A 10-mm-thick work piece, initially at 25C, is to be annealed at a temperature above 725C for
Question:
A 10-mm-thick work piece, initially at 25°C, is to be annealed at a temperature above 725°C for a period of at least 5 minutes and then cooled. The work piece is opaque and diffuse, and the spectral distribution of its emissivity is shown schematically. Heating is effected in a large furnace with walls and circulating air at 750°C and a convection coefficient of 100 W/m2 ? K. The thermo physical properties of the work piece are p = 2700 kg/m3, c = 885 J/kg ? K, and k = 165 W/m ? K.
(a) Calculate the emissivity and the absorptivity of the work piece when it is placed in the furnace at its initial temperature of 25°C.
(b) Determine the net heat flux into the work piece for this initial condition. What is the corresponding rate of change in temperature, dT/dt, for the work piece?
(c) Using the Too/!i/Radiation/Band Emission model of IHT, calculate and plot the emissivity of the work piece as a function of temperature for the range from 25 to 750°C.
(d) Assuming applicability of the lumped capacitance method, calculate the time required for the work piece to reach 725°C. Use the DER function in IHT to represent the temperature-time derivative in your energy balance. Also use the IHT code of part (c) to represent the emissivity as a function of work piece temperature.
(e) Calculate the time for the work piece to cool from 750°C to a safe-to-touch temperature of 40°C, if the surroundings and cooling air temperature are 25°C and the convection coefficient is 100 W/m2 ? K.
(f) Assuming that the work piece temperature increases from 725°C to 750°C during a 5 minute annealing period, after which cooling is initiated, sketch the temperature history of the work piece from the start of heating to the end of cooling. Identify key features of the process and determine the total time requirement, is the lumped-capacitance method of analysis justified?
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KNOWN Workpiece initially at 25C to be annealed at a temperature above 725C for a period of 5 minutes and then cooled furnace wall temperature and convection conditions cooling surroundings and convec...View the full answer
Fundamentals of Heat and Mass Transfer
ISBN: 978-0471457282
6th Edition
Authors: Incropera, Dewitt, Bergman, Lavine
