Skip to main content An official website of the United States government Here's how you know Here's how you know Official websites use .gov A .gov website belongs to an official government organization in the United States. Secure .gov websites use HTTPS A lock ( Lock Locked padlock icon ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites. Search Log in Dashboard Publications Account settings Log out Search… Search NCBI Primary site navigation Search Logged in as: Dashboard Publications Account settings Log in Search PMC Full-Text Archive Search in PMC Journal List User Guide PERMALINK Copy As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsement of, or agreement with, the contents by NLM or the National Institutes of Health. Learn more: PMC Disclaimer | PMC Copyright Notice Sci Rep . 2026 Mar 2;16:11779. doi: 10.1038/s41598-026-41922-4 Search in PMC Search in PubMed View in NLM Catalog Add to search Thermal analysis of flat plate solar air heater system with radiation reflectors and W-shaped roughness: artificial neural network & machine learning approach Piyush Kumar Jain Piyush Kumar Jain 1 Department of Mechanical Engineering, Bansal Institute of Science & Technology, Bhopal, India Find articles by Piyush Kumar Jain 1 , Kawal Lal Kurrey Kawal Lal Kurrey 2 Department of Industrial and Production Engineering, School of Studies of Engineering & Technology, Bilaspur, India Find articles by Kawal Lal Kurrey 2 , Vikas Pandey Vikas Pandey 3 Department of Electrical Engineering, Babu Banarasi Das University, Lucknow, Uttar Pradesh 226028 India Find articles by Vikas Pandey 3 , Jitesh R Shinde Jitesh R Shinde 4 Department of Electronics Engineering (VLSI Design & Technology), CSMSS Chh. Shahu College of Engineering, Chh. Sambhajinagar (Aurangabad), Maharashtra India Find articles by Jitesh R Shinde 4 , Abhishek Narayan Tripathi Abhishek Narayan Tripathi 5 School of Electronics Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu India Find articles by Abhishek Narayan Tripathi 5 , Niraj Kumar Dewangan Niraj Kumar Dewangan 6 Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India Find articles by Niraj Kumar Dewangan 6, ✉ Author information Article notes Copyright and License information 1 Department of Mechanical Engineering, Bansal Institute of Science & Technology, Bhopal, India 2 Department of Industrial and Production Engineering, School of Studies of Engineering & Technology, Bilaspur, India 3 Department of Electrical Engineering, Babu Banarasi Das University, Lucknow, Uttar Pradesh 226028 India 4 Department of Electronics Engineering (VLSI Design & Technology), CSMSS Chh. Shahu College of Engineering, Chh. Sambhajinagar (Aurangabad), Maharashtra India 5 School of Electronics Engineering, Vellore Institute of Technology, Vellore, Tamil Nadu India 6 Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India ✉ Corresponding author. Received 2025 Dec 29; Accepted 2026 Feb 23; Collection date 2026. © The Author(s) 2026 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ . PMC Copyright notice PMCID: PMC13065819 PMID: 41772045 Abstract The lower thermal behavior of solar-based thermal systems limits the contribution of solar systems to meet current energy demand of industries. The Flat Plate Solar Air Heater (FPSAH) is extensively utilized in many applications requiring reasonable heat but struggles from inherent limitation in convective heat release and mediocre efficiency. In this study, the challenges are addressed with a novel means of dual mode augmented technique. This mode integrated absorber surface of the FPSAH system by introducing two radiation reflectors on either edge of the rectangular channel. Primarily these reflectors forward back the solar irradiance over the absorber plate, thus increasing the actual solar flux. Simultaneously, a W-shaped artificial rib roughness pattern is merged on the underneath (air-side) of the absorber plate. This coarseness is intended to persuade measured flow disorder inside the channel that disrupt the boundary layer development and may consequently augment convective heat transfer. Experimental testing is conducted with different combinations of roughened absorber surface and radiation reflectors. The performance enhancement is evaluated in terms of Nusselt number ( Nu ) and thermal efficiency of the FPSAH system. The maximum Nu achieved is 1.63 times higher using a set of radiation reflectors along with W-shaped roughness on the absorber surface compared to the plain configuration without radiation reflector. Finally, artificial neural network (ANN) and machine learning (ML) algorithms were used to predict Reynolds number in each set of experiments. A very good curve fitting was achieved by the Robust Regression algorithm with for the testing dataset and by the Random Forest Regression algorithm for ML. Keywords: Solar air heater, Radiation reflectors, W-shaped roughness, Artificial neural network, Machine learning, Thermal efficiency, Nusselt number Subject terms: Energy science and technology, Engineering, Mathematics and computing, Physics Introduction The lower thermal features and wide use of solar-based thermal systems in moderate temperature applications draw attention for modifying the systems to give enhanced thermal performance 1 − 3 . The solar energy-based air heater, i.e., FPSAH system, is used for various low-temperature applications such as crop drying, space heating, and water distillation. The simple operational design, low maintenance cost, and silent operation with environmentally friendly behavior are the key advantages of the FPSAH system. The main hindrance in using FPSAH is its low heat transfer (HT) coefficient between the absorber plate and flowing air. Conservation of solar radiation with maximum heat loss adversely affects thermal efficiency 4 . Utilizing solar air heaters contributes to lowering the overall carbon footprint of a building or process and aligns with global efforts toward sustainable energy solutions and climate action. A decreasing heat release rate elevates the plate’s temperature, thereby leading to increased heat losses to the atmosphere. Investigators have persistently attempted to enhance the HT coefficient of the FPSAH system through diverse methodologies, such as corrugated surfaces with V-patterns 5 – 7 , trapezoidal corrugated surfaces 8 , and extended surfaces (fins) to maximize thermal performance by increasing surface area for convective heat transfer 9 – 11 . However, these approaches often result in higher power consumption for air movement. Several studies introduced artificial roughness in the form of ribs to generate turbulence adjacent to the heat transfer surface, minimizing friction while increasing turbulence inside the duct. Circular ribs were initially investigated 12 , followed by transverse patterns 13 , 14 , inclined patterns 15 , 16 , and V-patterns, which were found most efficient 17 . Modifications of V-patterns, such as discrete V-patterns, staggered elements, and gaps, have