx

Conduction

Natural and forced convection Convection

P = dQ/dt = e AT4

Black body radiation Radiation

Greenhouse effect Thermal pollution

Global Warming

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End of Chapter

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Documents

Chapter11 Thermal conduction - Weebly · A metal rod heated at one end will transfer thermal energy to the other end by conduction. In this method, some of the electrons in the metal