RADIATIVE HEAT TRANSFER

Prabal TalukdarAssociate ProfessorAssociate Professor

Department of Mechanical EngineeringIIT DelhiIIT Delhi

E-mail: prabal@mech.iitd.ac.in

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Introduction

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Thermal Radiation

• Radiation heat transfer can take place in a vacuum. It pdoes not need a medium unlike conduction/convection

• Thermal radiation is the stream of electromagnetic di ti itt d b t i l tit t f itradiation emitted by a material entity on account of its

finite absolute temperature • Infrared radiation from a common household radiator orInfrared radiation from a common household radiator or

electric heater is an example of thermal radiation, as is the light emitted by a glowing incandescent light bulb. Th l di ti i t d h h t f th• Thermal radiation is generated when heat from the movement of electrons within atoms is converted to electromagnetic radiation

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g• Dominant in high temperature applications

Spectrum of Electro-magnetic RadiationRadiation

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Thermal radiation falls in the range of 10-1-102 µm of the Electro-magnetic spectrum.

Emission Process

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Volumetric Phenomenon Surface phenomenon

Emission by a surfacey

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Gray Diffuse

Solid angleg

Plane Angle Solid Angle

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Solid angleg

• dω= dAn/r2 = (r2 sinθ dθ dΦ)/r2 =sinθ dθ dΦdω dAn/r (r sinθ dθ dΦ)/r sinθ dθ dΦ

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Solid Angle for a Hemisphereg p

2di2ddid2/ 2/2

θθφθθ∫ ∫∫ ∫π ππ

sr2dsin2ddsindw0 0h 0

π=θθπ=φθθ= ∫ ∫∫ ∫

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Spectral Intensityp y

• Iλ,e(λ,θ,φ)=dq/(dA1cos θ.dω.dλ)• Iλ,e is the rate at which radiant energy is emitted at the wave length λ

in the (θ, φ) direction, per unit area of emitting surface normal to this direction, per unit solid angle about this direction and per unit wavelength interval dλ about λ.

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Heat Flux

• dqλ=dq/dλ—rate at which radiation of wavelength λ leaves dA1 and passes through dAn (unit: W/µm)

• dqλ= Iλ,e(λ,θ, φ) dA1cos θ dω• Spectral radiation flux associated with dA is• Spectral radiation flux associated with dA1is

S f

φθθθφθλ= λλ ddsincos),,(Idq e,"

• Spectral heat flux associated with emission into hypothetical hemisphere above dA1 is

∫∫π

λ

π

λ φθθθφθλ=λ2/

e

2" ddsincos),,(I)(q

• Total heat flux associated with emissions in all directions and at all wavelengths is then

∫∫ λλ φφ0

e,0

),,()(q

MECH/IITD∫∞

λ λλ=0

"" d)(qq

Emissive Power

• Emissive power is the amount of radiation• Emissive power is the amount of radiation emitted per unit surface area

• Spectral hemispherical emissive powerSpectral , hemispherical emissive power

• Eλ(λ)(W/m2.µm)= ∫∫π

λ

π

φθθθφθλ2/

e,

2

ddsincos),,(I

– Eλ →based on actual surface area– Iλ e→based on projected surface area

∫∫00

λ,e p j

• Total hemispherical Emissive power:∞

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λλ= ∫∞

λ d)(EE0

Relation between Emissive Power and Intensityand Intensity

∫∫ππ 2/2

• Eλ= ∫∫ λ φθθθφθλ0

e,0

ddsincos),,(I

• For a diffuse surface, Iλ(λ,θ,φ)= Iλ(λ)

∫∫ππ 2/2

Eλ =

E = π I (λ) Spectral basis

∫∫λ φθθθλ00

e, ddsincos)(I

Eλ= π Iλ,e(λ) Spectral basis

E=πIe Total basis

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E πIe Total basis