RADIATIVE HEAT TRANSFER
Prabal TalukdarAssociate ProfessorAssociate Professor
Department of Mechanical EngineeringIIT DelhiIIT Delhi
E-mail: [email protected]
MECH/IITD
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
MECH/IITD
g• Dominant in high temperature applications
Spectrum of Electro-magnetic RadiationRadiation
MECH/IITD
Thermal radiation falls in the range of 10-1-102 µm of the Electro-magnetic spectrum.
Solid angleg
• dω= dAn/r2 = (r2 sinθ dθ dΦ)/r2 =sinθ dθ dΦdω dAn/r (r sinθ dθ dΦ)/r sinθ dθ dΦ
MECH/IITD
Solid Angle for a Hemisphereg p
2di2ddid2/ 2/2
θθφθθ∫ ∫∫ ∫π ππ
sr2dsin2ddsindw0 0h 0
π=θθπ=φθθ= ∫ ∫∫ ∫
MECH/IITD
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.
MECH/IITD
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:∞
MECH/IITD
λλ= ∫∞
λ d)(EE0