Application of the Finite Pointset Method in Solving Dual-Phase Lag Equation

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.