been extensively studied 11 , 18 – 22 . Similarly, arc patterns and broken arc designs were explored 23 , 24 . Multi-pattern rib roughness configurations were also examined for thermal behavior improvements 25 . Some approaches focused on modifying ducts using radiation reflectors to augment thermal characteristics. A square duct FPSAH system with radiation reflectors showed an increase in HT coefficient and Nusselt number up to 44% compared to a plain configuration 26 . The W-pattern of roughness demonstrated better thermal performance than simple V-patterns. W-shaped ribs provide flow separation, reattachment, and secondary flow generation. At lower flow velocities or Reynolds numbers ( ), flow conditions are insufficient to distort the thermal boundary layer, reducing heat discharge 27 . Selecting an optimum attack angle ( ) of in W-shaped ribs enhances secondary vortices and critical flow behavior near the surface, improving thermal performance 27 . W-pattern roughness also reduces pressure drop compared to transverse patterns. A single-pass FPSAH system using rib roughness and reflectors was experimentally examined, showing increased thermal efficiency with higher air mass flow rates 28 . Studies on solar towers with Rankine cycles using thermodynamic laws and numerical techniques in GNU Octave have also been reported 29 . The collective effort to conclude various approaches of using rib roughness in FPSAH systems were conducted 22 , 50 to identify the scope to conduct the study in prescribed area of solar dryer systems and to observe the different approaches to proceed the studies further. From the literature, it is evident that no effort has been made to combine artificial roughness with radiation reflectors for FPSAH systems. Radiation reflectors redirect solar rays toward the absorber surface, raising its temperature, while artificial roughness interrupts thermal boundary layer formation, enhancing convective heat transfer. Numerous methods to expect the thermal behavior of solar dryer 35 , 40 were also implemented earlier in many studies. In addition to above research work a different aspect of filling nano fluid under different climatic conditions were also conducted to analyze FPSAH system 51 . The novelty of research lies in the cooperative integration of distinct thermal enhancement techniques specifically, W-shaped rib roughness and radiation reflectors to investigate their combined impact on convective-radiative heat transfer performance. This approach addresses the complex interplay between fluid-side convective augmentation and radiative heat transfer control, a combination that has not been extensively studied in a unified manner. Rib roughness, a passive heat transfer augmentation technique, is widely recognized for its ability to disrupt thermal boundary layers and induce turbulence, thereby increasing the Nusselt number (Nu). The Nusselt number is a dimensionless ratio quantifying the enhancement of heat transfer due to convection relative to pure conduction. Additionally, artificial neural networks (ANN) and machine learning (ML) algorithms are employed to predict Nusselt number variations, making the study more effective and innovative. In recent years, ANN and ML have gained prominence in engineering applications. The key objectives of present research work are to broadly examine the shared influence of radiation reflectors over the absorber plate roughened with W-shaped rib roughness on the convective-radiative heat discharge augmentation in FPSAH system. It also demands a detailed analysis over W shaped rib rough absorber plate that how it contributes in enrichment of Nusselt Number (Nu). Another equally important objective is to develop and implement healthy extrapolative models for Nusselt number disparities using advanced machine learning (ML) algorithms, particularly artificial neural networks (ANN). Machine learning (ML) Machine Learning (ML) has been widely applied in various engineering domains. For instance, ML is used in welding processes such as friction stir welding for classification and defect examination, and in resistance spot welding to predict mechanical properties 30 – 32 . Various heat transfer processes have been optimized using robust method optimization techniques 33 , 34 . The multi-layer perceptron (MLP) architecture of neural models is among the most utilized in solar air heater applications 35 . For solar thermal collectors, several ML techniques such as Random Forest and Support Vector Regression have been employed for predicting hourly energy output 36 . ML algorithms empower machines to learn directly from data rather than relying on predefined equations 37 . ML approaches are broadly categorized into two branches: supervised learning and unsupervised learning. Supervised learning includes classification and regression, while unsupervised learning covers clustering applications. In recent decades, ML algorithms have expanded significantly across various fields. Ensemble learning, which combines predictions from multiple ML algorithms, often yields more accurate results than a single model 38 . Robust Regression is a type of regression analysis designed to overcome limitations of traditional parametric and non-parametric methods. It serves as an alternative to least squares, particularly when influential observations distort the data. This method attempts to determine the relationship between independent and dependent variables 39 . In this study, both Random Forest and Robust Regression techniques are employed to predict Nusselt number ( Nu ) values during experiments. Artificial neural network (ANN) modelling A neural network is a computational model that mimics the hierarchical structure of neurons by connecting nodes in layers 40 . It organizes information into conceptual levels, and its activity is defined by the connectivity and significance of these connections. During training, the weights are updated periodically according to a learning algorithm until the network performs the task accurately. The ANN approach is highly effective for problems involving nonlinear and complex relationships among variables. In the Multi-Layer Perceptron (MLP) architecture, neurons are arranged into layers: an input layer, an output layer, and one or more hidden layers. These layers consist of interconnected neurons 41 , as illustrated in Fig. 1 . Fig. 1. Open in a new tab ANN architecture used for predicting Nu and . One of the objectives of this research is to develop an ANN model capable of predicting the Nusselt number ( Nu ) and thermal efficiency ( ) in a heat exchanger as a function of various parameters. Details of experimental testing Experimental test facility The experimental analysis of W-shaped rib roughness with radiation reflectors was performed using an outdoor test rig shown in Fig. 2 a. The measurement of the rectangular duct was obtained using ASHRAE standards 42 . Plywood of 18 mm thickness was used to fabricate the sidewalls of the SAH duct, which