RADIATIONPREPARED UNDER THE GUIDANCE OF

Prof. Dr. Manish Mehta BVM Engineering College , V.V Nagar

NAME ENROLLMENT NO.MARMIK PATEL 140080125025REJOICE PARACKAL 140080125026MANAN SHAH 140080125027SHREYANSH AGHERA 140080125028

Compiled by

CONCEPT OF DIFFERENT BODIES BLACK BODY:- A black body is an object that absorbs all the radiant energy reaching its

surface from all the directions with all the wavelengths.It is perfect absorbing body. so , for black body; The black body is a hypothetical body . However its concept is very important . When the black body absorbs heat , its temperature raises.

WHITE BODY:- If all the incident radiation falling on the body are reflected , it is called a white body.

for white body,

GREY BODY:- A grey body is defined as a body whose absorptivity of a surface does not vary with variation in

temperature and wavelength of the incident radiation. OPAQUE BODY:- When no radiation is transmitted through the body , it is called as opaque

body. for opaque body;

KIRCHOFF’S LAW• This law states that the ratio of total power to absorptivity is constant for al the substances which

are in thermal equilibrium with the surroundings. This can be written inn mathematical form for bodies as follow,

Assume out of any four body , any one body , say fourth one ,is black body .Then;

But according to the definition of emissivity , we have;

From equation (2) in general , we can say that;

Let us consider a small body with area A1 and absorptivity a1.The small body (1) is covered by a large radiation body (2) with area A . If the large body is a black body than the total emissive power of body (2) is Eb. The energy fall on the body(1) from body (2) is Eb . Of this energy , body (1) will absorbed the energy a1*A1*Eb . When thermal equilibrium is arrieved , the heat absorbed by the body (1) must be eual to the heat emitted (E1) from body 1 . So at equilibrium,

………………….(1)Now remove body 1 and put body 3 of area A3 and absorptivity a3 .repeat the same procedure again. …………………(2)

from equation 1 and 2, we have;

According to the definition of emissivity,

Above equation represents the proof of the kirchoff’s law.

The Bernoulli Equation• It is an approximate relation between pressure, velocity and elevation

• It is valid in regions of steady, incompressible flow where net frictional forces are negligible

• Viscous effects are negligible compared to inertial, gravitational and pressure effects.

• Applicable to inviscid regions of flow (flow regions outside of boundary layers)

• Steady flow (no change with time at a specified location)

• The value of a quantity may change from one location to another. In the case of a garden hose nozzle, the velocity of water remains constant at a specified location but it changes from the inlet to the exit (water accelerates along the nozzle).

Steady flow

Acceleration of a Fluid Particle• Motion of a particle in terms of distance “s” along a streamline• Velocity of the particle, V = ds/dt, which may vary along the streamline• In 2-D flow, the acceleration is decomposed into two components, streamwise acceleration as, and normal acceleration, an.

2

nVaR

• For particles that move along a straight path, an =0

Fluid Particle Acceleration• Velocity of a particle, V (s, t) = function of s, t

• Total differential

• In steady flow,

• Acceleration,

V VdV ds dts t

or dV V ds Vdt s dt t

0;and ( )V V V st

sdV V ds V dVa V Vdt s dt s ds

Derivation of the Bernoulli Equation (1)• Applying Newton’s second law of conservation of linear momentum

relation in the flow field( ) sin dVPdA P dP dA W mV

ds

ds is the massm V dA

W=mg= g ds is the weight of the fluiddA sin =dz/ds

- - dz dVdpdA gdAds dAdsVds ds

,dp gdz VdV

21Note V dV= ( ),and divding by 2d V

21 ( ) 02

dp d V gdz

Substituting,

Canceling dA from each term and simplifying,

Derivation of the Bernoulli Equation (2)

Integrating

2

constant (along a streamline)2

dp V gz

2

constant (along a streamline)2

p V gz

For steady flow

For steady incompressible flow,

Bernoulli Equation• Bernoulli Equation states that the sum of kinetic, potential and flow (pressure) energies of a fluid particle is constant along a streamline during steady flow.• Between two points:

2 21 1 2 2

1 2 or,2 2

p V p Vgz gz

2 21 1 2 2

1 2 2 2

p V p Vz zg g

2

pressure head; velocity head, z=elevation head2

p Vg

Example 1

Figure E3.4 (p. 105) Flow ofwater from a syringe

• Water is flowing from a hose attached to a water main at 400 kPa (g). If the hose is held upward, what is the maximum height that the jet could achieve?

