Only 10% of the energy dissipated by the tungsten filament of an incandescent lamp is in the form of useful visible light. Consider a 100 W lamp with a 10 cm spherical glass bulb. Assuming an emissivity of 0.85 for the glass and ambient air temperature of 20°C, what is the temperature of the glass bulb?

Question

GIVEN

• A spherical glass light bulb in air

• Bulb power consumption (P) = 100 W

• 10% of energy is in the form of visible light

• Diameter (D) = 10 cm = 0.1 m

• Bulb emissivity (?) = 0.85

• Ambient temperature (T?) = 20°C = 293 K

FIND

• The temperature of the glass bulb (Ts)

ASSUMPTIONS

• Ambient air is till

• The bulb has reached steady state

• The surrounding behave as a black body at T?

SKETCH



PROPERTIES AND CONSTANTS

Boltzmann constant (?) = 5.7 × 10–8 W/(m2 K4).

Answer 1

The rate of heat transfer by convection and radiation from the bulb must equal the rate of heat generation.



Since the fluid properties depend on the surface temperature, an iterative procedure must be used. For the first iteration, let Ts = 100°C = 373 K.

for dry air at the mean temperature of 60°C

Thermal expansion coefficient (?) = 0.00300 1/K

Thermal conductivity (k) = 0.0279 W/(m K)

Kinematic viscosity (?) = 19.4 × 10–6 m2/s

Prandtl number (Pr) = 0.71

The characteristic length for a 3-D body is given



The Grashof and Rayleigh numbers are



correlates data for 3-D bodies including spheres for 200 < RaL+ < 1.5 × 109



The rate of heat transfer by convection and radiation must equal the heat generation rate



Checking the units then eliminating them for clarity



By trial and error: Ts = 460 K = 187°C.

The results of further iterations are tabulated below



The bulb temperature, therefore, is approximately 182°C.

COMMENTS

Note that radiative transfer accounts for about 66% of the total heat transfer from the bulb.