Examining Shape Dependence on Small Mild Steel Specimens during Heating Processes

Abstract

With regard to the heating technology of small test specimens (D < 1 inch, i.e., 25.4 mm), only a limited amount of data and literature are available for making adequate technological decisions. Heating time of small geometric shapes is influenced by the technological parameters of the furnace, the temperature, the disposition technique in the furnace and the geometric characteristics of the workpiece. How to shorten heating time to achieve a suitable material structure is a vital question, while considerable energy is saved at the same time. Among the geometric characteristics, shape dependence is one of the important aspects that must be taken into account in terms of heating technology. Shape dependence is usually taken into account with empirically produced correction factors, which can result in significant oversizing of heating time, energy-wasting technology and material structure of insufficient fineness. In the course of our work, we investigated and compared the shape dependence of cylindrical and prismatic specimens with the same surface-to-volume ratios, which were combined with surface heat transfer analyses and geometric effect tests to formulate new approximate equations for determining heating time. As a result, we could mathematically derive a relationship between heating time, size and shape of the active surfaces, the correlation of which can shorten heating time by 20%. In addition, a shape factor (1.125) between cylinder and prismatic-shaped specimens was determined, which can be used with the new equation to calculate heating time for similar specimens. At last, a relationship is developed between the amount of heat that can be stored in the body during heat equalization and the complexity of the shape, which can be characterized through ratios depending on heating times and active surfaces in the function of total surface/volume ratio. Based on this relationship it can be determined more precisely when heat equalization occurs; therefore, shorter heating time can be achieved. In conclusion, with the help of this new method, optimal heating time for structural steel components, in the case of small cross-section and weight, can be determined.

Keywords: heat equalization; heat transfer; heating time; shape complexity factor; shape dependence; structural steel.

Figure 1

The assembled measurement system (left), the cylindrical (1), the prism-shaped (2) and the more complicated test specimen (3).

Figure 2

Temperature change on the surface and in the axis line of the test specimen in the case of cylinder and prismatic shapes.

Figure 3

Representation of data suitable for analysis in the case of cylindrical and prismatic specimens.

Figure 4

The measured thicknesses of scale using SEM-EDX: Hitachi S3400N (Hitachi, Berkshire, UK) and Bruker EDX detector (Bruker, Vienna, Austria).

Figure 5

Trends of convective heat transfers in the case of cylindrical (D20 × 60 mm) and prismatic-shaped (20.75 × 20.75 × 49.3) specimens.

Figure 6

Trends of aggregated heat transfers in the case of cylindrical and prismatic-shaped specimens.

Figure 7

The process of heat equalization from the point of view of the difference in the aggregated heat transfer coefficients during the heating.

Figure 8

The heat equalization trends of the cylindrical (blue curve) and prism-shaped (orange curve) specimens during heating.

Figure 9

Interpretation of fulfillment of the surface/volume ratio.

Figure 10

Representation and approximation of heating times with a third-degree polynomial.

Figure 11

Checking the adequacy of the three-degree polynomial by experiment.

Figure 12

The results of the mesh independence tests.

Figure 13

The heat equalization result is in the case of 1046.5 °C of furnace space temperature.

Figure 14

Shape with complex geometry (spindle model) and its heating process.

Figure 15

Heat equalization trends of the different complexity specimens.