# Examining Shape Dependence on Small Mild Steel Specimens during Heating Processes

## TL;DR

This paper explores how the shape of small steel specimens affects heating time and efficiency, offering new equations to optimize heating processes.

## Contribution

The study introduces new equations and a shape factor to reduce heating time by 20% for small steel specimens.

## Key findings

- A shape factor of 1.125 was determined between cylindrical and prismatic specimens to calculate optimal heating time.
- New equations were developed to correlate heating time with size, shape, and surface-to-volume ratios.
- A relationship was established between heat storage and shape complexity, improving heat equalization prediction.

## 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.