lecture 1,2,3,4,5

ME 301

CONDUCTIONANDRADIATIONHEATTRANSFER Md. Mahbubul Islam

Lecturer, Dept. of MechE BUET, Dhaka-1000

Download Course Materials from www.mislam.info/ocw.html

Suggested Reference books

•Heat and Mass transfer –A Practical Approach by Yunus A Cengel •Heat Transfer –A Basic Approach by M. Nekati Ozisik

•Fundamentals of Heat and mass Transfer by Incropera and Dewitt •Heat Transfer by J P Holman

TODAY’STOPIC

•Basic ideas of Radiation Heat Transfer •Thermal Radiation

•Electromagnetic Spectra

THREE BASIC MODES OF HEAT TRANSFER •Conduction

•Convection •Radiation

RADIATION HEAT TRANSFER IN CONTRAST WITH OTHER TWO MODE OF HEAT TRANSFER •Conduction and convection are short range phenomena, Mean Free Path (MFP) is very small •Radiation is a long range phenomena. MFP varies widely from 10-10to 1010 m

•Different in terms of required medium

THUS THERMAL RADIATION HEAT TRANSFER IS IMPORTANT IN •Combustion application (Fire, Furnace, Engines etc)

•Nuclear Reactions (in the sun, fusion reactor etc) •Atmospheric Re-entryspace vehicle

•Others are solar energy collector and the green house effect both due to radiation from high temp sun

EXAMPLE OF LOW TEMP RADIATION HEAT TRANSFER WITH PRESENCE OF OTHER MODE OF HEAT TRANSFER

•A florist used plastic coverings over flower flats. He observed water collecting in the plastic has formed ice a quarter inch thick (at night), when the official temp reading was far above freezing. •So why Ice was formed?

•Its due to the radiation loss occurring between the water covered surface and the very cooled outer space and the evaporative heat loss from the water

EXAMPLE OF LOW TEMP RADIATION HEAT TRANSFER WITH PRESENCE OF OTHER MODE OF HEAT TRANSFER

•Ancient Egyptians made ice by putting water filled porous earthen pot on the roof of the house during clear night.

•So why Ice was formed?

EXAMPLES OF RADIATION HEAT TRANSFER9 •A hot object is enclosed in a evacuated chamber

THERMAL RADIATION MECHANISM

•Electromagnetic Waves–Maxwell’s Electro-magnetic wave theory

•Can easily predict radiative properties of liquid and solids (including tiny particles) •Photons-Max Plank’s Quantum Mechanics

•Can explain radiative properties of gases

Review of previous class

•Introduction to Radiation Heat Transfer •Thermal Radiation Properties and Spectra At the end of the class you will come to know •Radiation properties of Surfaces

•Absorptivity, Reflectivity, Transmissivity, Emissivity •Blackbody, Graybody, Specularbody , Diffusebody •Kirchhoff’s Law

Little more about Radiation basics …

•For gases and for semi-transparent solids and salt crystals at elevated temp, emission is a volumetric phenomenon. That is radiation emitted from a finite volume of matter is the integrated effects of local emission throughout the volume.

•In most solids and liquids radiation emitted from interior surface is strongly absorbed by the adjoining molecules. So radiation that is emitted from solid or liquid originates from molecules that are within a distance of 1μmfrom the exposed surface… so this is a surface phenomenon.

Absorptivity =

=

0≤ α≤ 1

=

0≤ρ≤ 1

=

0≤ τ≤ 1

IRRADIATION, G: Radiation flux incident on a surface is called irradiation. Proof: α+ ρ+ τ= 1

EMISSIVITY

•Emissivity of a surface represents the ratio of the radiation emitted by the surface at a given tempto the radiation emitted by a BLACKBODY at the same temp.

•Emissivity depends on •Body temp

•Wavelength of the emitted energy •Angle of emission

BLACK BODY RADIATION

•Any body above 0 K emits radiation in all directions over a wide range of wavelength. •Amount of radiated energy emitted from a surface at a given wavelength contingent on •material of the body

•surface condition •surface temperature

•Different body may emit different radiation per unit surface area so interest is on the max amount of radiation

DEFINITION OF BLACK BODY

•A blackbody can be defined as a perfect emitter and absorber of radiation. •Any specified temp no body can emit more energy than blackbody •Example-Carbon black, Carborundum, Platinum black, Gold black etc.

•Large isothermal cavity with a small opening. The small opening closely resemble a blackbody. •Is it necessary for a body to be physically black for being considered as BLACKBODY?

•NO

DEFINITION OF GRAY BODY

•If the radiativeproperties α, ρ, τof a body are assumed to be uniform over the entire wavelength spectrum, such body is called gray body.

