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The primary purpose of this work is to analyze the intermediate behaviors in the thermal response of an absorber plate of a flat-plate solar collector, considering the non-Fourier effects. The Caputo fractional derivative is applied and the time-fractional single-phase-lag (FSPL) model is presented to study the non-diffusive process in the heat conduction through the absorber plates. In addition, the effect of variations in different parameters such as Vernotte number, dimensionless time, and thermo-physical parameter are studied on the temperature response of absorber plates. It has been apparent that the thermo-physical parameter can significantly affect the thermal behaviors of absorber plates, and that for small quantities of this parameter, the temperature distribution follows the wave-like behaviors. To validate this model, the fractional model is presented for a thin metal film, and non-diffusive heat conduction has been investigated in detail, and the results of the fractional model are compared to those of the dual-phase-lag (DPL) model, which proves the precision of the fractional model proposed in this work. Also, the effect of variation in the time rate of the initial condition has been conducted on the thermal distribution of metal films. It has been discussed that the fractional model proposed can describe a wide range of behavior in thermal response, including diffusive-like and wave-like behaviors. In addition, it has been found that the non-Fourier effects are quite remarkable at earlier times, so it would be important to consider such effects when the time instances are smaller than the relaxation time.
Mozafarifard et al. (Sat,) studied this question.