1 Introduction

Solar air heat technology may be used in several applications to minimize the carbon footprint of traditional heating systems, including fossil fuels, and offer a more sustainable way to generate thermal energy. A traditional solar air heater (SAH) typically having a flat wooden duct with a base plate having synthetic roughness, a transparent glazing and insulating material on the base and side-wise. SAH applications are usually limited to low-temperature gradient uses such as water heating, room heating, crop drying, agricultural season extensions, preheating, process heating, commercial ventilation makeup air, air conditioning and space heating and cooling [1, 2]. SAH's usage in low-temperature gradient applications can be ascribed to the reduced heat transfer between air and the roughened absorber plate, which is caused by the reduced convection heat transfer coefficient. Several studies have focused on different strategies to enhance the convection coefficient by employing a variety of design options with different roughness geometry and to analyse the SAH thermohydraulic performance parameter (THPP) [3].

The basic methods used by researchers to increase the single-pass SAH (SPSAH) performance were variations in geometry parameters, operation parameters and the addition of the number of passes of fluid flow [4, 5]. Since the application of double-pass SAH (DPSAH) increases the collector surface area, it offers considerable gains in heat transfer [6]. Double-pass SAH with cross-flow [7, 8], recycling [9] and parallel flow [10] are different DPSAH arrangements that were used as the primary factors that affected the performance [11,12,13].

Besides these reports, several researchers have focused specifically on the effect of ribs and baffles on the heat transfer enhancement over a smooth SAH. As per the literature, the most influencing parameters in rib roughness include relative roughness height (e/Dh), relative roughness pitch (p/e), angle of attack (α), aspect ratio (W/H), collector slope (β) and rib geometry [13,14,15,16,17,18,19]. For multiple V-shaped ribs, Arya et al. [20,21,22], Tabish et al. [23, 24] Ravi and Saini [25, 26], Singh and Kaur [27] and Kumar et al. [17, 28] have determined the optimum configuration variable combinations for multi-V rib configuration. When compared to SPSAH, Ravi and Saini [26] found that the DPSAH improved the Nusselt number ratio (Nu/Nus) by 3.4 times and the friction factor ratio (f/fs) by 2.5 times. Thakur and Thakur [29] observed a 2.3–4.1 times improvement in Nu value by applying W-shaped ribs with staggering as compared to a smooth SAH. Singh et al. [30, 31] analysed the effect of perforation with continuous rib in multi-V geometry in SPSAH and DPPFSAH and observed significant improvement because of the application of perforations. Singh et al. [32, 33] investigated the effect of variation in β and W/w for a distinct set of perforated multi-V ribs and found that the effectiveness of SPSAH improved significantly.

A review by Hernández and Quinonez [34] reveals that the application of DPPFSAH reduces drag forces to a minimal level, which handles high pumping power while having optimum thermal effectiveness. The rapid air flow rate of the supplementary streams via holes creates more turbulence during detachment and reattachment, which enhances the THP of SAH [35]. Because of the high airflow rate via secondary passages, DPPFSH’s perforated multi-V ribbed rough surfaces can play an essential role in improving Nu and reducing f values. The aim of the current study is to analyse the effects of variation in β and W/w values on THP for DPPFSAH and compare it with the SPSAH studied by Singh et al. [32] and other researchers. The current research thus seeks to explore the effect of perforations in ribs on the performance of DPPSAH.

2 Set-up Configuration and Roughness Parameter Details

A DPPFSAH set-up (Fig. 1a–c) is fabricated as per the ASHRAE standard (AHSRAE 93-77, 1977). The detailed description of set-up, fixed and variable parameters is mentioned in detail in earlier research work [31] and mentioned in Table 1.

Fig. 1
figure 1

a Experimental set-up, b cross-sectional view and c thermocouple and pressure tap placement in DPPFSAH [31]

Full size image
Table 1 Parameters being used in the study are listed below
Full size table

Figure 2a–c gives a visual representation of perforated multi-V rib roughness geometry taken up in this study.