were insulated externally because of its cost effectiveness and ease of fabrication with a required property of insulation. The top of the duct was covered with an absorber surface made of galvanized iron with dimensions of 600 mm 500 mm and a thickness of 1.2 mm. An absorber plate with a thickness of 1.2 mm has a significant influence on both thermal inertia and heat removal characteristics due to its limited conductive properties. The volumetric heat capacity of a 1.2 mm thick absorber plate is relatively low, resulting in reduced thermal inertia and a rapid temperature response to variations in solar irradiance 1 . Transparent glass was used to cover the absorber surface to reduce reflective solar radiation. Fig. 2. Open in a new tab ( a ) Schematic experimental test rig ( b ) Outdoor experimental test rig. The duct design was modified by attaching radiation reflectors at the edges of the testing duct. The placement of reflectors at the edge minimizes the heat loss from the sides of absorber plate and also redirected the radiations. The reflectors at the edge may enable more even temperature spreading over the plate and augmented convective heat release by modifying edge effects associated to increased heat loss. The mirrored reflector frame was hinged to the base duct and could be adjusted at any angle to reflect maximum possible radiation onto the exposed surface of the FPSAH system. The length of the mirrored reflectors was maintained equal to the test section (600 mm) with a height of 300 mm. The length of mirrored reflectors is maintained the same as the test section i.e. 600 mm with a height of 300 mm to direct maximum possible solar radiations on the active surface of absorber plate. This would maximize the potential for solar energy collection across the full length of the heat transfer zone. The tilt angle is maintained as from the horizontal to receive the solar radiation after getting deflected from the reflectors, an optimum position of reflector is essential for redirecting maximum possible radiations over the absorber plate. The key factors that influence the angle are position of sun throughout the day and geometry of collector and reflector. The tilt angle was maintained at from the horizontal to receive solar radiation after deflection from the reflectors. A glass mirror of 0.3 mm thickness with a polished surface was used. The absorber surface of FPSAH system combined with additional reflectors increases the solar flux over the flat surface as compare to the direct radiation alone, that improve the overall thermal characteristics of the surface. The reflectors redirect the solar radiations and distributed across the absorber surface uniformly. The even distribution of heat flux, lesser thermal gradients and better overall stability of system may possibly accomplish through optimum geometry of reflector. As recommended in prior studies, the duct was designed with an entrance length of and an exit length of 43 . The selected inlet length of 550 mm facilitates the development of a fully developed airflow profile, while the 275 mm outlet section incorporates a mixing chamber positioned after the calculated distance from the test section. The mixing chamber contains uniformly spaced baffles that enhance turbulence and ensure a uniform temperature distribution at the duct outlet 44 . Axial flow fans were employed to maintain forced convection across the prescribed mass-flow-rate range and were integrated with a speed-regulation controller to adjust airflow as needed. Table 1 summarizes the dimensional specifications and components utilized in the experimental setup. Table 1. Dimensions of experimental test setup. Duct sections Dimensions (mm) Inlet section 550 Test section 600 Exit section 275 Duct height ( H ) 25 Duct width ( W ) 500 Total duct length ( L ) 1425 Open in a new tab Procedure and measurement The experimental testing using the W-shaped roughened absorber surface of the FPSAH system was performed on clear sunny days between 10:00 a.m. and 1:30 p.m. A pyranometer was used to measure the heat flux received by the absorber surface during the investigation. The axial flow fan produced forced convection with different mass flow rates inside the duct. Wind velocity at the exit end was measured using an anemometer. Temperature readings were taken at several points along the duct using calibrated T-type thermocouple wires, and the readings were recorded by a digital data logger. A dimmer stat linked with the fan controlled the mass flow rate of air inside the duct. All data were noted under steady-state conditions, defined as the state where the data does not change for a definite period at a given location. The instruments used in the testing, such as the pyranometer and anemometer, were of standard make and model. Thermocouples were calibrated using a simple method by comparing the temperature of the same substance measured with a thermometer and a thermocouple connected to a digital temperature data logger. Additionally, the data obtained for the smooth absorber surface using similar instruments fell within the acceptable range, ensuring the standardization of instruments used. Experimentation The experimental test facility was located in an open area free from obstacles to receive direct solar radiation. The experimentation was conducted in April; hence, the best-suited timing to obtain intense solar radiation was between 10:00 a.m. and 1:30 p.m. The experiment was conducted at Rajasthan Technical University, Kota (Rajasthan), located at a latitude of North and longitude East, with an elevation of 271 meters above sea level. Air temperature at the inlet and outlet, along with the average temperature of the absorber surface, was utilized to assess various performance parameters. The study began with scrutiny of components and instruments used. The glass cover was cleaned, and all connections were checked before switching on the axial flow fan. The mirrored radiation reflectors were adjusted by tilting them to redirect maximum solar radiation onto the horizontal flat absorber surface. A dimmer stat linked with the fan was attuned to maintain the predefined flow proportion in the duct. The data collected from the experimental investigation included inlet air temperature ( ), average outlet air temperature ( ), mean absorber plate temperature ( ), heat flux of solar radiation ( T ), and wind velocity ( V ). Initially, inlet and outlet air temperatures were noted to calculate the mean bulk temperature of air ( ), which is the simple arithmetic mean of the inlet and outlet temperatures: 1 The average plate temperature ( ) was sensed at six different points along the centerline of the absorber plate. The Reynolds number ( Re ) was calculated using the air velocity ( V ) at the exit and the hydraulic diameter of the duct ( ): 2 where the hydraulic diameter is defined as: 3 The flow rate in terms of mass ( ) was calculated as: 4 where A is the rectangular duct cross-sectional area, . Using