An annealing process shown uses a hot plate operating at an elevated temperature

Question

An annealing process shown uses a hot plate operating at an elevated temperature of 635 C. The wafer, initially at a temperature of 28 C, is suddenly positioned at a gap separation of 0.3 mm from the hot plate. The emissivity of both the hot plate and the wafer is 0.63. The silicon wafer has a thickness of 0.74 mm, a density of 2700 kg/m3, and a specific heat of 875 J/kg*K. The thermal conductivity of the gas in the gap is 0.060 W/m*K. The wafer is insulated at the bottom. (a) Calculate the radiative heat flux across the gap. b) Calculate heat flux by conduction across the gap.

Explanation / Answer

A)Rate of energy radiation of an object (T is given by qo = A s ? T4 If the object is in a chamber with wall temperature of Tw and surrounding air of Ta, then the object receives heat radiation from both wall and air. qwall to object = A s ? Tw4 qair to object = A s ? Ta4 Hence, the net q for object to air and wall is: qnet = A s ? (T4-Ta4-Tw4) B) q = k A dT / s (1) where A = heat transfer area (m2, ft2) k = thermal conductivity of the material (W/m.K or W/m oC, Btu/(hr oF ft2/ft)) dT = temperature difference across the material (K or oC, oF) s = material thickness (m, ft)

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