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열전달 6판 해법 (Heat and mass transfer) incropera , wiley ch1 11장

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[해법] 열전달 6판(Heat and mass transfer) - incropera, wiley ch1-11장

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PROBLEM 1.41
KNOWN: Hot plate-type wafer thermal processing tool based upon heat transfer modes by
conduction through gas within the gap and by radiation exchange across gap.
FIND: (a) Radiative and conduction heat fluxes across gap for specified hot plate and wafer
temperatures and gap separation; initial time rate of change in wafer temperature for each mode, and
(b) heat fluxes and initial temperature-time change for gap separations of 0.2, 0.5 and 1.0 mm for hot
plate temperatures 300 < Th < 1300°C. Comment on the relative importance of the modes and the
influence of the gap distance. Under what conditions could a wafer be heated to 900°C in less than 10
seconds?
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions for flux calculations, (2) Diameter of hot plate and
wafer much larger than gap spacing, approximating plane, infinite planes, (3) One-dimensional
conduction through gas, (4) Hot plate and wafer are blackbodies, (5) Negligible heat losses from wafer
backside, and (6) Wafer temperature is uniform at the onset of heating.
PROPERTIES: Wafer: r = 2700 kg/m3, c = 875 J/kg×K; Gas in gap: k = 0.0436 W/m×K.
ANALYSIS: (a) The radiative heat flux between the hot plate and wafer for Th =
:
:


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