Fig. 2
figure 2

a Parameter denotation on multi-V perforated plate, b front view of ribs with variation in β, c perforated V-shaped roughness rib arrangements on both sides of the base plate

Full size image

3 Data Handling

Although the detailed description of the governing equations and data handling is discussed in the preceding work by the authors [31], the same equations are mentioned here in brief, for the improved readability of the current paper. The THP values were calculated by averaging the data values. The average temperature of base plate Tpmean can be calculated as [36]:

$$ T_{{{\text{pmean}}}} = \frac{1}{18}\left( {\mathop \sum \limits_{i = 1}^{18} Ti} \right) $$
(1)

The average air temperature Tamean can be found as:

$$ T_{{{\text{amean}}}} = \frac{{T_{{{\text{in}}}} + T_{{{\text{out}}}} }}{2} $$
(2)
$$\begin{aligned} {\text{ were}} \quad T_{{{\text{in}}}} &= \frac{{T_{{{\text{in1}}}} + T_{{{\text{in2}}}} }}{2}\quad {\text{and}}\\ { }T_{{{\text{out}}}} &= \frac{{T_{{\text{out 1}}} + T_{{\text{out 2}}} + T_{{\text{out 3}}} + T_{{\text{out 4}}} + T_{{\text{out 5}}} }}{5}\end{aligned} $$
(3)

Air mass flow rate is measured by:

$$ \dot{m} = c_{{\text{d}}} A_{{\text{o}}} \sqrt {\frac{{2\rho \left( {\Delta P_{{\text{o}}} } \right)}}{{1 - \left( {D_{{\text{o}}} /D_{{\text{p}}} } \right)^{4} }}} $$
(4)

where

$$ \Delta P_{0} = \rho_{m} g\Delta h_{o} \sin \theta $$
(5)

The velocity of air is considered as:

$$ V = m/\rho WH $$
(6)

Channel hydraulic diameter (\(D_{{\text{h}}}\)) can be found as:

$$ D_{{\text{h}}} = 4WH/2\left( {W + H} \right) $$
(7)

Test section friction factor (f) can be calculated as:

$$ f = 2\left( {\Delta p} \right)_{{\text{d}}} D_{{\text{h}}} /4\rho Lv^{2} $$
(8)

The heat transfer coefficient (h) is defined as:

$$ h = Q_{{\text{u}}} /A_{p} \left( {T_{pm} - T_{fm} } \right) $$
(9)

The useful heat gain (Qu) is measured as:

$$ Q_{{\text{u}}} = \dot{m}c_{{\text{p}}} \left( {T_{{{\text{out}}}} - T_{{{\text{in}}}} } \right) $$
(10)

By Eqs. (7) and (9), the Nusselt number is [37]:

$$ N_{{\text{u}}} = hD_{{\text{h}}} /K $$
(11)

The Reynolds number (Re) is measured as:

$$ {\text{Re}} = VD_{{\text{h}}} /v $$
(12)

Finally, the DPPFSAH thermal efficiency (ηthermal) was obtained as:

$$ \eta_{{{\text{thermal}}}} = \dot{m}C_{{\text{p}}} \Delta T/IA_{{\text{p}}} $$
(13)

4 Validation of Experimental Set-ups and Analysis of Uncertainties

An experimental set-up of DPPFSAH having a smooth plate with Re in the range of 2000–18,000 was tested for the validation study. The measured values of Nus and fs are put in comparison with the revised Dittus–Boelter and revised Blasius equations, respectively [38].

By modified Dittus–Boelter equation:

$$ {\text{Nu}}_{{\text{s}}} = 0.024{\text{Re}}^{0.8} \,\Pr^{0.4} $$
(14)

Modified Blasius equation:

$$ f_{{\text{s}}} = 0.085{\text{Re}}^{ - 0.025} $$
(15)

An illustrative connection between empirical and theoretical Nus and fs results for Re is shown in Fig. 3.

Fig. 3
figure 3

Nus and fs measured and theoretical results for a smooth DPPFSAH

Full size image

The Nu, f and Re were calculated using empirically collected data, including airflow, intake and exit average temperature, solar irradiation and pressure losses. For error analysis, this study uses the Kline and McClintock [39] method. The author provides a detail of uncertainty calculation in the earlier published work [32]. The mean error percentages of Nu, Re and f are observed as ± 1.83%, ± 1.65% and ± 3.28%, respectively.

5 Results and Discussions

The assessment of design and performance variables on the THPP of DPPFSAH that has been artificially roughened using perforated multi-V ribs was investigated and analysed.