Eqs. ( 5 ) and ( 6 ), the air’s further usable heat gain ( ) and its heat transfer coefficient ( h ) were evaluated [45]: 5 6 Finally, the thermal performance parameter of the FPSAH system, the Nusselt number ( Nu ), was calculated as: 7 Investigated roughness and flow parameters The experimental investigation was performed with different configurations: plain absorber surfaces, roughened absorber surfaces, and radiation reflectors. The present work involves an experimental analysis of an FPSAH system roughened with a W-shaped artificial roughness design combined with radiation reflectors to augment the thermal characteristics of the system. A galvanized iron (GI) sheet of 1 mm thickness was used to fabricate the roughness geometry and served as the absorber surface in the present experimental testing. Galvanized iron is steel coated with zinc oxide, which improves its properties and functionality such as durability and strength. The density ( ) of steel ranges from 7.85 to 8.15 g/cm 3 . The thermal conductivity ( k ) of GI is 204.2 W/mK and specific heat ( C ) is 896 J/kg·K. Hence, the thermal diffusivity ( ) can be calculated as: 8 A circular copper wire having a cross-sectional diameter of 2 mm was used to design the roughness due to its higher thermal conductivity. The roughness was fabricated with basic geometrical parameters optimized in 21 . The basic geometrical parameters such as roughness pitch ( q ) of 20 mm and attack angle ( ) of were considered to design the roughness. The dimensionless parameters considered in the present experimental testing are q / h , , and . Similar values of geometrical parameters were used to fabricate the W-shaped roughness design 21 . The optimum parameters that give maximum rise in thermal features of the FPSAH system are , , and . The copper ribs were first cut into pieces of prescribed length. The complete detailed design with optimum geometrical dimensions was marked on the surface of the absorber plate, and then copper pieces were glued over the surface to fabricate the roughened absorber plate for testing purposes. The details of investigated parameters used in the design are presented in Table 2 . The representation and detailed view of the W-shaped geometry are presented in Fig. 3 a and b, respectively. Table 2. Details of investigated roughness and flow parameters. Parameters Value Relative roughness height ( ) 0.047 Relative roughness pitch ( q / e ) 10 Relative attack angle ( ) 0.667 Flow velocity of air ( V ) 1.94, 2.59, 3.24, 3.88 m/s Density of air ( ) 1.174 kg/m 3 Reynolds number ( Re ) 6036, 8045, 10060, 12072 Open in a new tab Fig. 3. Open in a new tab W-shaped rib roughness: ( a ) Schematic representation; ( b ) Photographic view. Result and discussion Validation of experimental test rig The experimental test rig, including a basic configuration of the absorber surface devoid of a radiation reflector, was subjected to ambient conditions. The thermal performance was assessed based on the Nusselt number ( Nu ) and the convective heat transfer coefficient ( ). The dimensionless parameter Re represented flow conditions inside the duct. The theoretical value of Nu given by the Dittus-Boelter equation was compared with the Nu obtained from the experiment to validate the experimental data. The Dittus-Boelter formula is: 9 The experimental values of Nu were compared with those obtained theoretically using Eq. ( 8 ) for the plain configuration of the absorber surface without radiation reflector. The comparison plot is shown in Fig. 4 , and the values are found to be within a reasonable range of 6%, validating the experimental results. Fig. 4. Open in a new tab Comparative plot of theoretical and experimental Nusselt number. Likewise, the frictional penalty or pressure drop during experimentation with the plain surface was calculated using the Modified Blasius equation: 10 The experimental values of f were compared with the theoretical values using Eq. ( 9 ) for the plain configuration. The comparison plot is shown in Fig. 5 , and the values are found to be within a reasonable range of 10%. Fig. 5. Open in a new tab Comparative plot of theoretical and experimental friction factor. The wind velocity ( V ) was obtained using an anemometer, and the corresponding air density ( ) was used to measure the air flow rate ( ). The heat gain by the flowing air ( ) is calculated using Eq. ( 10 ) 21 , and the heat transfer coefficient ( ) is calculated using Eq. ( 11 ) 45 : 11 12 where is the mean bulk air temperature, calculated as , and is the absorber plate temperature. The non-dimensional analysis of inlet air temperature and plate temperature was conducted using the absorber plate temperature coefficient ( ) defined as: 13 The temperature coefficient ( ) of the absorber plate is plotted against Re in Fig. 6 . The value indicates the heat releasing characteristics of the hot absorber plate corresponding to air flow rate. It is observed that the average plate temperature reduces with a rise in Re , likely due to higher temperatures at lower flow rates. Increased flow rate results in an improved rate of heat release from the absorber surface. Fig. 6. Open in a new tab Variation of absorber plate temperature coefficient against Reynolds number. It is also observed that the absorber plate gains higher temperature with the use of a radiation reflector compared to the plain configuration. A further increase in is noted with the artificially roughened surface of the FPSAH system along with reflectors. The heat received by the air across a small span around the absorber plate is used to calculate the thermal efficiency of the FPSAH system. The thermal efficiency is defined as the ratio of useful heat gained to total solar radiation incident on the absorber surface: 14 Uncertainty in results The uncertainties in experimental results are estimated using the method proposed by Kline and McClintock (1953). The uncertainty in measurement is given by: 15 where are uncertainties in individual measurements, and is the total uncertainty. The major uncertainties in the current study are: Nusselt number: 7.9% – 10.22% Reynolds number: 2.38% – 4.76% Influence of radiation reflectors The influence of radiation reflectors on the thermal performance of the FPSAH system was analyzed. Reflectors were attached to the edges of the FPSAH system with a plain configuration. The outcomes in terms of Nu with and without radiation reflectors are plotted in Fig. 7 . A considerable rise in heat transfer was observed with the use of radiation reflectors, with a percent increase in Nu ranging from 18 to 27%. Fig. 7. Open in a new tab Effect of radiation reflector on Nusselt number with plain surface. Radiation reflectors redirect more solar radiation toward the absorber surface, increasing its temperature and enhancing convective heat transfer to the air. The upper layer of flowing air gets heated by the hot absorber surface, and molecular exchange due to density differences improves thermal characteristics. To