Heat Transfer Introduction

Whenever two objects with different temperatures come into contact, energy flows from the hotter object to the cooler.

Heat Transfer Thermal Conduction

Transfer of energy (heat) arising from temperature differences between adjacent parts of a body is thermal conduction or heat conduction.

The constituent particles (atoms, molecules, or ions) in solids vibrate about their mean positions . As the temperature rises the amplitudes of their vibration increases. Thus, heat transfer takes place in solids. In metals free electrons play a major role in heat transfer.

Heat Transfer Thermal Conduction

Consider a solid-slab of uniform cross-section. Suppose temperatures of two cross sections ABCD and EFGH, at distance x and x + x, from one end of the solid, are T + T and T respectively. Thus for the separation x the temperature difference is T.

Heat Transfer Thermal Conduction

t/x- is known as temperature gradient For small value of x and T, the heat Q flowing between the two cross—section, perpendicular to the cross-sections in time t is directly proportional to time t, temperature gradient t/x and cross—section area A.

Heat Transfer

Thus,

( )

TQ A t

xT

Q kA tx

Q TkA a

t x

Here k is constant of proportionality called thermal conductivity of a given substance.

Thermal Conduction

Heat Transfer Thermal Conduction in a Bar

Consider a metallic bar of length L and uniform cross section A with its two ends maintained at different temperatures T1 and T2 respectively .

Heat Transfer

After sometime, a steady state is reached. These steady temperatures decrease along the length of the rod from its hot end to its cold end.

Let us assume the ideal condition that the sides of the bar are fully insulated so that no heat is exchanged between the sides and the surroundings.

Thermal Conduction in a Bar

The amount of heat energy received by the hot end in some time interval is equal to the amount or heat lost by the cold end in the same time interval. The sides of the rod are thermally insulated, hence the rod does not lose any heat through its sides.

Heat Transfer Thermal Conduction in a Bar

Hence, any cross-section of the rod, along its entire length has the same value of heat current dq/dt. Further, along the entire length of the rod the value or the temperature gradient dT/dx is same along the length. dq/dt and dT/dx remain constant with time.

1 2T TdT

dx L

This condition of the rod is called thermal steady state of the rod. In the thermal steady state, the temperatures of the two ends of the rod are T1 and T2, with T1 > T2.

Heat Transfer Thermal Conduction in a Bar

1 2

1 2

1 2

( )

( )

tan

from equation a

T TdQkA b

dt L

T TQ dQkA is cons t

t L dt

T TQ kA t

L

Heat Transfer ExampleThermal Resistance

1 2

1 2

( )

/

fromequation b

T TH kA

L

T TH

L kA

Thermal resistance (RH) is given by: RH = L/kA

Unit of thermal resistance (RH) is kelvin/watt

Heat Transfer

A 25 cm long rod of a cross-section of 1.5 cm2 has one of its end in thermal contact with steam at 100C and the other end is in thermal contact with ice at 0C in its thermal steady state. Find

Examples

(1) the temperature gradient along the rod(2) the rate of heat conduction

Heat Transfer Solution

Given, A = 1.5 Cm2 T1 = 100C T2 = 0C L = 25 cm

1 2

0 1

100 0

25

4

T TdT

dx L

C cm

Temperature gradient,

Heat Transfer

1 2

1

100 00.9 1.5

25

5.4

T TdQkA

dt L

dQcal s

dt

Rate of heat conduction

Solution

Heat Transfer Convection

Convection is heat transfer by the mass movement of a fluid in the vertical (up/down) direction.

Heat Transfer

Natural convection is responsible for many familiar phenomena.

As a gas or a liquid is heated, it warms, expands, and rises because it is less dense. When the gas or liquid cools, it becomes denser and falls. As the gas or liquid warms and rises, or cools and falls, it creates convection current.

Convection

Heat Transfer Convection

Heat Transfer

Water heats up much less quickly, air above the ocean also takes longer to increase in temperature. The result is that a higher pressure is maintained.

With a high pressure above the water and a lower pressure above the land, conditions are perfect for a small breeze to develop. Wind blows from the sea towards the land along the pressure gradient in an attempt to equalize pressure. This is known as a sea breeze.

Sea Breeze

Heat Transfer

In the night, land cools down much quicker than does the waters of the ocean. As the land becomes cooler, so does the air above it. This results in air becoming more dense, forming a high pressure, causing winds to blow outward towards the sea. This is known as a land breeze.