5.1 Near-wall flow development

Figure 4A, b shows how perforation in a multi-V rib causes complicated fluid flow patterns at the wall surfaces when compared to an unbroken rib. The fluid flow area and stream reattachment interval beneath the ribs limit the quantity of transferred energy from the base plate [40]. Geometry parameters drive the THP enhancements, which may be addressed through Reynolds number (Re), rib roughness and duct characteristics. In perforated ribs, the zone of reattachment shrinks, and the growth of upstream and downstream vertices reduces, leading to even more close connections for fresh fluid flow with the heated surface and improved thermal interaction inside the reattachment zone [41].

Fig. 4
figure 4

Near-wall flow development of a continuous rib (β = 0.0) [41], b perforated rib [42]

Full size image

The stream's mixing between the two neighbouring perforated ribs and front vortices is also improved by perforation in the ribs, allowing it to flow alongside it. Tariq et al. [42] suggest that this improves flow capacity and lowers pressure drop, leading to less pumping power required to sustain fluid flow. Furthermore, the perforation allows cooler secondary air to easily replace trapped air in the vortex that combines it with the main flow, enhancing heat transfer beyond the ribs. Perforation promotes mixing throughout the rib and plate contact area and lowers vortices for smaller Reynolds numbers. It can accelerate the levels of turbulent mixing in the stream. Figure 5a, b shows this phenomenon of producing turbulence between the two consecutive ribs. As a result of the increased turbulence, rib perforation rises THP.

Fig. 5
figure 5

Flow movement and development of vortices a continuous rib, b perforated rib in the DPPFSAH duct [42]

Full size image

5.2 Effect of Operating Variables

In this section, the influence of different variables is studied by maintaining the other parameters' values unchanged. The changes in varying parameters have been mapped with Re, W/w and β, and their effects are described and analysed in detail.

5.2.1 Effect of Reynolds Number (Re)

Because of a substantial improvement in mixing and turbulence in the secondary stream attributed to the perforations, Fig. 6a–d demonstrates a substantial enhancement in Nu values for higher values of Re, resulting in a larger Nu and enhanced thermal outcomes of DPPFSAH. In DPPFSAH, at β = 0.27, the optimal value of Nu is 556.19 for W/w = 6 at Re = 18,000, respectively. Figure 8a indicates the comparison between Nu for different β values at W/w = 6 for perforated multi-V rib and the flat duct in SPSAH and DPPFSAH, and it is clearly evident that the roughened DPPFSAH outperforms the roughened SPSAH in all cases. Figure 7a–d explains the change in f value with different β values for a range of Re in the DPPFSAH and shows a considerable reduction because of additional flow developed due to perforated ribs, which decreases the flow barrier and decreases energy requirement. The minimal value of f = 0.04476 is shown in DPPFSAH with β = 0.31 at W/w = 2 and Re = 18,000. Figure 8b shows the comparison between different f values for different β values at W/w = 6 in SPSAH and DPPFSAH. SPSAH with roughness shows minimum values for friction factor as compared to DPPFSAH in all cases. Under the same operating circumstances, perforation in multi-V ribs reduces energy consumption significantly.

Fig. 6
figure 6

Influence of Re on Nu for different β value a 0.0, b 0.21, c 0.27 and d 0.31 at different W/w values in DPPFSAH

Full size image
Fig. 7
figure 7

Influence of Re on f for different β value a 0.0, b 0.21, c 0.27 and d 0.31 for different W/w values in DPPFSAH

Full size image
Fig. 8
figure 8

Comparison between a Nu and Re and b f and Re of SPSAH and DPPFSAH for different β values

Full size image

5.2.2 Effect of Relative Roughness Width (W/w)

Figure 9a–d illustrates the influence of W/w on Nu for different β values, and the figure indicates that increasing W/w initially improves Nu in all four conditions, attaining a maximum value at W/w = 6, and any additional rise in the W/w decreases the Nu value. It is expected that, at W/w = 6, flow mixing induced due to the proposed geometry has attained its maximum value and any further rise in W/w could disrupt the improvement in secondary flow due to flatness growth in roughness geometry and reduce rib effectiveness, which reduces thermal effectiveness. While Fig. 10a–d illustrates the influence of W/w on f, the f value regularly increases with an augmentation in W/w value due to the turbulence formed in the flow.

