A new fractional Cattaneo model for enhancing the thermal performance of photovoltaic panels using heat spreader: energy, exergy, economic and enviroeconomic (4E) analysis

Abstract

A new fractional non-Fourier (Cattaneo) photovoltaic (PV) model is presented to enhance the thermal performance of a PV system combined with a heat spreader (HS). The fractional Cattaneo model is shown to be effective in examining transient processes across the entirety of a PV system, in contrast to the conventional Fourier model’s inability to predict system performance. Consequently, a comparison is conducted between the classical Fourier model with the fractional Fourier and fractional Cattaneo models for the PV system. The impact of using an aluminum heat spreader, with rectangular and trapezoidal shapes, has been developed under hot and cold climate conditions. The findings show that adding a trapezoidal heat spreader reduced the cell temperature by 20 K in summer and 12 K in winter. The reduction in the PV temperature led to an enhancement in daily average power by approximately 28% and 37% in hot and cold weather, respectively. Moreover, economic, exergoeconomic, and enviroeconomic assessment is introduced. The outcomes revealed that the electrical production costs of the rectangular and trapezoidal HS systems are 0.272 and 0.214 $/kWh, respectively, while about 0.286 $/kWh for the conventional PV panel. Based on the environmental study, the estimated CO2 reduction for PV, PV with rectangular HS, and PV with trapezoidal spreader is 0.5504, 0.7704, and 0.8012 tons, respectively. Finally, real experimental data are used to validate the fractional Cattaneo model. The results demonstrate that there is a great fitting with the measured data, with errors in PV power and exergy efficiency of just 0.628% and 3.84%, respectively, whereas their corresponding values for the classical model are 5.72 and 13.13%.

Fractional non-Fourier modeling of laser drilling process

“…Recent observations indicate that the behavior has been more effectively elucidated by employing the fractional extension of the classical Cattaneo equation [14,31,39]. This extension serves as an empirical constitutive equation presented in a one-dimensional form, as illustrated in [56,57]:…”

“…Specifically, Cattaneo [38] developed a non-Fourier model by including a partial time derivative of the heat flux multiplied by the material's thermal relaxation time, combining the Cattaneo equation with the energy equation leads to the hyperbolic heat conduction equation, which makes heat flux and temperature behavior as a wave. Eman et al [39] introduce a fractional non-Fourier PV model that improves PV system thermal performance by accurately capturing transient processes, in contrast to the limitations of the conventional Fourier model. Qi et al [31] employed the time-fractional heat conduction equation of Cattaneo's type to analyze temperature distributions during laser heating.…”