Various research on the heat loss of the roller

In steady-state heat conduction problems, thermal conductivity (λ) plays a critical role in determining the rate and efficiency of heat transfer. This is clearly illustrated in Figure 3. The steel roller, which has a high thermal conductivity, allows for relatively fast heat transfer. Although it operates in a temperature range below 800°C, the areas outside the kiln wall still exhibit thermal behavior similar to that of porcelain rollers used in high-temperature zones. These regions experience higher temperatures, making the thermal properties of the material even more significant. When simulating the heat dissipation of a porcelain roller, variable thermal conductivity is typically considered. However, as shown in Figure 3, the temperature distribution along the roller within the kiln wall remains largely linear. This can be explained by Fourier’s law: $ q = \lambda \frac{dT}{dx} $. In steady-state conditions, the heat flux through any cross-section is constant. For the steel roller, the large λ value results in a smaller temperature gradient, leading to a nearly flat temperature curve. On the other hand, the porcelain roller has a much lower thermal conductivity, and its variation with temperature is minimal. As a result, small changes in λ have little impact on the overall temperature profile. This observation suggests that using an average thermal conductivity value during calculations can simplify the process without significantly compromising accuracy. Additionally, the temperature at different points along the roller, including the ends, varies depending on the location within the kiln. As temperature increases, the steel roller shows a more pronounced response compared to the porcelain one. In the higher temperature region where the steel roller is located, the temperature rises sharply, reaching up to around 250°C, while the surrounding area may reach nearly 100°C. This leads to substantial heat loss from the steel roller to the environment. In contrast, the porcelain roller, with its low thermal conductivity, is used in the high-temperature zone of the kiln. This results in a significant temperature difference between the inside and outside of the kiln wall. Such a large temperature gradient can induce considerable thermal stress within the porcelain roller, increasing the risk of deformation or cracking. These issues can ultimately reduce the service life of the porcelain roller. Therefore, in practical applications, careful consideration must be given to these thermal effects to ensure reliable performance and longevity of the components.

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