Fig. 9
figure 9

Nu versus W/w plots for different β values a 0.0, b 0.21, c 0.27 and d 0.31 in DPPFSAH

Full size image
Fig. 10
figure 10

f versus W/w plots for different β values a 0.0, b 0.21, c 0.27 and d 0.31 in DPPFSAH

Full size image

5.2.3 Effect of Open Area Ratio (β)

Figure 11A shows Nu increasing as it rises to β = 0.27, then decreasing as it rises again for a further increase in β value. Nu is optimal at β = 0.27, although it is minimal at β = 0.0. The radial development of a secondary flow will be higher at a given linear distance if the perforation diameter is larger. That leads to more fluid flow mixing and reduces the flow zone on the downside of each rib. Once the β value reaches 0.27, the fluid flow through the perforations drops, which may be insufficient to improve the flow through the aperture, resulting in reduced flow turbulence and fluid mixing, and therefore reduced thermal efficacy. The valve can be managed in such a way that the flow passing out of the hole is better mixed, resulting in regional turbulence and improved heat transfer between the flow and the base plate. In the current set of investigations, the optimal THP was obtained by keeping the β value at 0.27. This may be the best value for such a perforated multi-V rib design arrangement and airflow circumstances. Figure 11b depicts the effect of variation in β values on the f value for the same other parameters. Since a greater β value implies fewer resistive forces in fluid flow, the f starts reducing for an increase in β value.

Fig. 11
figure 11

a Nu versus β and b f versus β for different rib combinations in DPPFSAH

Full size image

5.2.4 Effect on Nusselt Number and Friction Factor Ratio

Figure 12A, b shows the Nu/Nus and Re relationships in DPPFSAH for different rib combinations and a comparison of SPSAH and DPPFSAH with different β values at W/w = 6. At Re = 6000, the perforated rib with β = 0.27 attains the maximum value of Nu/Nus = 9.66, which continues for all W/w values. For further increment in Re values, a sudden decrease in Nu/Nus values which turn into a gradual increase and again achieved optimum values at Re = 18,000. The plausible explanation behind the underlying phenomenon is that a further increase in β value after Re = 6000 lowers Nu/Nus. This is fair given that roughness-induced air mixing reached its optimal value at β = 0.27, and any further increases in Re levels may interrupt the creation of secondary flow, leading a reduction in Nu/Nus.

Fig. 12
figure 12

a Nu/Nus versus Re for different β in DPPFSAH and b Nu/Nus versus Re comparison for SPSAH and DPPFSAH with different β values at W/w = 6

Full size image

Similarly, Fig. 13a, b depicts the influence of Re on f/fs in DPPFSAH for various β levels and a comparison between SPSAH and DPPFSAH with different β values at W/w = 6, trends show that f/fs start decreasing with an increase in β value because of the formation of a decent secondary airflow via the perforations. The maximum value of f/fs can be observed as 12.31 at β = 0.0, for W/w = 10 at Re = 4000.

Fig. 13
figure 13

Influence of Re on f/fs for different β in a DPPFSAH and b comparison of SPSAH and DPPFSAH with different β values at W/w = 6

Full size image

5.3 Thermohydraulic Performance

The combination of Nu and f generates contradictory contexts wherein evaluating the advantages of employing artificial roughness becomes challenging. Hence, Webb and Eckert [43] suggested the thermohydraulic performance parameter (THPP), which equates thermal performance to frictional losses and helps in finding the gain in THPP for suggested roughness as compared to the plain duct for the same power requirements. THPP can be written as:

$$ {\text{THPP}} = \left[ {\frac{{{\text{Nu}}_{{\text{r}}} }}{{{\text{Nu}}_{{\text{s}}} }}} \right]/\left[ {\frac{{{\text{f}}_{{\text{r}}} }}{{{\text{f}}_{{\text{s}}} }}} \right]^{\frac{1}{3}} $$
(16)

Further, the concept of the thermal efficiency improvement factor (TEIF) can be invoked to characterize how perforated ribs enhance heat transmission over continuous solid ribs (β = 0). It may be expressed as:

$$ {\text{TEIF}} = \frac{{\left( {\eta_{{{\text{themal}}}} } \right)_{{{\text{per}}{.}}} - \left( {\eta_{{{\text{themal}}}} } \right)_{{{\text{cont}}{.}}} }}{{\left( {\eta_{{{\text{themal}}}} } \right)_{{{\text{cont}}{.}}} }} $$
(17)

Figure 14a, b depicts the relationship between THPP and TEIF with Re for various values of β in DPPFSAH, with optimal results obtained in all cases for β = 0.27. The optimum value of THPP for DPPFSAH is 3.96 at Re = 14,000 at W/w = 6, and the maximum value of TEIF attains a value of 1.33 at β = 0.27, W/w = 2 and Re = 14,000, respectively. When compared with the smooth channel, the proposed roughness results in a significant increase in THPP and TEIF numbers.

