Technological implications of the Rosenthal solution for a moving point heat source in steady state on a semi-infinite solid

This paper introduces a theoretical framework for the analysis and optimization of melting processes that use focused moving heat sources. Specifically, we consider the Rosenthal solution for a moving point heat source in steady state on a semi-infinite solid. Firstly, we analyze the feasibility of the thermal problem while constraining the melt pool size and aspect ratio. We then express the maximum allowable velocity and the corresponding power as explicit functions of the constraints and material properties. Finally, we examine a wide range of melting processes within a dimensionless framework derived from the above solution. The paper concludes with an application example concerning lack of fusion porosity in powder bed fusion additive manufacturing, which shows the reliability of analytical estimates despite the complexity of the underlying physics. This makes it possible to outline a direct procedure for optimizing the main process parameters given a few basic requirements. Ultimately, the proposed methods are not intended to replace other modeling and experimental approaches, but rather to complement their capabilities and encourage more efficient use of available resources. In addition, reframing seemingly different problems within a common perspective can improve understanding, reveal new levels of similarity, and sometimes even allow for global solutions.