Sphere-to-Sphere Radiative Transfer Coefficient for Packed Sphere System

Abstract

Rapid sintering is one of the most attractive metalworking technologies due to its ability to fabricate the final product with different microstructure in an economical manner. During this process, the high heating rate would induce a great thermal gradient to the sintering part. Such temperature differences affect the microstructure of the product, which in turn leads to the occurrence of microstructure defects. However, for this non-isothermal sintering, the present Radiative Transfer Equation approach or Units/Cells approach cannot effectively compute the temperature distributions inside the porous media, so as to predict the part defects. Cumbersome computations are needed for the Radiative Transfer Equation approach. For the Units/Cells approach, the use of regular assembly in the model limits the analysis of complex packed sphere systems. This study seeks to simplify the entire computational process for different packed sphere systems. By introducing a Radiative Transfer Coefficient (RTC) approach, the computation of radiative heat transfer within the porous bed can be enhanced. The newly introduced Radiative Transfer Coefficient is defined as the ratio of radiative energy exchange, including direct and indirect exchange, from the emitting sphere to the receiving sphere, which is a function of the system microstructure and radiative properties. A set of energy-balanced algebraic equations can then be established. With an appropriate initial energy guess for each sphere, these equations can be solved by the Gauss-Seidel iteration scheme, thereby computing the radiative heat transfer in packed sphere systems with different microstructures and radiative properties. The temperature for each sphere can therefore be computed right away. This model has been validated in different perspectives. With this RTC approach, the overall computational time required is significantly shorter, providing a set of fine-resolution temperature solution.