# A Descriptive Review to Access the Most Suitable Rib’s Configuration of Roughness for the Maximum Performance of Solar Air Heater

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## Abstract

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## 1. Introduction

_{x}and CO

_{2}, in the environment. Solar energy is an indigenous and most promising energy source available worldwide. Among all available renewable sources of energy, solar energy is an infinite source of energy and also has the largest potential to fulfill the energy demand on earth. Solar energy can be converted into heat energy by using solar collector devices. Solar air heater (SAH) is the best example of these solar collector devices. The SAH heats the flowing air by absorbing direct and diffused solar radiation from low to moderate temperature for distinct applications, such as building heating, drying of vegetables, drying of fruits, timber seasoning, crop drying, space heating, and many other industrial and domestic purposes. It is free from problems related to freezing and corrosion. SAH can also be used to increase the efficiency and performance of a conventional drying system by integrating these systems in many applications, such as conveyer and fluidized bed drying systems.

## 2. Performance of SAH

#### 2.1. Heat Transfer Performance

#### 2.2. Hydraulic Performance

## 3. Historical Background of Conceptualization of Artificial Roughness in SAH

^{+}).

^{+}, which are shown in Figure 2.

^{+}> 0) is the same for a smooth and rough pipe, and the roughness exists entirely within the laminar sublayer. In the transitionally rough flow region, the magnitude of f increases with the rise in roughness Re as the value of f is a function of roughness Re in this range (70 > e

^{+}> 5). The thickness of the laminar sublayer is the same as the height of the roughness element in this region. Additionally, in the fully rough flow region, the value of f is not depending on the roughness Re in this range (e

^{+}> 70). The friction factor follows the quadratic law of resistance. The height of the roughness extends through the laminar sublayer.

^{+}is greater than 35. Vilemas and Simonis [11] experimentally investigated friction and convective heat transfer in inner rough tubes for Re numbers 5000 to 500,000. They also developed correlations for friction and heat transfer as given below;

_{e}≥ 0.0025:

- a = −0.4 when e
^{+}< 35 and a = 0 when e^{+}≥ 35 - b = −0.13 when p/e < 10 and $b=0.53{(\alpha /90\xb0)}^{0.71}$ when p/e ≥ 10

- i = 0 when e
^{+}< 35 and i = 0.28 when e^{+}≥ 35 - j = 0.5 when α < 45° and j = −0.45 when α ≥ 45°

_{h}, a geometrically similar roughness has the same effect on the convection coefficient and f. The convective coefficient decreases, and the value of f increases as e/D

_{h}increases. Gupta et al. [14] experimentally investigated that as the relative height of artificial roughness escalates, the optimum flow rate shifts to a lower value. They studied that the Stanton number increases up to Re = 12,000 and decreases after further increment in the value of Re.

## 4. Effect of Distinct Roughness Parameters

#### 4.1. Effect of Relative Rib Height

_{h}on the thermohydraulic performance of the SAH. The reattachment occurs only for a small value of e/D

_{h}and does not take place for higher values. The separation and reattachment of flow produced maximum convective heat transfer within a laminar sublayer region. Reattachment occurs only for a small value of e/D

_{h}(Figure 2). Amel Boulemtafes-Boukadoum et al. [15] investigated the performance of the SAH with the help of transverse ribs and also distributed ribs on heat transfer in the upward SAH. They used nondimensional heights of ribs as 66 and 50. The values of e/D

_{h}at which the highest rate of heat transfer was achieved for distinct roughness geometries are shown in Table 1.

#### 4.2. Effect of Relative Rib Pitch

_{h}and varying the value of pitch, as shown in Figure 3. The reattachment occurs only when the value of p/e is more than 8. The convection coefficient has the highest values near the reattachment point. The values of p/e at which highest rate of heat transfer was achieved for distinct roughness geometries are shown in Table 2.