identify the effect of reflectors, the temperature difference is plotted against predefined air flow rates in Fig. 8 . It is observed that air acquires significantly more heat using radiation reflectors under similar flow conditions. Fig. 8. Open in a new tab Heat gained by air with respect to mass flow rate. Figure 9 shows the rise in thermal efficiency of the FPSAH system. The system with radiation reflectors and a plain absorber surface gains more heat compared to the system without reflectors. The thermal efficiency ranges from 1.27 to 1.43 times higher with reflectors. Fig. 9. Open in a new tab Thermal efficiency of plain configured surface with and without radiation reflectors. Influence of artificial roughness with radiation reflectors The importance of using artificial roughness underneath the absorber surface has been explained in many earlier studies. The dimensions and geometrical arrangement of roughness were taken as recommended 21 . The relative roughness pitch ( q / h ) of W-shaped roughness was set at 10, with a rib inclination of from the edge of the plate. W-shaped of rib roughness modifies the fluid flow characteristics. The multiple folds of rib roughness in W shape causes flow parting, reattachment of fluid flow and generation of secondary flow that improves the heat discharge form the surface. Apart from achieving better fluid flow behavior it is easy to design the shape of W from rib pieces with optimum heat release and minimum pressure drop. The rib roughness elements interrupt the smooth flow of air and produce secondary flow and vortices inside the passage. The flow resistance leads to enhance the frictional behavior and hence pumping power. That can be reduced by considering optimum geometrical parameters such as relative roughness altitude where is hydraulic diameter of passage of fluid flow and relative roughness pitch ( P / e ). If heat transfer enrichment is significantly advanced than frictional penalty, implementing roughness is valuable. Proper optimization of roughness may augment heat discharge with minimum pumping loss. The implementation of artificial roughness design on the absorber surface along with radiation reflectors led to a significant improvement in the thermal performance of the FPSAH system. The maximum Nusselt number ( Nu ) for FPSAH with W-shaped roughness and radiation reflector was obtained as 1.63 times that of the plain configured FPSAH system without reflector, and 1.28 times that of the plain configured FPSAH system with reflector. Figure 10 displays the overall outcomes of thermal performance in terms of Nu for different configurations. Fig. 10. Open in a new tab Nusselt number of different sets used in FPSAH system. A higher rise in heat release rate was observed with the artificially roughened FPSAH system using radiation reflectors. This may be due to the random flow behavior of air inside the duct and increased heat exposure to the absorber surface. The use of radiation reflectors not only increases the temperature of the absorber surface but also enhances heat loss to the atmosphere. Therefore, it is necessary to transfer maximum heat from the surface to the flowing fluid. Artificial roughness diminishes thermal boundary layer formation near the absorber surface by creating more turbulence inside the duct. W-shaped rib roughness develops a critical flow pattern attributed to the formation of secondary flows along the ribs and flow reattachment in the inter-rib region. The combination of artificial roughness and radiation reflectors results in substantial enhancement in the FPSAH system. To evaluate the thermal characteristics of different FPSAH configurations, Fig. 11 shows the thermal productivity of the system corresponding to various Reynolds numbers. Higher thermal efficiency is achieved by the system with a roughened absorber surface and radiation reflector. The thermal efficiency ranges from 1.37 to 1.84 times that of the system without reflector and roughness. Fig. 11. Open in a new tab Thermal efficiency of different sets used in FPSAH system. Machine learning application In this part, two machine learning (ML) algorithms were used to predict Nu values for three experimental configurations: smooth surface only, smooth surface with reflector, and roughened surface with reflector, as shown in Table 3 . Random Forest and Robust Regression were applied using Python programming on the Google Colaboratory platform. Table 3. Experimental sets used in machine learning. Case V (m/s) (°C) (°C) (°C) Re Nu f Smooth surface only 2.1 29.52 32.69 60.09 6036 21.22 20.71 0.0096 0.0099 2.8 29.84 32.82 59.21 8045 26.72 26.98 0.0089 0.0091 3.5 29.88 32.61 57.31 10060 31.94 33.05 0.0084 0.0086 4.2 30.06 32.71 56.54 12072 36.95 39.89 0.0080 0.0082 Smooth surface with reflector 2.1 29.44 33.86 64.97 6036 21.22 25.11 0.0096 0.0308 2.8 29.55 33.71 62.67 8045 26.72 33.83 0.0089 0.0267 3.5 29.93 33.61 61.01 10060 31.94 39.71 0.0084 0.0261 4.2 30.17 33.52 58.56 12072 36.95 47.48 0.0080 0.0258 Roughened surface with reflector 2.1 28.85 34.55 65.35 6036 21.22 32.07 0.0096 0.0308 2.8 29.04 33.68 62.12 8045 26.72 38.08 0.0089 0.0267 3.5 29.13 33.16 57.46 10060 31.94 48.32 0.0084 0.0261 4.2 29.25 32.86 53.54 12072 36.95 60.79 0.0080 0.0258 Open in a new tab The performance of the ML models was evaluated using metrics such as Mean Squared Error (MSE), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and R-squared ( ) value. Table 4 shows the results for both regression methods. Random Forest Regression achieved a curve fitting of 0.94 for the testing dataset, while Robust Regression provided a better fit with a curve fitting of 0.99. Table 4. Estimation of testing and training using machine learning algorithms. Algorithm Testing Training MAE MSE RMSE MAE MSE RMSE Robust regression 1.94 9.18 3.02 0.93 0.01 5.60 0.01 0.99 Random forest regression 3.65 20.63 4.54 0.69 1.65 5.33 2.31 0.94 Open in a new tab Artificial neural network (ANN) A total of 610 experimental results were used to train the ANN model, split into three sets: 412 training data, 104 test data, and 94 validation data. Selecting the appropriate ANN architecture is crucial due to its significant influence on prediction accuracy 46 , 47 . After evaluating various neural network configurations, the model was optimized by minimizing MSE. Figure 12 shows the 30-neuron ANN structure used for Nu prediction. The Levenberg-Marquardt learning algorithm and a linear transfer function were used in the output layer. Fig. 12. Open in a new tab Hidden layer’s optimal performance was determined to be 30 neurons. Tables 5 and 6 show the correlation coefficients for training, testing, and validation datasets. Figure 13 illustrates the total number of iterations completed during training. Table 5. ANN performance for Nusselt number prediction. HL Neurons Train Val Test All 1 10 0.93641 0.99990 0.99991 0.94921 1 15 0.93643 0.99992 0.99993 0.94923 1 20 0.93647 0.99994 0.99995 0.94935 1 25 0.93655 0.99996 0.99997 0.94939 