## 1 Introduction  
Rising energy demand is a major challenge for the global economy. Meeting the energy needs of today's world is becoming harder. As solar energy becomes increasingly affordable, it presents a remarkable opportunity to supplant a significant portion of the fossil fuels currently driving our electricity generation. This shift is crucial for tackling global climate change. Recently, the global interest in renewable energy has surged due to the depletion of the world's energy supplies. Solar energy is a prominent source of clean power, with solar collector systems that heat water receiving significant attention [1]. Solar air heaters are commonly used to dry farm products, warm greenhouses and homes, and in industrial drying processes [2]. Using a rough surface beneath the absorber enhances heat and fluid flow efficiency. Most methods improve performance by increasing surface area, inhibiting boundary layer development, and creating more turbulence. However, these often cause greater pressure drops and resistance, requiring more power for pumping [3]. Some research on solar air heaters (SAHs) has focused on developing models to improve thermal efficiency by understanding and enhancing the convective heat transfer between the absorber plate and the working air. Since the Nusselt number represents the efficiency of heat transfer due to convection, studies have aimed to relate it to various design and operating parameters like air flow rate, absorber plate geometry, and surface roughness. Also, CFD simulations are widely used to predict the Nusselt number for various SAH designs, enabling researchers to simulate heat transfer under different airflow conditions and absorber plate geometries. Such simulations help in understanding how parameters like plate corrugation angle, pitch, and air inlet temperature impact the Nusselt number and overall efficiency. The performance of the ribbed solar air heater is greatly influenced by factors like the relative roughness pitch (P/e) and the relative roughness height (e/D). For improved results, it is important that the roughness height is greater than the thickness of the transition sub-layer [4]. [PERSON] and [PERSON] numerically studied the turbulent flow in a solar-assisted semi-circular cross-section air heater with transversely intentionally roughened surfaces. It has been suggested that a relative height of roughness of 0.042 is the threshold for good thermo-hydraulic performance. It is observed that the relative roughness height has a considerable effect on the Nusselt number and friction factor [5]. [PERSON] conducted an experimental investigation to determine the effect of rib designs on friction and heat transfer in a square duct. The results showed that the triangular-shaped rib outperformed all other rib profiles in terms of heat transfer performance for the same rib pitch and rib height [6]. [PERSON] and [PERSON] carried out a study to explore how different levels of surface roughness affect heat transfer, friction, and overall thermal-hydraulic efficiency. Within the tested range, the highest ratio of heat transfer, known as the Nusselt number ratio, was 2.73. This peak value occurred when the roughness spacing ratio was 7.14, with the fluid flow measured at a Reynolds number of 15,000 [7]. [PERSON] et al. carried out a CFD analysis on the thermal efficiency of a solar air heater with a square section rough absorber panel. They used the RNG k-\(\epsilon\) turbulence model and focused on 16 different roughness patterns with Reynolds numbers of 20,000 and 4000. Variations in roughness parameters significantly affected the Nusselt number and the friction factor, as seen by the comparison with a smooth duct. Moreover, the Nusselt number was found to rise as the Reynolds number increased [8]. In the study conducted by [PERSON], an artificially rough solar-assisted air heater design with a square, semicircular, and triangular cross-section was subjected to numerical analysis.