Heat transfer dynamics in the absorber plates of a flat-plate solar collector using both Fourier and revised non-Fourier analyses

Recent years have seen an increased focus on non-Fourier heat conduction models for simulating microscale and ultrafast transient thermal processes. These models are particularly relevant in scenarios where classical Fourier theory fails to capture non-equilibrium transport mechanisms, thermal wave propagation, and phase-lag effects that occur in heat and mass transfer at small temporal and spatial scales. Motivated by these limitations, this study focuses on an analytical investigation of both Fourier and non-Fourier heat conduction phenomena in the absorber plate of a flat-plate solar collector. To accomplish this, we apply the single-phase-lag model, incorporating the overall loss coefficient, to the energy equation to examine non-Fourier heat transfer behaviour. Analyzing a recurring heat transfer module of the collector plate, the corresponding parabolic and hyperbolic energy equations are then solved using the method of separation of variables. We validate our analytical results through numerical simulations based on the finite difference method. Additionally, we analyse the influence of key parameters, including the Vernotte number, dimensionless time, and thermo-geometric parameter, on the temperature response of the absorber plate. Our proposed model is further validated by comparison with published results from Kundu and Lee [ 40 ], who did not account for the phase lag associated with the loss coefficient. But the single-phase lag model developed by Cattaneo–Vernotte is essential for the thermal analysis of an absorber plate and cannot be ignored, as was the case in previous work. A significant difference in temperature distribution is observed, underscoring the importance of phase lag effects in accurately predicting the transient thermal response of the absorber plate and the transient thermal performance of flat-plate solar collectors. The current results indicate that higher Vernotte numbers and thermo-geometric parameters significantly affect the temperature response and the delay in heat propagation within the absorber plate. For example, the most significant difference observed is 98.69% in the average non-Fourier temperature response compared to its Fourier values at a Fourier number of 0.1 and a Ve of 2.0, as predicted by the current model for convective heat transfer to the working fluid across the evaluated parameter range. The largest deviation in thermal response occurs on the plate under isothermal conditions, specifically at the point where the working fluid absorbs energy. This maximum difference reaches 94.87%, as indicated by the published model [ 40 ] for Ve = 1 and Fo = 0.1. Finally, as this analysis presents an accurate phase-lag model compared to the published model, it is thus essential for predicting correct results.