Engineering Mechanics

Proceedings Vol. 31 (2025)

ENGINEERING MECHANICS 2025

Copyright © 2025 Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prague

 

Korczak A.
pages 89 - 92, full text

This study presents the pioneering development of Finite Pointset Method (FPM) for dual-phase lag (DPL) equation in bioheat transfer. The paper explores its mathematical formulation, possible practical applications, and concludes with a numerical example comparing FPM results to analytical solutions, demonstrating the method’s accuracy and versatility. To solve DPL equation, this paper proposes FPM, a meshless numerical technique that eliminates the need for structured meshes. FPM employs scattered nodes and weighted least-squares approximation, making it particularly effective for complex geometries and irregular boundaries. Its Lagrangian formulation simplifies the enforcement of boundary conditions compared to traditional methods. DPL heat conduction model is a key advancement in heat transfer analysis, addressing limitations of classical models like Fourier’s law in handling rapid heat flux and non-equilibrium conditions. By incorporating time delays for both heat flux response and temperature gradient establishment, DPL offers a more accurate depiction of thermal processes in systems with thermal inertia. Its applications extend from biological heat transfer in thermal therapies to micro- and nanotechnology, advanced materials science, and aerospace engineering.

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All papers were reviewed by members of the scientific committee.