Fig. 14
figure 14

a THPP versus Re and b TEIF versus Re for different β values in DPPFSAH

Full size image

5.4 Correlations for Nu and f for DPPFSAH

To establish the Nu and f correlations, the DPPFSAH functional connection has been established for each set of data of Nu and f. These are influenced by rib architecture and geometrical variables [44, 45], i.e. Re, W/w and β. For parameters in the ranges of β = 0.21–0.31, W/w = 2–10 and Re = 2000–18,000, the correlation is valid. Nu and f have the following functional relationships:

$$ {\text{Nu}} = f_{n} \left( {{\text{Re}} ,\beta ,W/w} \right) $$
(18)
$$ f = fn\left( {{\text{Re}} ,\beta ,W/w} \right) $$
(19)

5.4.1 Nusselt Number Correlation

The Nu correlation was created by applying a regression analysis approach. Figure 15a shows the final correlation for Nu through curve fitting for experimental data sets and can be expressed as,

$$ {\text{Nu}} = 0.0769 \times 10^{ - 3} ({\text{Re}})^{0.8953} \left( \beta \right)^{0.2417} \left( \frac{W}{w} \right)^{0.1244} $$
(20)
Fig. 15
figure 15

Correlation equation and trained line for a Nu and b f for DPPFSAH

Full size image

5.4.2 Friction Factor Correlation

Figure 15B shows the f statistics plotted against the operating parameters, and the correlation for the f could be represented as:

$$ f = 0.4234 \times 10^{ - 3} ({\text{Re}} )^{ - 0.2964} \left( \beta \right)^{ - 0.3897 } \left( \frac{W}{w} \right)^{0.1836} $$
(21)

Figure 16a, b compares experimental and projected Nu and f values, revealing that the predicted Nu and f value are well within ± 14% and ± 7% of the empirical observations. So, the existing correlations may expect Nu and f for the factors investigated in this work, within acceptable limits.

Fig. 16
figure 16

Comparison of actual and anticipated findings of a Nu, b f for developed a correlation for DPPFSAH

Full size image

5.5 Comparison of Performance

Table 2 compares optimal values of Nu/Nus, f/fs and THPP of suggested rib roughness with other comparable rib designs examined by the researcher for DPSAH. Table 2 shows that in the current experimental set-up for a specific range of parameters, ribs having an open area ratio (β) = 0.27 outperformed the other set-ups compared in this study.

Table 2 Comparative of purposed rib configuration Nu/Nus, f/fs and THPP with the other comparable published rib shapes for SAH
Full size table

6 Conclusions

The THPP evaluations and airflow movements in a DPPFSAH duct demonstrate that perforated multi-V ribs created a considerable improvement in performance outcomes over a perforated SPSAH and smooth DPPFSAH, respectively. The following concise summary outlines the findings of the study:

  • Increasing the perforation size in multi-V rib DPPFSAH decreases friction losses and reattachment frequency and vortices’ dimensions behind the rib, improving fluid mixing and lowering blower power requirements by allowing secondary flow. It also improves the re-circulation region of flow on the ribs' base, resulting in a higher THPP for the DPPFSAH.

  • In DPPFSAH, the optimal performance was reported at an open area ratio (β) = 0.27 for all four values of β ranging from 0.0 to 0.31.

  • The best THPP results were obtained with a relative roughness width (W/w) = 6 for five different W/w values ranging from 2 to 10. For DPPFSAH, the optimum results for Nu/Nus, f/fs, THPP and TEIF were discovered at 9.66, 12.31, 3.96 and 1.33, as compared to the smooth plate, respectively.

  • The established correlations will be helpful in determining Nu and f values that indicate efficient thermal performance and less energy usage, within a set range of W/w, β and Re.

Perforated DPPFSAH outperforms the perforated SPSAH, followed by the continuous DPPFSAH and continuous SPSAH. The observations of the current study show the potential opportunity for the application of perforation in the various proposed rib geometries, so the researcher can examine these roughness for better performance and new optimum values can be drawn for rib roughness parameters of SAH.