Example 2

• Water discharge from a large tank. Determine the water velocity at the outlet.

Example 3

change in flow conditions• Frictional effects can not be neglected in long and narrow flow

passage, diverging flow sections, flow separations• No shaft work

Limitations on the use of Bernoulli Equation

A black body (also blackbody) is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A white body is one with a "rough surface [that] reflects all incident rays completely and uniformly in all directions."[1]

A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic radiation called black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by thetemperature alone (see figure at right), not by the body's shape or composition.

A black body in thermal equilibrium has two notable properties: It is an ideal emitter: at every frequency, it emits as much energy as –

or more energy than – any other body at the same temperature.

Black Body Radiation

It is a diffuse emitter: the energy is radiated isotropically, independent of direction.

An approximate realization of a black surface is a hole in the wall of a large enclosure (see below). Any light entering the hole is reflected indefinitely or absorbed inside and is unlikely to re-emerge, making the hole a nearly perfect absorber. The radiation confined in such an enclosure may or may not be in thermal equilibrium, depending upon the nature of the walls and the other contents of the enclosure.[3][4]

Real materials emit energy at a fraction—called the emissivity—of black-body energy levels. By definition, a black body in thermal equilibrium has an emissivity of ε = 1.0. A source with lower emissivity independent of frequency often is referred to as a gray body.[5][6] Construction of black bodies with emissivity as close to one as possible remains a topic of current interest.[7]

Kirchhoff in 1860 introduced the theoretical concept of a perfect black body with a completely absorbing surface layer of infinitely small thickness, but Planck noted some severe restrictions upon this idea. Planck noted three requirements upon a black body: the body must (i) allow radiation to enter but not reflect; (ii) possess a minimum thickness adequate to absorb the incident radiation and prevent its re-emission; (iii) satisfy severe limitations upon scattering to prevent radiation from entering and bouncing back out. As a consequence, Kirchhoff's perfect black bodies that absorb all the radiation that falls on them cannot be realized in an infinitely thin surface layer, and impose conditions upon scattering of the light within the black body that are difficult to satisfy

Kirchhoff's perfect black bodies

Black-body Radiation

lpeak = 2.9 x 10-3 mT(Kelvin)

Light

inte

nsity

UV IR

lpeak vs Temperature

lpeak = 2.9 x 10-3 mT(Kelvin)T

3100K(body temp)

2.9 x 10-3 m3100 =9x10-6m

58000K(Sun’s surface)

2.9 x 10-3 m58000 =0.5x10-6m

infrared light

visible light

“Room temperature” radiation

The Planck DistributionA. A. Michelson (late 1900s): “The grand underlying principles (of physics) have been firmly established... ...the future truths of physics are to be looked for in the sixth place of decimals.”

Planck credited with the birth of quantum mechanics (1900) - developed the modern theory of black-body radiation

Quantum nature of radiation1st evidence from spectrum emitted by a black-body

What is a black-body?An object that absorbs all incident radiation, i.e. no reflection

A small hole cut into a cavity is the most popular and realistic example.None of the incident radiation escapes

What happens to this radiation?

•The radiation is absorbed in the walls of the cavity•This causes a heating of the cavity walls•Atoms in the walls of the cavity will vibrate at frequencies characteristic of the temperature of the walls•These atoms then re-radiate the energy at this new characteristic frequencyThe emitted "thermal" radiation characterizes the equilibrium

temperature of the black-body

Black-body spectrum

Black-body spectrum•Black-bodies do not "reflect" any incident radiation

They may re-radiate, but the emission characterizes the black-body only•The emission from a black-body depends only on its temperature

We (at 300 K) radiate in the infraredObjects at 600 - 700 K start to glowAt high T, objects may become white hot

Wien's displacement Law

lm T = constant = 2.898 × 103 m.K, or lm T1

Found empirically by Joseph Stefan (1879); later calculated by Boltzmanns = 5.6705 × 108 W.m2.K4.A black-body reaches thermal equilibrium when the incident radiation power is balanced by the power re-radiated, i.e. if you expose a black-body to radiation, its temperature rises until the incident and radiated powers balance.

