PROBLEM 1.41
KNOWN: Hot platetype 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 temperaturetime change for gap separations of 0.2, 0.5 and 1.0 mm for hot
plate temperatures 300 < Th < 1300¡ÆC. 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¡ÆC in less than 10
seconds?
SCHEMATIC:
ASSUMPTIONS: (1) Steadystate conditions for flux calculations, (2) Diameter of hot plate and
wafer much larger than gap spacing, approximating plane, infinite planes, (3) Onedimensional
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 =
:
:
