Natural Convection and Direct
Radiation Heat Transfer from an
Electric Light Bulb
Aim
 Calculate local natural convection heat-transfer
coefficients for a sphere
 Calculate the local boundary layer
 Calculate experimental mean Nusselt number
 Compare experimental and theoretical Nusselt
numbers
Apparatus
 Spherical silica glass light
bulb with tungsten filament
 Eight thermocouples
 Voltmeter,
 Ammeter
 Experimental applied
wattages ranged from
approximately 5 W to 250W
 DO NOT Exceed more than
260 watt
Theory
 Assumptions made:
 True sphere
 Voltage delivered to filament is radiated uniformly
 Heat flux from wattage absorbed by bulb is of uniform
magnitude
 Temperature difference between surrounding air and
ambient environment approximated by linear function
Radiant Heat of the Bulb
A perfect blackbody is a surface that
reflects nothing and emits pure thermal
radiation.
The Tungsten filament of a light bulb is
modeled as a good blackbody radiator.
Because all light from the filament is
thermal radiation and almost none of it is
reflected from other sources.
The curve for 2,600°C shows that
radiation is emitted over the whole range
of visible light.
 The total power emitted as thermal radiation by a
blackbody depends on temperature (T) and surface area
(A).
 The Surface temperature of the filament would be equal
to the blackbody temperature if the filament behave as
perfect radiator.
 However, real surfaces usually emit less than the
blackbody power, typically between 10 and 90 percent.
The relation between the blackbody temperature and and the surface
Temperature could be derived from Stefan-Boltzmann formula
TBB4 = eTs4
Where the Emissivity indicates the deviation of an object from a perfect blackbody radiator
It has been determined with an optical pyrometer that when 256 watts is
delivered to the tungsten filament that its blackbody temperature TBBr is
3400°R. Since the hemispherical emissivity of tungsten is low (ε = 0.230
Table 2 on labbook) the true temperature of the tungsten coil is
Ts =
TBBr
e
1
4
=
3400
0.693
You can determine the blackbody temperature at specified power supplied
æPö
TBB = TBBr ç ÷
è Pr ø
1
4
The waves radiated from the filament will either transmit through the glass as light
or be absorbed by the glass and lost through radiation and convection. The glass
bulb transmits all of the radiation only between 0.35 micron (lower bound) and 2.70
micron (higher bound).
By using the Planck’s Law, the fraction of wave transmitted throw the glass could be
determined.
fL a lLTBB
fH a lH TBB
Planck Radiation Functions Please see Table 1
Thus the fraction of the watts delivered to the filament, which is transmitted by the glass is: f
f = fH - fL
The remainder fraction of watts which is absorbed by the glass
and is lost by convection and radiation from the glass = 1-f
Pdelivered = (1- f )P
Since the glass bulb is modeled as a sphere, so the temperature profile on
the surface is symmetric. By knowing the area of the ideal glass bulb (0.315
ft2), the thermal flux leaving the bulb can be determined
q
P
´ 3.412
= Y = deliverd
= Btu hr -1 ft -2
A
0.315
The flux is transported out both by radiation and natural convection
Y = hT (T -T¥ )
hT = total heat transfer coefficient
hT = hc + hR
where
hc = the convection transfer coefficient and
hR = the radiation transfer coefficient
and
T = the localized bulb temperature which is a function of position (in °Rankine )
T∞ is a the ambient temperature in the laboratory
The radiation Heat Transfer Coefficient hR is a function of
the difference between the surface temperature of the
glass and the ambient temperature and the emissivity of
the silica glass.
éæ T ö4 æ T ö4 ù
êç
÷ -ç ¥ ÷ ú
êëè 100 ø è 100 ø úû
hR = 0.173* e glas *
T - T¥
εglass = 0.876 (independent of temperature for all practical purposes)
In this experiment,
Prandtal Number, Nusselt Number, and Grashofe Number may be calculated.
However, to calculate these numbers,
1It is necessary to determine the mean heat transfer
coefficients.
This can be done by applying the Simpson’s Rule using the
heat transfer coefficient (hC) at several positions on the bulb.
2-
Determine the mean air film temperature Tf of the
boundary layer
Tf = T¥ +
DT
2
Where DT
The mean temperature difference (glass surface temperatureambient temperature) may be computed by dividing the mean
total heat flux by hT obtained from Simpsons
DT = Y hT = Y (hc + hR )
Mean Nusselt Number
-
Nu =
hc r
k
Where r is the radius of the bulb
Nusselt number can also be approximated using McAdams
equation
Nu = 0.53 (Gr Pr)
Gr = Grashof Number =
1
4
gbr 2 DTR3
m2
Pr = Prandtl Number =
C pm
k
Although natural convection is mostly turbulent flow of fluid,
But there is always a layer near the surface that is laminar
(T – Tair)
T
Bulb glass
Tair
The approximate thickness of the boundary layer may
be found by the following equation
For local position
d=
k
hC
where k is the thermal conductivity and  is the
boundary layer thickness.
 Increasing temperature yields more radiation (all wavelengths)
 Increasing temperature shifts the peak of the energy-flux curve
to lower wavelengths/higher frequencies
Literature Cited
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Bird RB, Stewart WE, Lightfoot EN. Transport Phenomena, Wiley, 2002.
Chen G. 2003. Nanoscale heat transfer and information technology. Rohsenow
Symposium on Future Trends in Heat Transfer at MIT on May 16, 2003. Accessed
May 01, 2006 at <http://web.mit.edu/hmtl/www/papers/CHEN.pdf>.
Incropera FP, DeWitt DP. Introduction to Heat Transfer, Wiley, 1985.
Saddawi, S. 2006. Natural convection and radiation heat transfer from an electric
light bulb, Lab Manual, 36-44.
Wikipedia. 2005. Black body spectrum as a function of wavelength. Accessed April
30, 2006 at <http://en.wikipedia.org/wiki/Image:Bbs.jpg>.