Literature review
2.5 Thermal modelling of PV/T collector
expressions for instantaneous thermal efficiency and temperature dependent electrical efficiency.
Dubey and Tiwari (2008)[185] designed and fabricated a PV/T solar water heater of capacity 200 litres and analysed it under varying atmospheric conditions. They neglected the heat capacity of the module in thermal modelling compared to the heat capacity of water in the storage tank. Additionally, they considered one-dimensional quasi-static heat conduction model without accounting for the Ohmic losses in their PV cell. Skoplaki and Palyvos (2009)[186] compiled different expressions for photovoltaic power output and efficiency according to the actual requirements. Torres-lobera and Valkealahti (2014)[187] considered finer details of radiation, including view factors for radiation heat transfer between surfaces to formulate a thermal model considering a mean invariant temperature throughout the module. Based on these observations researchers have developed a dynamic thermal model considering the mean temperature to be invariant throughout the module and took into account all the radiation losses with a proper view factor. Bambrook and Sproul (2016)[188]
developed a steady-state model of PV/T air collector and proposed an expression for temperature variation of PV cells along the length of the collector neglecting heat losses due to radiation and free convection. One of the important works on numerical modelling of a PV/T cell was performed by Slimani et al. (2016)[189]. The authors developed a thermodynamic model considering all major and minor losses. According to Slimani et al.
(2016) [189] the overall energy efficiency increased with the use of a glazing material above the PV cells and an absorber plate above the thermal insulator with the flow of coolant both over and beneath the PV cells.
Amori and Taqi Al-Najjar (2012)[190] developed a mathematical model and applied it to the climatic conditions of Iraq. This model was derived in terms of operating, climatic and design conditions. Their model incorporated some additions and corrections to the radiative and convective heat coefficients for losses at the top surface and the air duct with widely applicable sky temperature correlation. Khelifa et al. (2016)[191] developed a mathematical model for a PV/T water collector and studied temperatures of various layers of PV/T cell and predicted the cooling fluid outlet temperature. The authors also validated the model through an experimental study on a sheet and tube PV/T cell. They reported that coolant flow in the tubes reduced the PV module temperature by 15-20%. Huide et al. (2017)[192] studied three different solar energy systems, namely, PV/T, PV and thermal. They developed simulation models for all three systems. They reported that PV/T system was the most suitable for urban residential buildings and rural housing applications as well because of its high net electricity
output. The set of equations developed in the study considered the thermal resistance of each layer of the PV/T collector.
Simonetti et al. (2018)[193] developed and validated a thermal model for a PV/T cell under a transient regime based on the control volume approach. The PV/T collector considered in the study was an unglazed, sheet-and-tube PV/T cell consisting of a PV module and an aluminium absorber plate glued to the Tedlar layer with copper tubes soldered on the back of the absorber plate. Recently many researchers have attempted various approaches to improve the performance of PV/T cells. Paradis et al. (2018)[194] numerically investigated a new configuration of a PV/T collector used as an evaporator in a CO2 trans-critical heat pump system. The solar absorber plate made of stainless steel was embedded to the back of the monocrystalline silicon PV cell, stainless steel tubes were arranged in a serpentine fashion and bonded to the solar absorber plate with two-phase CO2 flow inside the tubes. Their results showed that heat dissipation and uniformity of temperature distribution across the wall was better for copper pipe compared to that for the stainless steel. It has been reported that cooling with CO2 reduces the mean temperature from 320.6 K to 294 K and the overall collector efficiency reported reaching as high as 72.3%. Another important innovation in the field of PV/T collector performance enhancement is an integration of a micro-channel heat pipe array to the rear surface of the PV module. Modjinou et al. (2017)[195] proposed a PV/T module comprising of c-Si solar cells and wide microchannel heat pipes (MHP) filled with acetone as the heat transfer fluid. The MHP-PV/T module was investigated using both numerical (MATLAB) and experimental methods. The authors reported the daily thermal and electrical efficiencies to be 50.7% and 7.6%, respectively. Rejeb et al.(2020)[196] developed a transient two-dimension multi-physics model for the PV/T sheet-tube collector. The state variable variations were predicted by the finite volume method. The model has taken into consideration the impact of antireflective and low-emissivity coating and thermal resistance between the absorber plate and the cooling fluid. The addition of an anti-reflective coating on the photovoltaic module leads to an increase of both the electrical and thermal performances.
Yu et al. (2020)[197] proposed a novel 2D irradiance - temperature coupling model that can predict the irradiance and temperature of every single PV cell. Results of the study indicate that the non-uniform distribution of irradiance exerted a significant effect on photovoltaic efficiency but a modest influence on thermal efficiency. The set of equations derived in the proposed model incorporated the thermal resistance of the individual layer of the PV/T collector.
The thermal models reviewed in this section could be suitable for the dynamic system simulation applications. However, the models did not consider the Ohmic heat generation in the PV layer and the role of therm contact resistance between different layers of the PV/T collector.
As evident from the literature studied, extensive numerical and experimental studies were carried out on PV/T systems. Although the literature can provide important tools for simulations of PV/T collectors, the deviations observed between experimental and numerical values are significant under outdoor conditions. Based on the study it has been found that the deviation in results of the experimental and numerical investigation may be due to non- consideration of the effect of thermal contact resistance and Ohmic loss at PV layer on the performance of a PV/T system in the developed models. Hence, it becomes essential to develop an accurate and comprehensive mathematical model to predict the performance of a PV/T system effectively.