1 30 0.93661 1.00000 1.00000 0.94941 1 40 0.93658 0.99994 0.99998 0.94938 Open in a new tab Table 6. ANN performance for thermal efficiency prediction. HL Neurons Train Val Test All 1 10 0.83202 0.99991 0.99992 0.87158 1 15 0.83205 0.99995 0.99994 0.87160 1 20 0.83206 0.99996 0.99996 0.87161 1 30 0.83209 0.99997 0.99997 0.87163 1 40 0.83212 1.00000 1.00000 0.87165 1 50 0.83208 0.99996 0.99996 0.87164 Open in a new tab Fig. 13. Open in a new tab Number of iterations. Figure 14 a and b show the comparison between thermal efficiency and Nusselt number of rough surfaces with reflectors, evaluated using the ANN model and experimental results respectively. Fig. 14. Open in a new tab Comparative analysis of thermal efficiency and Nusselt number: ( a ) ANN prediction results; ( b ) Experimental validation results. Error analysis Different error metrics have been used to evaluate the results 48 . The detailed formulae are provided below. Mean absolute error The sum of all absolute discrepancies between the expected and observed values. It can be evaluated using 16 Root mean square error It is a square root of MSE, which brings metric back to the same unit as the target variable, and it can be mathematical written as 17 Mean square error The sum of the squared discrepancies between the expected and observed values 49 . It can be calculated using 18 R-square It shows how dependent variable’s volatility can be predicted by independent variables. 19 where is predicted value and is an actual value. is sum of residue and is sum of total squares. Correlation Functional relationship of correlations Experimental analysis and effects of various roughness parameters and Reynolds number (Re) on thermal features is discussed to develop the statistical correlations that cover all the geometric and flow factors. Various rough parameters have a strong effect on Nusselt number and can be declared in form of functional relationship shown in Eq. ( 20 ). 20 Correlation for Nusselt number To determine functional connections a regression analysis is performed. Nu has created statistical correlations that match the experimental outcomes of every plate that was examined. Obtained value of Nu and Re are plotted on log-log scale for recorded data of all plates and is shown in Fig. 15 . Analysis of regression to linearly fit the curve going through the points specified by an Eq. ( 21 ). 21 22 The acquired value of is now dependent on additional geometrical factors related to roughness. Hence, & q / h is considered as the next parameter and plotted for the regression analysis. The points are fitted by using second order polynomial passing through the points obtained to get correlation for ‘Nu’. 23 Fig. 15. Open in a new tab Plot of ln (Nu) in terms of ln (Re). Figure 16 shows a comparison between experimental ‘Nu’ and that predicted from correlation equations. It is realized that almost all data points lie within the deviance line ± 10%. Hence correlation developed is sensibly acceptable for predicting Nu of roughened solar heater with the parameter range investigated. Fig. 16. Open in a new tab Comparison of experimental Nusselt number against predicted Nusselt number from correlation. Conclusions Based on the experimental study made on rectangular passage of FPSAH system with roughened broad wall at one side, thermal characteristics were investigated. The rectangular duct of the FPSAH system is tested under different combinations of applying radiation reflectors at the edges along with roughened absorber surface. Additionally, artificial neural network (ANN) and machine learning (ML) algorithms were used to forecast Reynolds number in each set of experiments. The following conclusions have been drawn from the present study. Incorporation of radiation reflectors at edges of the FPSAH system expressively augmented temperature of absorber surface as compared to system without radiation reflectors by redirecting and concentrating additional incident solar radiation onto the absorber surface, thereby reducing optical losses and improving solar energy utilization. An increase in ‘Nu’ has been observed with simultaneous use of W-shaped artificial roughness along with radiation reflectors as W shaped roughness element effectively promoted the disorder and improves convective heat discharge. The combined effect of improved disorder and amplified concentration of solar radiations leads to a significant improvement in thermal performance of FPSAH system. The FPSAH system configured with W-shaped artificial roughness and radiation reflectors gives remarkable augmentation in Nusselt number as 1.62 times over plain configuration of absorber plate. The dual mode of FPSAH system exhibit a significant improvement in thermal efficiency, recorded an augmentation of approximately 1.84 times over the plain configuration of the system. Machine Learning (ML) algorithms can be effectively applied to predict the Reynolds number based on relevant operating and geometrical paremeters. Amongst different ML module, Robust Regression is found to be the best suitable algorithm for estimating the Re value under different experimental conditions. The use of Artificial Neural Network (ANN) reveals high accurate prediction capability for the experimental data with an acceptable coefficient value of 1.00, that confirms the effectiveness of applying ANN model in the fundamental association amongst input parameters and system performance. In addition, optimal ANN model and ML algorithm results are found to be more accurate than predicted results from published correlations. To summarize, this technique has the potential to contribute to a better understanding of heat exchanger dynamic behavior in the future. The solar air heater can be used for space heating in homes, greenhouses, and agricultural settings. The warm air generated can be circulated to maintain comfortable indoor temperatures or promote plant growth. Additionally, can be also implemented in industries that require moderate heating, such as drying processes in food, textiles, or lumber, and can benefit from the efficient heat generated by solar air heaters. Acknowledgements The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. List of symbols Area of heated plate (m ) Cross-sectional area of orifice plate (m ) Specific heat of fluid (kJ kg K ) Orifice discharge coefficient Hydraulic diameter of rectangular duct (m) p Roughness height (mm) H Rectangular duct height (mm) Convective heat transfer coefficient (W m K ) k Thermal conductivity of flowing air (W m K ) L Absorber plate length (mm) Mass flow rate of air (kg s ) q Roughness pitch (mm) Useful heat gain (W) Mean air temperature (K) Inlet air temperature (K) Outlet air temperature (K) Average heated plate temperature (K) V Air velocity (m s ) W Duct width (mm) Dimensionless parameters Relative roughness height Nu Nusselt number (rough plate) Nu Nusselt number (smooth plate) q / h Relative roughness pitch Pr Prandtl number Re Reynolds number W / H Aspect ratio Greek symbols Angle of attack (degree) Density of air (kg m ) Kinematic viscosity (m s ) Thermal efficiency Author contributions P. K. Jain led the research work, conceptualized the study, and coordinated the overall project development. K. L. Kurrey contributed to the methodology design, simulation setup, and data analysis. V. Pandey carried out performance evaluation, experimental validation, and assisted in result interpretation. J. R. Shinde supported algorithm/model development and contributed to system implementation. A. N. Tripathi contributed to conceptualization, manuscript preparation, and formatting according to journal guidelines. N. K. Dewangan provided supervision, technical guidance, methodology refinement, and final manuscript review and approval. All authors reviewed and approved the final version of the manuscript. Funding Open access funding provided by Manipal Academy of Higher Education, Manipal. