Fundamentals of Heat and Mass Transfer – Problem 1.57

A furnace for processing semiconductor materials is formed by a silicon carbide chamber that is zone-heated on the top section and cooled on the lower section. With the elevator in the lowest position, a robot arm inserts the silicon wafer on the mounting pins. In a production operation, the wafer is rapidly moved toward the hot zone to achieve the temperature-time history required for the process recipe. In this position, the top and bottom sur- faces of the wafer exchange radiation with the hot and cool zones, respectively, of the chamber. The zone temperatures are T_h = 1500 K and T_c = 330 K, and the emissivity and thickness of the wafer are ε = 0.65 and d = 0.78 mm, respectively. With the ambient gas at T_∞ = 700 K, convection coefficients at the upper and lower surfaces of the wafer are 8 and 4 W/m²-K, respectively. The silicon wafer has a density of 2700 kg/m³ and a specific heat of 875 J/kg-K. For an initial condition corresponding to a wafer temperature of T_wi = 300 K and the position of the wafer shown schematically, determine the corresponding time rate of change of the wafer temperature, (dT_w /dt).

All sample problem and notes are based off the following textbook: Fundamentals of Heat and Mass Transfer Seventh Edition

ISBN-13: 9780470501979

ISBN-10: 0470501979

Edition: 7

Author: Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera, David P. DeWitt

Publication date: 2011

Publisher: Wiley

Format: Hardcover 1072 pages