#### 4.3. Effect of the Cross Section of Rib

#### 4.4. Effect of Angle of Attack

#### 4.5. Effect of Relative Gaps in Continuous Rib

#### 4.6. Effect of Reynolds Number

## 5. Artificial Roughness/Turbulators

#### 5.1. Transverse Ribs

_{h}increases, convective heat transfer goes on decreasing, and the value of f increases. The f and Nu are augmented 4.25 and 2.38 times, respectively, in comparison with a smooth duct. Gupta et al. [14] also experimentally investigated the thermohydraulic performance at p/e = 10 by using transverse roughness at Re varying from 3000 to 18,000; the aspect ratio of the duct varied from 6.8 to 11.5, and e/D

_{h}= 0.018 to 0.052. The St number increases up to Re = 12,000 and decreases for a higher value of Re. Singh et. al. [57] studied the effect of broken transverse ribs on the performance of the SAH for Re ranging from 3000 to 18,000. They used rib parameters of e/D

_{h}equal to 0.043 and p/e equal to 10. The maximum THPP is 2.10 at Re of 15,000. The highest value of thermal efficiency for smooth ducts and with multiple broken ribs is 44.26% and 72.25%, respectively. Additionally, the maximum effective efficiency is 44.25% and 69.15%, respectively. Prasad and Mullick [58] studied the effect of a small-diameter wire as roughness in transverse direction to the direction of the flow. The protruding wires as a roughness element augment the convection coefficient. The collector efficiency factor increases from 0.68 to 0.72 corresponding to the enhancement in thermohydraulic performance equal to 14% at Re = 40,000.

_{h}values from 001 to 0.03 at Re values of 5000 to 20,000. The value of e+ varied from 8 to 42. They obtained an optimum performance of 71% at e+ value of 24. Sahu and Bhagoria [20] studied the effects of a transverse broken rib (Figure 8) on the thermohydraulic performance of the SAH with e/D

_{h}= 0.0338 and a p/e range of 10–30. The height of the roughness was 15 mm, and values of Re = 3000–12,000. They reported that the value of Nu is the maximum for p/e = 20 and also studied that the smooth duct shows better thermal performance at low Re (i.e., below 5000 in comparison with a roughened duct). The heat transfer was augmented in the range of 1.25 to 1.40.

#### 5.2. Inclined Ribs

_{h}ranged from 0.023 to 0.050. The thermal efficiency was enhanced 1.16 to 1.25 times over the smooth duct. Aharwal et al. [63] studied the effect of a square cross-section inclined repeated rib with gaps (Figure 10) on the SAH for the value of e/D

_{h}equal to 0.0337, α equal to 60°, and p/e equal to 10 at Re ranging from 3000 to 18,000. The gap in inclined ribs generates a secondary flow, which creates extra turbulence and thermal performance. The friction factor and Nu were augmented up to 2.87 and 2.59 times, respectively, over the smooth duct. Further, Aharwal et al. [17] analyzed the performance by varying different parameters, such as e/Dh, α, p/e, and the relative gap position. The e/Dh, p/e, and α varied from 4 to 10, 0.018 to 0.0337, and 30° to 90°, respectively. The f and Nu were augmented up to 3.6 and 2.83 times, respectively, over the smooth duct for e/D

_{h}= 0.037, gap position = 0.25, and a gap width of 1. The flow over inclined ribs is shown in Figure 11. Lu and Jiang [64] experimentally investigated the effect of an inclined rib at α = 45° on the performance of the SAH in a rectangular duct. Further, they numerically investigated the thermohydraulic performance of an inclined rib with inclination angles as 0°, 10°, 20°, 30°, 45°, 60°, and 90°. The 60° inclined rib showed the highest convective heat transfer, and the 20° inclined rib showed the best thermohydraulic performance.

#### 5.3. V-Shaped Ribs

_{h}is kept fixed at 0.043. The thermohydraulic performance of the SAH strongly depends on the number of symmetrical gaps and g/e in the limbs. The f and Nu was augmented 3.67 and 3.6 times, respectively. The highest value of Nu is achieved at three symmetrical gaps and further, incremented in the number of gaps, degrading the thermal performance. The value of Nu increased up to g/e equal to 4 and thereafter decreased. Deo et al. [26] analyzed the effect of a multigap V-shaped down-rib combined with a staggered rib (Figure 16) on the performance of the SAH.

_{h}= 0.043, g/e = 1, α = 60°, and p/e = 10. The highest augmentation in Nu was found up to 3.18 times over the smooth duct. Jain and Lanjewar [70] analyzed the thermohydraulic performance of the SAH by using a V-shaped rib with symmetrical gaps combined with staggered ribs. The parameters p/e and Re varied from 10 to 16 and 3000 to 14,000, respectively, for a fixed value of p’/p = 0.65, α = 60°, and r/e = 4. The highest augmentations in the friction factor and Nu were 3.13 and 2.30, respectively, for p/e = 12.

