Energy has been the driving force for industrialization and worldwide economic growth. The rapid exhaustion of fossil fuel reserves, which predominate the existing energy structure, necessitates the immediate development of alternative renewable energy sources. Solar energy is an abundant, renewable, and non-polluting resource [1,2]. An STC is an efficient method for capturing and transforming solar energy into thermal energy for heating purposes [3,4]. The optimal design of an STC guarantees maximum solar energy utilization; it captures solar radiation and conveys the heat to the flowing air. Nevertheless, the limited effectiveness of an STC is attributed to the low heat absorption of the collector and the inadequate thermal conductivity of air. Improving the heat transfer rate via active and passive techniques is a principal solution investigated by researchers to tackle these difficulties [5,6]. Among these two methods, passive methods have gained prominence because of their simplicity and lack of external power requirements compared with active ones. The passive techniques include the use of treated surfaces [7], artificial rough surfaces [8], extended surfaces [9], turbulators [10], nanofluids [11], and swirl flow devices [12,13].

Artificially rough surfaces on the absorber plates are an efficient passive method for improving the heat transfer in STCs. By disturbing the laminar sub-layer and generating turbulence, they markedly enhance the convective heat transfer relative to other passive techniques, such as extended surfaces or swirl flow devices. Their design is straightforward, economical, and facilitates manufacturing, rendering them suitable for extensive, budget-friendly applications. In contrast to more intricate methods, artificially roughened surfaces result in low-pressure losses, attaining an improved equilibrium between heat transmission and pumping power. Common designs on the absorber plates include ribs [14], grooved surfaces [15], dimples [16], and protrusions [17].

Ribs have certain benefits compared to other artificial roughness methods. Their geometry is highly customizable, allowing for optimization under specific operating conditions while balancing the growth of heat transfer and pressure drop. Ribs enhance the effective efficiency compared to more disruptive approaches such as protrusions, ensuring a practical balance between performance and energy losses [18]. The increase in the heat transfer is calculated in terms of the Nusselt number ($Nu$) which is a ratio of the convective to conductive heat transfer from the absorber plate to a fluid. The artificial roughness results in the enhancement of friction which is measured in terms of the friction factor ($f$). The Reynold number ($Re$) provides information about the type of flow.

Thakur and Thakur [19] have examined the effect of W-shaped ribs. W-shaped ribs offer distinct benefits over V-shaped ribs by generating four secondary flow vortices rather than two. These vortices augment turbulence and more effectively disrupt the thermal barrier layer, resulting in enhanced heat transfer. Wang et al. [20] have used S-shaped ribs with gaps to enhance the performance of STCs; the S-shape creates flow reattachment zones and secondary vortices, more effectively breaking laminar layers. The S-shaped ribs enhance the thermal efficiency by as much as 48%, achieving a maximum Nu increase of 5.42. Shayan et al. [21] also found that by using an S-shaped rib, the S-shape induces flow reattachment zones, hence enhancing the heat transmission dramatically. It attains a Nu of 4.875 times greater than that of a smooth duct. The characteristics of S-shaped roughness provide it with an efficient design for STCs, optimizing the heat transfer enhancement while minimizing friction losses.

