Annealing, an important step ¡n semiconductor materials processing, can be accomplished by rapidly healingthe silicon wafer to a high temperature for a short period of time. The schematic shows a method involving the use of a hot plate operating at an elevated temperature T h . The wafer, initially at a temperature of T w , i , is suddenly positioned at a gap separation distanceL from the hot plate. The purpose of the analysis is tocompare the heat fluxes by conduction through the gaswithin the gap and by radiation exchange between thehot plate and the cool wafer. The initial time rate ofchange in the temperature of the wafer, ( d t w / d t ) t , is alsoof interest. Approximating the surfaces of the hot plateand the wafer as blackbodies and assuming their diameter D to be much larger than the spacing L . the radiativeheat flux may be expressed as q ″ r a d = σ ( T h 4 − T w 4 ) .The silicon wafer has a thickness of d = 0.78 mm , adensity of 2700 kg/ni’. and a specific heat of 875 J/kg ⋅ K . The thermal conductivity of the gas in the gapis 0 .0436 W/m ⋅ K . (a) For T h = 600 ° C and T w , i = 20 ° C , calculate the radiative heat (lux and the heat flux by conductionacross a gap distance of L = 0.2 mm . Also determine the value of ( d t w / d t ) t , resulting from each ofthe heating modes. (b) For gap distances of 0.2, 0.5, and 1 .0 mm, determinethe heat fluxes and temperature-time change as afunction of the hot plate temperature 300 ≤ T h ≤ 1300 ° C . Display results graphically. Comment on the relative importance of the two heat transfer modes and the effect of the gap distance onthe heating process. Under what conditions could awater he heated to 900°C in less than 10 s?
Annealing, an important step ¡n semiconductor materials processing, can be accomplished by rapidly healingthe silicon wafer to a high temperature for a short period of time. The schematic shows a method involving the use of a hot plate operating at an elevated temperature T h . The wafer, initially at a temperature of T w , i , is suddenly positioned at a gap separation distanceL from the hot plate. The purpose of the analysis is tocompare the heat fluxes by conduction through the gaswithin the gap and by radiation exchange between thehot plate and the cool wafer. The initial time rate ofchange in the temperature of the wafer, ( d t w / d t ) t , is alsoof interest. Approximating the surfaces of the hot plateand the wafer as blackbodies and assuming their diameter D to be much larger than the spacing L . the radiativeheat flux may be expressed as q ″ r a d = σ ( T h 4 − T w 4 ) .The silicon wafer has a thickness of d = 0.78 mm , adensity of 2700 kg/ni’. and a specific heat of 875 J/kg ⋅ K . The thermal conductivity of the gas in the gapis 0 .0436 W/m ⋅ K . (a) For T h = 600 ° C and T w , i = 20 ° C , calculate the radiative heat (lux and the heat flux by conductionacross a gap distance of L = 0.2 mm . Also determine the value of ( d t w / d t ) t , resulting from each ofthe heating modes. (b) For gap distances of 0.2, 0.5, and 1 .0 mm, determinethe heat fluxes and temperature-time change as afunction of the hot plate temperature 300 ≤ T h ≤ 1300 ° C . Display results graphically. Comment on the relative importance of the two heat transfer modes and the effect of the gap distance onthe heating process. Under what conditions could awater he heated to 900°C in less than 10 s?
Solution Summary: The author calculates the heat flux due to radiation and conduction across the gap and the temperature of the wafer.
Annealing, an important step ¡n semiconductor materials processing, can be accomplished by rapidly healingthe silicon wafer to a high temperature for a short period of time. The schematic shows a method involving the use of a hot plate operating at an elevated temperature
T
h
. The wafer, initially at a temperature of
T
w
,
i
, is suddenly positioned at a gap separation distanceL from the hot plate. The purpose of the analysis is tocompare the heat fluxes by conduction through the gaswithin the gap and by radiation exchange between thehot plate and the cool wafer. The initial time rate ofchange in the temperature of the wafer,
(
d
t
w
/
d
t
)
t
, is alsoof interest. Approximating the surfaces of the hot plateand the wafer as blackbodies and assuming their diameter D to be much larger than the spacing L. the radiativeheat flux may be expressed as
q
″
r
a
d
=
σ
(
T
h
4
−
T
w
4
)
.The silicon wafer has a thickness of
d
=
0.78
mm
, adensity of 2700 kg/ni’. and a specific heat of
875
J/kg
⋅
K
. The thermal conductivity of the gas in the gapis
0
.0436
W/m
⋅
K
.
(a) For
T
h
=
600
°
C
and
T
w
,
i
=
20
°
C
, calculate the radiative heat (lux and the heat flux by conductionacross a gap distance of
L
=
0.2
mm
. Also determine the value of
(
d
t
w
/
d
t
)
t
, resulting from each ofthe heating modes. (b) For gap distances of 0.2, 0.5, and 1 .0 mm, determinethe heat fluxes and temperature-time change as afunction of the hot plate temperature
300
≤
T
h
≤
1300
°
C
. Display results graphically. Comment on the relative importance of the two heat transfer modes and the effect of the gap distance onthe heating process. Under what conditions could awater he heated to 900°C in less than 10 s?
4) In a tempering process, glass plate, which is initially at a uniform temperatureTi, is cooled by suddenly reducing the temperature of both surfaces to Ts Theplate is 20 mm thick, and the glass has a thermal diffusivity of 6x 10-7 m2/s.(a) How long will it take for the midplane temperature to achieve 50% of itsmaximum possible temperature reduction? Ans t= 63 s(b) If (Ti -T5) = 300°C, what is the maximum temperature gradient in the glass atthe above time? Ans. -2.36 104 °C/m.
An underwater sonar that maps the ocean bathymetry is encapsulated in a sphere with a diameter of 85 mm. During operation, the sonar generates heat at a rate of 300W. What is the sonar surface temperature when it’s located in a water column where the temperature is 15o C and the water current is 1 m/sec?
The sonar was pulled out of the water without turning it off, thus, it was still working. The air temperature was 15o C and the air speed was 3 m/sec. What was the sonar surface temperature? Was there any reason for concern?
Recent studies show that the major energy consumption
in Fijian villages is wood which is used
for cooking on open fires. Typical consumption of wood
is 1 kg/person/day. (a) Estimate the heat
energy required to boil a 2 litre pot full of water.
Assuming this to be the cooking requirement of
each
person, compare this with the heat content of the
wood, and thus estimate the thermal
efficiency of the open fire. (b) How much timber has to
be felled each year to cook for a village
of 200 people ? Assuming systematic replanting, what
area of crop must the village therefore
set aside for fuel use if it is not to make a net
deforestation ?
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