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

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%.