Unified analytical framework for non-Fourier heat conduction in graded cylindrical media: Applications to perovskite solar cells and borehole heat exchangers

This study develops the first unified analytical framework for transient, non-Fourier heat conduction in functionally graded (FG) cylindrical media within the dual-phase-lag (DPL) paradigm. Through rigorous mathematical analysis, radial exponential grading is shown to yield a governing equation that cannot be reduced to closed-form solutions, thereby motivating a new modelling strategy. Accordingly, for the first time, we develop an axially graded DPL formulation with height-dependent Robin boundary conditions. This approach restores analytical solvability while incorporating exponential grading and non-Fourier effects. The analytical solution is expressed as an explicit, demonstrably convergent eigenfunction expansion and validated against finite-element simulations across ultrashort and long-time regimes. The obtained framework is then demonstrated through applications to two contrasting renewable energy technologies: solar perovskite absorbers and borehole heat exchangers (BHE). In perovskite absorbers, upward Br − grading causes classical Fourier theory to overestimate the power-conversion efficiency by up to 1.91%. By contrast, downward grading induces a 3.5% temperature overshoot and a 5.10% efficiency loss at high irradiance relative to the DPL–FGM model. In borehole heat exchangers, axial grading strongly affects long-term subsurface heat retention. At F o ≈ 1600 , isotropic media reach temperatures approximately 33.33% higher than graded configurations under Neumann boundary conditions. Conversely, FGMs maintain wall temperatures more than 27% lower across all boundary regimes. Overall, the framework connects non-Fourier heat transfer from micro- to macro-scales and enables accurate analytical modelling of graded cylindrical domains.