In a groundbreaking development poised to reshape how we understand and manage heat conduction, researchers have introduced a novel analytical approach within the peridynamic framework. This innovation, detailed in a recent study published in *Archives of Mechanics* (which translates to *Archives of Mechanics*), offers a fresh perspective on solving heat conduction problems with external sources, a critical factor in various industrial applications, particularly in the energy sector.
At the helm of this research is Dr. S. Fan from the School of Mechanics and Construction Engineering at Jinan University, who, along with colleagues, has tackled the complexities of nonlocal heat conduction. The study focuses on transforming inhomogeneous governing equations into homogeneous ones using Duhamel’s principle, a mathematical technique that simplifies the analysis of systems subjected to time-varying external forces.
Dr. Fan explains, “By employing Duhamel’s principle, we were able to derive peridynamic analytical solutions through separation of variables. This approach not only simplifies the problem but also ensures compatibility between the spatial functions in the peridynamic solution and their classical continuum mechanics counterparts.”
The research introduces a nonlocal factor, a crucial innovation that measures the nonlocal effect in heat conduction. This factor is particularly significant in the energy sector, where understanding and managing heat transfer is essential for optimizing performance and efficiency. The study demonstrates that the nonlocal factor appears not only in the exponential term but also in other components of the solution, indicating persistent nonlocal effects even as time approaches infinity.
Dr. Fan elaborates, “Unlike peridynamic systems without external sources, our examples reveal that the nonlocal factor has a more profound and enduring impact. This finding has significant implications for industries relying on heat conduction, as it provides a more accurate and comprehensive understanding of heat transfer processes.”
The study also highlights the varying influence of different kernel functions. The kernel function with n = 0 exhibits the strongest nonlocal influence, while n = 2 results in the weakest nonlocal behavior. This insight could guide the development of more efficient and effective heat conduction systems in the energy sector.
The research not only expands the scope of peridynamic analytical solutions but also offers new insights into nonlocal heat conduction phenomena. These findings provide a valuable foundation for future studies and practical applications in the energy sector, where managing heat transfer is crucial for optimizing performance and efficiency.
As the energy sector continues to evolve, the ability to accurately model and predict heat conduction processes will be increasingly important. This research by Dr. Fan and colleagues represents a significant step forward in this field, offering a powerful tool for understanding and managing heat transfer in a wide range of industrial applications.
In the words of Dr. Fan, “This work significantly expands the scope of peridynamic analytical solutions and offers new insights into nonlocal heat conduction phenomena, providing a valuable foundation for future studies in this field.” With its potential to revolutionize heat conduction modeling, this research is poised to make a lasting impact on the energy sector and beyond.