Experimental investigations necessitate the extensive testing of all the parameters of the SAH with roughness ribs, making the process both expensive and time intensive. Moreover, conducting an exhaustive analysis of the influence of every variable on the heat transmission, friction factor, and performance of the heat exchanger is thorough and rigorous. Consequently, an optimization methodology should be utilized to quantitatively forecast the diverse elements influencing the system performance and ascertain the principal criteria for an ideal design. Plenty of researchers have focused on improving and optimizing the performance of various STCs through diverse methodologies. MCDM methodologies, like VIKOR, MOORA, MABAC, and TOPSIS, provide the concurrent optimization of opposing objectives, such as heat transfer, pressure drop, and effective efficiency, providing equitable solutions. These methods effectively investigate the design space by examining many factors, including roughness geometry and the $Re$, with fewer experimental trials, thus conserving time and money. The amalgamation of analytical and experimental methodologies, exemplified by hybrid techniques, guarantees elevated precision and efficient decision making, facilitating optimal SAH designs with negligible validation discrepancies. Benhamza et al. [22] investigated the optimization of a finned STC for food drying through a mix of experimental analysis and response surface methodology (RSM). The optimization method aims to attain three primary objectives: thermal efficiency, output air temperature, and exergetic improvement potential (IP). The research determines the ideal design parameters as a length-to-width ratio of 1.28, an air duct height of 0.067 m, and 49 fins. Under these conditions, the SAH attains a thermal efficiency of 51.78% and an IP of 1397.34 W, indicating a 15.76% increase in thermal efficiency and a 19.33% improvement in IP relative to baseline designs. These findings indicate considerable potential for enhancing the SAH efficacy in food drying applications. Mohanty et al. [23] examined the optimization of a three-sided roughened STC via a combination of RSM and Multi-Objective Particle Swarm Optimization (MOPSO). Critical parameters, such as the $Re,$ mass flow rate, and relative roughness pitch, have been changed to optimize thermal efficiency and the $Nu.$ The optimization determined the optimal performance at the $Re$ ranging from 12,000 to 13,000 and a relative roughness pitch of 10 mm, resulting in a thermal efficiency between 63% and 75% and a $Nu$ between 65 and 80. A confirmatory test corroborated the results with a 3.39% margin of error. This hybrid optimization method provides significant insights for upgrading SAH designs and improving energy efficiency while reducing the pressure drop. Kumar et al. [24] used hybrid CRITIC-COPRAS MCDM techniques to examine the effectiveness of an impingement jet solar air heater. Mishra et al. [25] examined the optimization of geometric parameters for multi-arc protrusion obstacles in an impingement jet solar air path utilizing the AHP-TOPSIS MCDM methodology. Chauhan and Kim [26] optimized the effectiveness of an STC through the application of the VIKOR approach, an MCDM tool. The entropy approach is initially employed to allocate weights to various characteristics, indicating their significance. VIKOR subsequently rates potential absorber designs utilizing utility and regret metrics, locating the best options that reconcile heat transfer enhancement with pressure loss minimization. The research found that dimpled and protruded arc-shaped absorbers markedly enhance thermal and exergetic efficiency compared to traditional designs. Singh et al. [27] performed an extensive evaluation of the multi-objective optimization via the ratio analysis (MOORA) method and its fuzzy extensions, emphasizing applications in many domains, such as SAH optimization. MOORA evaluates alternatives by optimizing advantageous criteria and minimizing detrimental ones, providing an effective method for balancing trade-offs in decision making. In solar air heaters, MOORA is employed to optimize parameters such as the absorber plate design, airflow rate, and thermal efficiency, hence enhancing the performance through the assessment of numerous conflicting criteria. Its incorporation of entropy or fuzzy methodologies improves the decision making in uncertain conditions. Goel et al. [28] enhanced the efficiency of an SAH by incorporating hybrid artificial roughness beneath the absorber plate, which integrates transverse ribs and discrete inclined ribs. This study used RSM to analyze the impacts of four critical parameters: relative roughness height, pitch, attack angle, and the$Re.$Empirical models for the $Nu$, $f,$ and thermo-hydraulic performance ($\eta$) were constructed via regression analysis. The AHP-WASPAS approach determines an ideal configuration, corroborated by experimental validation. The sensitivity analysis and rank reversal tests validate the resilience of the proposed decision framework, notwithstanding a slight susceptibility to alterations in weights. The AHP-WASPAS method is a hybrid MCDM strategy that integrates the Analytical Hierarchy Process and the Weighted Aggregated Sum Product Assessment. This combination harnesses the advantages of both methodologies to enhance the decision-making precision and dependability, especially for intricate issues with several competing criteria. Salman et al. [29] examined analytically the performance enhancement of a jet-impinged solar air collector, including dimple-roughened absorber plates. The study used a hybrid MCDM approach to determine the ideal geometric and flow characteristics that enhance heat transfer and reduce frictional losses. The ideal design was established with a dimple height ratio of 0.027, a pitch ratio of 0.27, and an arc angle of 60° at the $Re$ of 15,000.

The published literature recommends the availability of AHP and MABAC methods as decision-making techniques in various domains. MCDM techniques have been utilized extensively to explore the optimum design parameters of artificial roughness. However, their implication in the design optimization of STC roughened with SSRs has yet to be examined. In the current analytic study, the findings of previous experimental work [30] were used to optimize the SSR parameters leading to the best performance of roughened STC. This earlier study [30] established the fundamental impact of S-shaped ribs on heat transfer and flow dynamics, demonstrating significant improvements in ${\mathit{N}\mathit{u}}_{\mathit{R}\mathit{p}}$ and thermal efficiency. However, this came at the cost of enhanced friction. The enhancement in heat transfer and friction factors has been comprehensively studied at various mass flow rates(m) with air as working fluid. However, none of the design considerations satisfy the desirable outcome of achieving the best heat transfer with minimal friction increase. So, in the present analytical examination more analysis is carried out to select the most appropriate combination of design parameters resulting in the best performance of roughened STC utilizing hydrid MCDM techniques. The novelty of the present work lies in the fact that the present analytic examination is able to recognize/verify the suitable combination of design parameters leading to best performance of STC roughened with SSRs. The main objective of present analytical examination is to support designers and researchers in the domain of solar heating systems in the identification and selection of appropriate design parameters. The ${\mathit{P}}_{\mathit{R}}/{\mathit{e}}_{\mathit{R}\mathit{H}}$ spacing between ribs influences reattachment points of flow and directly affects the heat transfer rates. Relative roughness height (${\mathit{e}}_{\mathit{R}\mathit{H}}/{\mathit{D}}_{\mathit{h}\mathit{d}}$) affects turbulence intensity and friction. Arc angle modifies the secondary flows. The ${\mathit{W}}_{\mathit{D}\mathit{u}\mathit{c}\mathit{t}}/{\mathit{w}}_{\mathit{R}\mathit{S}}$ ratio is used to quantify the extent of artificial roughness applied to surfaces. This roughness enhances heat transfer by creating turbulence and disrupting the laminar sub-layer. The research highlights the use of a hybrid MCDM technique, AHP-MABAC, to select the best combination of roughness parameters—${\mathit{P}}_{\mathit{R}}/{\mathit{e}}_{\mathit{R}\mathit{H}}$, ${\mathit{W}}_{\mathit{D}\mathit{u}\mathit{c}\mathit{t}}/{\mathit{w}}_{\mathit{R}\mathit{S}},$ ${\mathit{e}}_{\mathit{R}\mathit{H}}/{\mathit{D}}_{\mathit{h}\mathit{d}}$, and ${\mathit{\alpha }}_{\mathit{A}\mathit{r}\mathit{c}}$. This combination resulted in the optimal performance of the roughened STC. This study emphasizes the possibility of integrating STC with SSRs to markedly improve performance of SAHs, applicable in energy-efficient heating systems.