Thus, in the day we often see sea breezes, while in the evening we see land breezes in coastal regions.

Land Breeze

When electromagnetic waves travel through space, it is called radiation. The sun warms the Earth through the radiation of electromagnetic waves.

Heat Transfer Radiation

In an electromagnetic wave electric and magnetic fields oscillate in space and time. Electromagnetic waves can have different wavelengths and can travel in vacuum with the speed of light i.e., 3 × 108 m s–1 .

The energy associated with electromagnetic radiation is called radiant energy. All bodies emit radiant energy, whether they are solid, liquid or gases.

Heat Transfer Black Body

This propety is valid for radiation corresponding to all wavelengths and to all angles of incidence. Therefore, the black body is an ideal absorber of incident radiation.

A black body is an ideal body which allows the whole of the incident radiation to pass into itself ( without reflecting the energy ) and absorbs within itself this whole incident radiation (without passing on the energy).

Heat Transfer Black Body Radiation

Consider a spherical cavity . Its inner surface is blackened and rough. It has a small hole. A radiation entering this cavity through this entrance hole undergoes many reflections and each time it is partly absorbed and partly reflected when it reaches the hole again it is almost left with no energy.

Heat Transfer

The portion of cavity just opposite to hole is such that radiation can not be reflected back immediately after it enters the cavity in the opposite direction to come out.

Black Body Radiation

This pin hole can he considered a perfect black body. If such a cavity is uniformly heated, radiations coming out of it can be considered to be black body radiation. This radiation is also called cavity radiations.

Heat Transfer Absorptivity

The ratio of the radiant energy absorbed to the amount of radiant energy incident on the surface is called absorptivity (a) of that surface at a given temperature.

radiant energy absorbeda

incident radiant energy

For a completely black body a =1

Heat Transfer Total Emissive Power

The amount of radiant energy emitted per unit area per second from a surface at a given temperature for all possible wavelengths is called the total emissive power (w) of surface of that temperature.

Heat Transfer Spectral Emissive Power

Emissive power (wf) for a particular frequency ‘f ’ is called spectral emissive power.

If we use wavelength instead of frequency f. Therefore, sum of the spectral emissive powers for all the frequencies gives the total emissive power.

ff

W W W

The magnitude of ‘wf ‘ on the temperature , material of the surface and frequency ‘f ’ .

Heat Transfer Emissivity

The ratio of the total emissive power of a surface to the total emissive power of the surface of a perfectly black body kept under the same conditions is called emissivity (e) of that surface.

For the surface of a completely black body, e = 1

Heat Transfer Kirchhoff’s Law

“The values of emissivity and absorptivity are equal for any surface.”

a = e

Therefore, the surface which is a good absorber, also a good emitter and the surface which is a good reflector (i.e. a poor absorber) is also a poor emitter .

Heat Transfer Wien’s Displacement Law

The Wien's Displacement Law state that the wavelength carrying the maximum energy is inversely proportional to the absolute temperature of a black body.

i.e. λmaxT = b

Where, λmax =  Wavelength of maximum intensity (meters) T =  Temperature of the blackbody (Kelvin ) b  =  Wien's displacement constant  =  2.9 × 10-3 m-K

Heat Transfer Stefan Boltzmann’s Law

The Stefan-Boltzmann law states the amount of radiant energy emitted by a surface per unit area in unit time (i.e. total emissive power) is directly proportional to the fourth power of its absolute temperature (T).

i.e. W = eTσ 4

Where,T = absolute temperaturee = emissivity of the surfaceσ = Stefan-Boltzmann constant = 5.67 10-8 W/(m2 K4)

Heat Transfer

The “greenhouse effect” is a naturally occurring phenomenon that keeps the Earth’s surface and atmosphere at a comfortable, life-sustaining temperature. without this effect, life on Earth would not exist.

Green House Effect

However, increasing amounts of carbon dioxide from the burning of oil, gas and coal are enhancing this natural effect, causing the planet to warm up the levels that cannot be explained by natural variability.

Although some of that energy is emitted directly into space, clouds and greenhouse gases such as carbon dioxide absorb rest of the energy. Some of this absorbed energy is radiated back to the Earth’s surface and as a result its temperature is maintained.

Green House Effect Heat Transfer

Sunshine warms the Earth. The planets atmosphere, land and oceans absorb some of this warmth while the rest is radiated away as infrared energy.