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Data availability The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request. Declarations Competing interests The authors declare no competing interests. Footnotes Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. References 1. Mandi, B. et al. Improvement and nocturnal extension of the efficiency of a solar still. Int. J. Photoenergy 2021 , 1–11. 10.1155/2021/6631121 (2021). [ Google Scholar ] 2. Menni, Y. et al. Combination of baffling technique and high-thermal conductivity fluids to enhance the overall performances of solar channels. Eng. Comput. 38 , 607–628. 10.1007/s00366-020-01165-x (2022). [ Google Scholar ] 3. Aramesh, M., Pourfayaz, F., Haghir, M., Kasaeian, A. & Ahmadi, M. H. Investigating the effect of using nanofluids on the performance of a double-effect absorption refrigeration cycle combined with a solar collector. Proc. Inst. Mech. Eng. Part A J. Power Energy 234 , 981–993. 10.1177/09576509198898 (2019). [ Google Scholar ] 4. Alawee, W. H., Hassan, J. M. & Mohammad, W. S. Experimental and numerical study on the improvement of uniformity flow in a parallel flow channel. Eng. Technol. J. 34 , 847–856. 10.30684/etj.34.5A.4 (2016). [ Google Scholar ] 5. Choudhury, C. & Garg, H. Design analysis of corrugated and flat plate solar air heaters. Renew. Energy 1 , 595–607. 10.1016/0960-1481(91)90003-8 (1991). [ Google Scholar ] 6. Choudhury, C. & Garg, H. Performance prediction of a corrugated cover solar air heater. Energy Convers. Manage. 32 , 115–122. 10.1016/0196-8904(91)90151-8 (1991). [ Google Scholar ] 7. Kumar, P. G. et al. Effect of using low-cost thermal insulation material in a solar air heating system with a shot blasted V-corrugated absorber plate. Thermal Sci. Eng. Progress 14 , 1–10. 10.1016/j.tsep.2019.100403 (2019). [ Google Scholar ] 8. Lakshmi, D., Layek, A. & Kumar, P. M. Performance analysis of trapezoidal corrugated solar air heater with sensible heat storage material. Energy Proc. 109 , 463–470. 10.1016/j.egypro.2017.03.069 (2017). [ Google Scholar ] 9. Garg, H., Jha, R., Choudhury, C. & Datta, G. Theoretical analysis on a new finned type solar air heater. Energy 16 , 1231–1238. 10.1016/0360-5442(91)90152-C (1991). [ Google Scholar ] 10. Murali, G., Nandan, B. S., Reddy, N. S. K., Teja, D. & Kumar, N. K. Experimental study on double pass solar air heater with fins at lower and upper channel. Mater. Today Proc. 21 , 578–583. 10.1016/j.matpr.2019.06.718 (2020). [ Google Scholar ] 11. Singh, S., Dhruw, L. & Chander, S. Experimental investigation of a double pass converging finned wire mesh packed bed solar air heater. J. Energy Storage 21 , 713–723. 10.1016/j.est.2019.01.003 (2019). [ Google Scholar ] 12. Saini, J. Use of artificial roughness for enhancing performance of solar air heater, in XVII National and VI ISHME/ASME Heat and Mass Transfer Conference 05–07 (Kalpakkam, India, Jan, IGCAR, 2004). [ Google Scholar ] 13. Prasad, K. & Mullick, S. Heat transfer characteristics of a solar air heater used for drying purposes. Appl. Energy 13 , 83–93. 10.1016/0306-2619(83)90001-6 (1983). [ Google Scholar ] 14. Prasad, B. & Saini, J. Effect of artificial roughness on heat transfer and friction factor in a solar air heater. Sol. Energy 41 , 555–560. 10.1016/0038-092X(88)90058-8 (1988). [ Google Scholar ] 15. Gupta, D., Solanki, S. & Saini, J. Thermohydraulic performance of solar air heaters with roughened absorber plates. Sol. Energy 61 , 33–42. 10.1016/S0038-092X(97)00005-4 (1997). [ Google Scholar ] 16. Saini, S. & Saini, R. Development of correlations for Nusselt number and friction factor for solar air heater with roughened duct having arc-shaped wire as artificial roughness. Sol. Energy 82 , 1118–1130. 10.1016/j.solener.2008.05.010 (2008). [ Google Scholar ] 17. Momin, A.-M.E., Saini, J. & Solanki, S. Heat transfer and friction in solar air heater duct with V-shaped rib roughness on absorber plate. Int. J. Heat Mass Transf. 45 (16), 3383–3396. 10.1016/S0017-9310(02)00046-7 (2002). [ Google Scholar ] 18. Patel, S. S. & Lanjewar, A. Experimental analysis for augmentation of heat transfer in multiple discrete V-patterns combined with staggered ribs solar air heater. Renew. Energy Focus 25 , 1–9. 10.1016/j.ref.2018.03.003 (2018). [ Google Scholar ] 19. Maithani, R. & Saini, J. S. Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with V-ribs with symmetrical gaps. Exp. Thermal Fluid Sci. 70 , 220–227. 10.1016/j.expthermflusci.2015.09.010 (2016). [ Google Scholar ] 20. Deo, N. S., Chander, S. & Saini, J. S. Performance analysis of solar air heater duct roughened with multigap V-down ribs combined with staggered ribs. Renewable Energy 91 , 484–500. 10.1016/j.renene.2016.01.067 (2016). [ Google Scholar ] 21. Lanjewar, A., Bhagoria, J. & Sarviya, R. Heat transfer and friction in solar air heater duct with W-shaped rib roughness on absorber plate. Energy 36 , 4531–4541. 10.1016/j.energy.2011.03.054 (2011). [ Google Scholar ] 22. Jain, S. K., Agrawal, G. D. & Misra, R. A detailed review on various V-shaped ribs roughened solar air heater. Heat Mass Transf. 12 , 3369–3412. 10.1007/s00231-019-02656-4 (2019). [ Google Scholar ] 23. Ghritlahre, H. K. et al. Application of ANN model to predict the performance of solar air heater using relevant input parameters. Sustain. Energy Technol. Assess. 40 , 100764. 10.1016/j.seta.2020.100764 (2020). [ Google Scholar ] 24. Hans, V. S., Gill, R. S. & Singh, S. Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with broken arc ribs. Exp. Thermal Fluid Sci. 80 , 77–89. 10.1016/j.expthermflusci.2016.07.022 (2017). [ Google Scholar ] 25. Gill, R. S., Hans, V. S., Saini, J. S. & Singh, S. Investigation on performance enhancement due to staggered piece in a broken arc rib roughened solar air heater duct. Renew. Energy 104 , 148–162. 10.1016/j.renene.2016.12.002 (2017). [ Google Scholar ] 26. Parashar, R., Pandey, S., Hasija, V. & Karanth, K. V. Experimental analysis of a square duct solar air heater with radiation reflectors. Int. J. Appl. Eng. Res. 13 , 123–130. 