## 1 Introduction  
Urban heat islands (UHIs) form due to the loss of natural land cover in modern cities, which is replaced by dense concentrations of paved roads, buildings, and other materials that can absorb and retain heat. This effect not only drives up the cost of energy for things such as air conditioning, for example, but also boosts the levels of air pollution and the danger of heat-related illnesses, as well as mortality rates. Paved surfaces are a significant contributor to the formation of urban heat islands (UHIs) because they occupy around 30 to 45 percent of the total area of cities, making paved surfaces one of the largest contributors to UHIs [1]. As UHIs are a contributing factor to global warming, the United Nations has designated it as a key element of UNESCO SDG No. 13, aimed at addressing climate change and its consequences. To limit global warming to 1.5 \({}^{\circ}\)C above pre-industrial levels, the global emissions need to be reduced by 45% below 2010 levels by 2030. Utilizing pavement solar collectors (PSCs) as a source of renewable energy, i.e., solar energy, as an alternative to burning fossil fuels and lowering greenhouse gas emissions is one way to address this issue. The most common method for constructing PSC involves burying a pipe network beneath the surface of a pavement's uppermost levels. The surface of the pavement is able to absorb solar radiation on days when the sun is out. The energy is subsequently transferred to the fluid flowing through the pipes, which can be utilized for immediate heating or stored for future use [2]. Reducing the amount of thermal stress that might lead to rutting in concrete and asphalt pavement lowers the pavement's temperature and lengthens its service life [3]. Hence, the implementation of PSC potentially reduces some of the detrimental consequences being brought to the environment. For example, the PCS system can be employed as an alternative approach to conventional winter road maintenance by providing heat to the pavement, making it an effective method for snow removal during the winter season. The conventional method for winter maintenance of roads consumes between 0.6 and 1.7 million tonnes of salt and sand annually [4]. Soil erosion is induced by road salting, which also poisons water supplies and threatens animals [5]. There have been many investigations into how to make PCS technology more effective. For instance, [PERSON] and [PERSON] (2014) devised three models with varying distances between the pipes (200 mm, 150 mm, and 100 mm) with a constant pipe diameter (20 mm) and depth (75 mm) from the pavement surface to determine how the distance affected heat extraction. It was discovered that when the pipe spacing was reduced from 200 mm to 150 mm while keeping the same pipe depth, the surface temperature decreased because of the increased heat absorption from the surface of the water flow in the pipes, and the outlet temperature increased from 320 K to 322 K. In addition, the author reported that serpentine pipes were more effective at collecting heat compared with straight pipes in asphalt pavement [6]. Meanwhile, [PERSON] et al. suggested that a pipe depth of 300 mm is recommended for ice melting in the winter [7]. Additionally, [PERSON] et al. 's (2022) research demonstrated that increasing the pipe length from 50 m to 200 m leads to a 52% reduction in the overall power extraction per meter of the pipe, dropping from 2.45 kW/m to 1.17 kW/m [8]. Besides pipe spacing, length, and depth, studies show that adjusting the albedo and the fluid flow rate can improve the PSC's efficiency by up to 49% [9]. For this reason, it is crucial to achieve maximum heat harvesting efficiency during the design phase by configuring and determining the best pipe length for the PSCs. The presence of pipes inside the pavement brings benefits because it reduces the temperature and reduces the thermal pressure on the pavement [10].