Stefan-Boltzmann LawPower per unit area radiated by black-body R = sT 4

Rayleigh-Jeans equationConsider the cavity as it emits blackbody radiationThe power emitted from the blackbody is proportional to the radiation energy density in the cavity. One can define a spectral energy distribution such that u(l)dl is the fraction of energy per unit volume in the cavity with wavelengths in the range l to l + dl.

Then, the power emitted at a given wavelength, R(l) u(l)

u(l) may be calculated in a straightforward way from classical statistical physics.

u(l)dl = (# modes in cavity in range dl) × (average energy of modes)

# of modes in cavity in range dl,n(l)dl8pl4dlAverage energy per mode is kBT, according to kinetic theory

u(l) = kBT n(l)8pkBT l4

Wien, Rayleigh-Jeans and Planck distributions( ) ( ) ( ) ( )

/

RJ W P /4 5 5

8 8; ;1B

TB

hc k T

k T e hcu u ue

l

l

p pl l ll l l

Wilhelm Carl Werner Otto Fritz Franz Wien

The ultraviolet catastropheThere are serious flaws in the reasoning by Rayleigh and JeansFurthermore, the result does not agree with experimentEven worse, it predicts an infinite energy density as l 0!(This was termed the ultraviolet catastrophe at the time by Paul Ehrenfest)

Agreement between theory and experiment is only to be found at very long wavelengths.

The problem is that statistics predict an infinite number of modes as l0; classical kinetic theory ascribes an energy kBT to each of these modes!

Planck's law (quantization of light energy)In fact, no classical physical law could have accounted for measured blackbody spectra

The problem is clearly connected with u(l) , as l 0

Planck found an empirical formula that fit the data, and then made appropriate changes to the classical calculation so as to obtain the desired result, which was non-classical.

Max Planck, and others, had no way of knowing whether the calculation of the number of modes in the cavity, or the average energy per mode (i.e. kinetic theory), was the problem. It turned out to be the latter.

The problem boils down to the fact that there is no connection between the energy and the frequency of an oscillator in classical physics, i.e. there exists a continuum of energy states that are available for a harmonic oscillator of any given frequency. Classically, one can think of such an oscillator as performing larger and larger amplitude oscillations as its energy increases.

Maxwell-Boltzmann statisticsDefine an energy distribution function ( ) ( ) ( )

0exp / ,such that 1Bf E A E k T f E

Then, ( )0 0

exp( / )B BE E f E dE EA E k T dE k T

This is simply the result that Rayleigh and others used, i.e. the average energy of a classical harmonic oscillator is kBT, regardless of its frequency.

Planck postulated that the energies of harmonic oscillators could only take on discrete values equal to multiples of a fundamental energy e = hf, where f is the frequency of the harmonic oscillator, i.e. 0, e, 2e, 3e, etc....

Then, En = nenhf n = 0, 1, 2...

Here, h is a fundamental constant, now known as Planck's constant. Although Planck knew of no physical reason for doing this, he is credited with the birth of quantum mechanics.

The new quantum statistics( ) ( )exp / exp /n n B Bf A E k T A nhf k T

Replace the continuous integrals with a discrete sums:

( )0 0

exp /n n Bn n

E E f nhf A nhf k T

( )0 0

exp / 1n Bn n

f A nhf k T

Solving these equations together, one obtains:

( ) ( ) ( )/

exp / 1 exp / 1 exp / 1B B B

hf hcEk T hf k T hc k Te l

e l

Multiplying by D(l), to give....

( )5

( )exp / 1B

hcuhc k T

lll

This is Planck's law

Grey Body Radiation

The calculation of the radiation heat transfer between black surfaces is relatively easy because all the radiant energy that strikes a surface is absorbed.

The main problem is one of determining the geometric shape factor, but once this is accomplished, the calculation of the heat exchange is very simple.

When nonblack bodies are involved, the situation is much more complex, for all the energy striking a surface will not be absorbed; part will be reflected back to another heat-transfer surface, and part may be reflected out of the system entirely.

The problem can become complicated because the radiant energy can be reflected back and forth between the heat-transfer surfaces several times.

The analysis of the problem must take into consideration these multiple reflections if correct conclusions are to be drawn.

We shall assume that all surfaces considered in our analysis are diffuse, gray, and uniform in temperature and that the reflective and emissive properties are constant over the entire surface. Two new terms may be defined:

As shown in Figure 8-24, the radiosity is the sum of the energy emitted and theenergy reflected when no energy is transmitted, or