Heating of massive blanks at different rates in periodic furnaces

Abstract

The heating of massive blanks in periodic furnaces is of great practical and scientific interest. Thorough analysis of the furnace's thermal operation must pre� cede the selection of the heating system, the determi� nation of the burner power at the design stage, the specification of optimal operating parameters, and the identification of the best heating graphs during fur� nace adjustment and operation. Numerical simulation offers an effective means of investigating heating sys� tems (1, 2). In the present work, we consider the heating of cylindrical blanks in periodic furnaces with a tele� scopic hearth (Fig. 1). In the singlestage conditions considered, the heattreatment cycle consists of two periods: (1) heating, with linear increase in the blank's surface temperature at a specified rate; (2) holding at constant surface temperature. The blank's initial tem� perature field is uniform: Tin = 873 K (600°C). The holding temperature is Tf = 1473 K (1200°C). The heating rate in the first period varies from 2 to 200 K/h. The holding time is such that the final temperature difference over the blank's cross section is no more than 50 K. We determine the heatflux density q w at the blank's surface corresponding to the specified heating rate; the temperature difference over the blank's cross sec� tion in the heating period and the holding period; the total residence time of the blank in the furnace; the holding time; and the scale thickness at the end of the heating cycle. Besides the rate of temperature rise in the heating period, the variable is the blank's diameter D (considered at 0.5�m intervals in the range 0.5-3 m). The blank consists of steel 20, whose thermal charac� teristics (and, in particular, its specific heat) depend significantly on the temperature. In simulation, we consider onedimensional non� steady heat conduction in an infinite cylinder (radius R = D/2), with variable thermophysical properties. To this end, we write the nonlinear heatconduction equation