•This concept is used to simplify the analysis. DEFINITION OF SPECULAR BODY

•If a body is mirror polished in such a way that it reflects the incident ray like mirror. The reflection is called specularreflection and the body is called specularbody.

•In this case angle of incident is equal to angle of reflection.

DEFINITION OF DIFFUSE BODY

•When a body is has certain roughness that the incident radiation is reflected in all direction and it is assumed that for ideal case the reflected radiation is constant for all the angle of reflection and independent of the incident

•This concept is used to simplify the analysis.

EMISSIVE POWER

TOTAL EMISSIVEP OWER,E

E = emitted energy from a surface/time/surface area. SPECTRAL EMISSIVE POWER, EV

•Ev= emitted energy/time/surface area /frequency •In can also be per unit wavelength Eλ.

KIRCHHOFF’S LAW

•At any temp the ratio of total emissive power, E to the total absorptivity,α is a constant for all the substances which are in thermal equilibrium with their environment.

•Derivation of Kirchhoff’s Law

STEPHEN BOLTZMANN LAW

•The emissive power of a blackbody is proportional to the fourth power of the absolute temperature of the body.

E = σT4

•Proof that : BLACKBODY is a perfect emitter.

•Different types of bodies •Kirchhoff’s Law

•S-B Law Today’s Topic •Planck’s Law

•S-B law and Wien’s Displacement Law from Planck’s Law •Various feature of Blackbody radiation

PLANCK’S LAW

•For a black surface bounded by a transparent medium with refractive index n, Planck’s Law is

•DERIVATION OF S-B LAW FROM PLANCK’S LAW.

•DERIVE WIEN’S DISPLACEMENT LAW FROM PLANCK’S LAW.

SALIENT FEATURES OF PLANCK’S LAW

•The emitted radiation is continuous function of wavelength. At any specified temperature it increases reaches a peak and then decreases with increasing wavelength.

•At any wavelength the amount of emitted radiation increases withincreasing temperature

•As temperature increases, the curve shifts to the left to the shorter wavelength region. Consequently a larger fraction of radiation is emitted at shorter wavelengths at higher temperature.

SALIENT FEATURES OF PLANCK’S LAW(CONT.)

•The significant amount of radiation emitted by the sun which may be approximated as blackbody at 5777K, the visible region of spectra..

•The area under the monochromatic emissive power vs wavelength at any temperature gives the rate of radiant energy emitted within the wavelength interval, dλ

Review of previous class •Planck’s Law

•S-B law from Planck’s Law

•Wien’s displacement law from Planck’s Law •Various feature of Blackbody radiation Today’s Topic

•Related problems: Planks Law and S-B law •Blackbody Radiation functions

•PROBLEM

•Determine the maximum wavelength emitted from the earth surface and from the Surface of the sun?

•PROBLEM2

•An isothermal cubical body is suspended in the air.The rate at which the cube emits radiation energy and the spectral black body emissive power are to be determined at 4μm wavelength

•BAND EMISSION AND RADIATION FUNCTION PROBLEM1

•The temperature of the filament to fan incandescent light bulb is 2500K.The fraction of visible radiation emitted by the filament and the wave length at which the emission peaks are to be determined.

SOLID ANGLE

Angle generated at the center of a sphere by any given surface areais known as Solid Angle.The differential solid angle dω= ds/r2

PROBLEM

Determine the solid angle with which the sun is seen from the earth. •Radius of the sun = 6.96 х108 m

•Distance of sun from the earth = 1.496 х1011 m Review of previous class

•Some problems related to S-B Law, Planck’s Law •Blackbody Radiation functions

•Solid angle Today’s Topic •Solid angle (contd.)

•Radiation Intensity and derivation of E = πIb •Hemispherical Emissivity

E = πIb DERIVATION

•Radiation Intensity for emitted radiation Ie(θ, Φ) is defined as the rate at which the radiation energy is emitted in the (θ, Φ) direction per unit area normal to this direction and per unit Solid Angle about this direction.

•In differential form the Emissive energy can be expressed as…

E = πIb DERIVATION

•Now Hemisphere above the surface intercepts all radiation rays emitted by the surface, so the emissive power from the surface to the hemisphere surrounding can be determined by integration. •The intensity of radiation emitted by a surface in general varies with the direction (Especially with zenith angle θ). But in practice for a diffusely emitting surface the intensity of the emitted radiation is independent of direction thus Ie= const.

EMISSIVITY

•Spectral Hemispherical Emissivity can be expressed as a ratio of Spectral emissive power of a real surface to that of the blackbody.

•Average value of emissivity over all wavelengths called Total Hemispherical emissivity.