10.1016/j.matpr.2022.09.297 (2018). [ Google Scholar ] 27. Lanjewar, A., Bhagoria, J. L. & Sarviya, R. M. Experimental study of augmented heat transfer and friction in solar air heater with different orientations of W-Rib roughness. Exp. Thermal Fluid Sci. 35 , 986–995. 10.1016/j.expthermflusci.2011.01.019 (2011). [ Google Scholar ] 28. Abdullah, A. et al. Experimental investigation of single pass solar air heater with reflectors and turbulators. Alex. Eng. J. 59 , 579–587. 10.1016/j.aej.2020.02.004 (2020). [ Google Scholar ] 29. Zolfagharnasab, M. H., Aghanajafi, C., Kavian, S., Heydarian, N. & Ahmadi, M. H. Novel analysis of second law and irreversibility for a solar power plant using heliostat field and molten salt. Energy Sci. Eng. 8 , 4136–4153. 10.1002/ese3.802 (2020). [ Google Scholar ] 30. Thapliyal, S. & Mishra, A. Machine learning classification-based approach for mechanical properties of friction stir welding of copper. Manuf. Lett. 29 , 29–52. 10.1016/j.mfglet.2021.05.010 (2021). [ Google Scholar ] 31. Mishra, A. Surface quality analysis of friction stir welded joints by using fourier transformation and local binary patterns algorithms. Soldagem & Inspeção 25 , 1–11. 10.1590/0104-9224/SI25.27 (2020). [ Google Scholar ] 32. Chaluvaraju, B. V. et al. Mechanical and corrosion studies of friction stir welded nano AlO reinforced Al-Mg matrix composites: RSM-ANN modelling approach. Symmetry 13 , 1–38. 10.3390/sym13040537 (2021). [ Google Scholar ] 33. Tian, W., Sun, W., Ni, B., Li, J. & Wu, Z. An interval robust design optimization method and its application in heat transfer problems. Eng. Optim. 53 , 1805–1818. 10.1080/0305215X.2020.1828399 (2020). [ Google Scholar ] 34. Grosu, L. et al. Steady state operation exergy-based optimization for solar thermal collectors. Environ. Progress Sustain. Energy 39 , 1–8. 10.1002/ep.13359 (2020). [ Google Scholar ] 35. Ghritlahre, H.K., Verma, M.: Solar air heaters performance prediction using multi-layer perceptron neural network-A systematic review, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, pp. 1–18, (2021), 10.1080/15567036.2021.1923869. 36. Ahmad, M. W., Reynolds, J. & Rezgui, Y. Predictive modelling for solar thermal energy systems: A comparison of support vector regression, random forest, extra trees and regression trees. J. Clean. Prod. 203 , 810–821. 10.1016/j.jclepro.2018.08.207 (2018). [ Google Scholar ] 37. Saravanan, A. et al. Thermal performance prediction of a solar air heater with a C-shape finned absorber plate using RF. LR and KNN Models Mach. Learn. Thermal Sci. Eng. Progress 38 , 1–12. 10.1016/j.tsep.2022.101630 (2023). [ Google Scholar ] 38. Nidhul, K., Thummar, D., Yadav, A. K. & Anish, S. Machine learning approach for optimization and performance prediction of triangular duct solar air heater: A comprehensive review. Sol. Energy 255 , 396–415. 10.1016/j.solener.2023.02.022 (2023). [ Google Scholar ] 39. Piri, S., Abdel-Salam, A.-S.G. & Boone, E. L. A wavelet approach for profile monitoring of Poisson distribution with application. Commun. Stati. Simul. Comput. 50 , 525–536. 10.1080/03610918.2018.1563151 (2021). [ Google Scholar ] 40. Ghritlahre, H. K. & Prasad, R. K. Investigation on heat transfer characteristics of roughened solar air heater using ANN technique. Int. J. Heat Technol. 36 , 102–110. 10.18280/ijht.360114 (2018). [ Google Scholar ] 41. Naphon, P. & Arisariyawong, T. Heat transfer analysis using artificial neural networks of the spirally fluted tubes. J. Res. Appl. Mech. Eng. 4 , 135–147. 10.14456/jrame.2016.14 (2018). [ Google Scholar ] 42. ASHRAE Standard, Methods of testing to determine the thermal performance of solar collectors, American Society of Heating, pp. 93–77, 1977. 43. Menni, Y. et al. Numerical calculations of the thermal-aerodynamic characteristics in a solar duct with multiple V-baffles. Eng. Appl. Comput. Fluid Mech. 14 , 1173–1197. 10.1080/19942060.2020.1815586 (2020). [ Google Scholar ] 44. Menni, Y., Chamkha, A. J., Ameur, H. & Ahmadi, M. H. Hydrodynamic behavior in solar oil heat exchanger ducts fitted with staggered baffles and fins. J. Appl. Comput. Mech. 8 , 774–790. 10.22055/JACM.2020.32468.2021 (2022). [ Google Scholar ] 45. Sahu, M. M. & Bhagoria, J. L. Augmentation of heat transfer coefficient by using 90 broken transverse ribs on absorber plate of solar air heater. Renew. Energy 30 , 2057–2073. 10.1016/j.renene.2004.10.016 (2005). [ Google Scholar ] 46. Sadeghzadeh, M. et al. Smart modeling by using artificial intelligent techniques on thermal performance of flat-plate solar collector using nanofluid. Energy Sci. Eng. 9 , 1649–1658. 10.1002/ese3.381 (2019). [ Google Scholar ] 47. Kaladgi, A. R. et al. Integrated Taguchi-GRA-RSM optimization and ANN modelling of thermal performance of zinc oxide nanofluids in an automobile radiator. Case Stud. Thermal Eng. 26 , 1–18. 10.1016/j.csite.2021.101068 (2021). [ Google Scholar ] 48. Gupta, M. K. & Kaushik, S. C. Performance evaluation of solar air heater for various artificial roughness geometries based on energy, effective and exergy efficiencies. Renew. Energy 34 (3), 465–476. 10.1016/j.renene.2008.05.020 (2009). [ Google Scholar ] 49. Yang, D. Correlogram, predictability error growth, and bounds of mean square error of solar irradiance forecasts. Renew. Sustain. Energy Rev. 167 , 112736. 10.1016/j.rser.2022.112736 (2022). [ Google Scholar ] 50. Azeez, K., Their, K. M. & Ibrahim, Z. A. Evaluation of flat plate solar heater filling in nanofluid under climatic of Iraq conditions. Case Stud. Thermal Eng. 39 , 102447. 10.1016/j.csite.2022.102447 (2022). [ Google Scholar ] 51. Azeez, K., Ahmed, R. I., Obaid, Z. A. & Azzawi, I. D. Heat transfer enhancement and applications of thermal energy storage techniques on solar air collectors: A review. J. Thermal Eng. 9 (5), 1356–1371. 10.18186/thermal.1001534 (2021). [ Google Scholar ] Associated Data This section collects any data citations, data availability statements, or supplementary materials included in this article. Data Availability Statement The datasets generated and/or analyzed during the current study are available from the corresponding author upon reasonable request. Articles from Scientific Reports are provided here courtesy of Nature Publishing Group ACTIONS View on publisher site PDF (3.9 MB) Cite Collections Permalink PERMALINK Copy RESOURCES Similar articles Cited by other articles Links to NCBI Databases Cite Copy Download .nbib .nbib Format: AMA APA MLA NLM Add to Collections Create a new collection Add to an existing collection Name your collection * Choose a collection Unable to load your collection due to an error Please try again Add Cancel Follow NCBI NCBI on X (formerly known as Twitter) NCBI on Facebook NCBI on LinkedIn NCBI on GitHub NCBI RSS feed Connect with NLM NLM on X (formerly known as Twitter) NLM on Facebook NLM on YouTube National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894 Web Policies FOIA HHS Vulnerability Disclosure Help Accessibility Careers NLM NIH HHS USA.gov Back to Top