_{h}= 0.040. They reported that a V-shaped rib combined with grooves shows the highest value of THPP as that of other investigated V-ribs of different arrangements. Nidhul et al. [73] used CFD and exergy analysis to study the effect of a secondary flow in the duct generated due to a V-shaped rib on the thermohydraulic performance of an SAH duct. Re ranged from 5000 to 20,000. The value of e/D

_{h}= 0.05, and p/e = 10. The reported value of the highest augmentation in Nu was 2.41 times over the smooth surface at Re = 7500 and α = 45°, and the maximum value of f was 2.53 times over the smooth surface at Re = 17,500 and α = 60°. Mishra et al. [74] used CFD analysis for a V-shaped down rib with multigap and turbulence promoters (Figure 18) to study the performance of a triangular-duct SAH in the Re range of 4000–20,000. The investigation covered an α range of 45° to 60° and a p/e range of 8 to 14. The maximum thermal performance was achieved at p/e = 10 and α = 45°. The THPP increased as Re increased from 4000 to 10,000, then thereafter decreased in the upper range of Re. Patel and Lanjewar [75] experimentally and numerically studied the effect of novel V-shaped ribs on the performance of the SAH. The study parameter varied as p/e = 6–14 whereas other parameters viz. p’/p = 4, r/e = 4, g/e = 4, α = 60°, e/D

_{h}= 0.043 and Ng = 3 with Reynolds number in the range of 4000 to 14,500. The highest augmentation took place in Nu = 1.55 to 2.26 and the friction factor = 2.63 to 3.40 at p/e equaling 10 and 8, respectively, in comparison with a smooth surface. The highest value of THPP = 1.59 was achieved at p/e = 10 and Re = 12,364. Further, Patel and Lanjewar [76] analyzed the effect of a V-shaped roughness geometry with staggered elements using additional gaps in symmetrically arranged elements of roughness (Figure 19) on the performance of the SAH. The distinct experimental parameters varied as e/D

_{h}equaled 0.043, g/e equaled 4, p/e equaled 10, p′/p equaled 0.4, Ng equaled 4, d/w equaled 0.25 to 0.85, and Re equaled 4000–15,000. The highest value of the THPP parameter was 1.82 at d/w equaling 0.65 and Re = 12,524. Alam et al. [77,78,79,80] experimentally analyzed the effect of V-shaped perforated blocks (Figure 20) on the performance of the SAH. The study encompassed parameter ranges of e/H = 0.4 to 1.0, p/e = 4 to 12, α = 60°, and Re = 2000 to 20,000. The highest augmentations in Nu and f were 6.76 and 28.84 over the smooth duct at e/H = 0.8 and p/e = 8. Further, Alam et al. [81] experimentally studied the effects of different types of perforation shapes on the performance of the SAH. They used square, rectangular, and circular types of perforation shapes in a 1–0.6 range of circularity. The value of α varied from 30° to 75°. The highest values of Nu and f were achieved at α = 60°. The noncircular shapes of perforation showed a higher thermal performance than that of circular shapes.

#### 5.4. Multi-V-Shaped Ribs

_{h}= 0.0454. The highest value of THPP equaling 4.24 was achieved. Kumar et al. [29] investigated the effect of a multi-V-shaped rib with gaps on the performance of a rectangular duct in a SAH, as shown in Figure 21. The ranges of various parameters were Re varying from 2000 to 20,000 and g/e = 0.5–1.5. The fixed value of α = 60°, e/D

_{h}= 0.043, and p/e = 10. The friction factor and Nu were augmented 6.13 and 6.32 times, respectively, in comparison with a smooth duct. The best value of THPP was achieved at g/e = 1 and d/x = 0.69. Further, Kumar et al. [84,85] studied the performance of this artificial roughness with the parameter’s W/w = 6, W/e = 12, e/D

_{h}= 0.0433, and g/e = 1.0. The value of α ranged from 30° to 75°. They reported that f and Nu are strong functions of α, and also, they have a maximum value at α = 60°. Jin et al. [86,87,88] numerically analyzed the effect of an inline and staggered multi-V-shaped rib on the performance of the SAH. The staggered arrangement had highest enhancement of 26% and 18% in Nu and THPP, respectively, over the inline arrangement of ribs. The maximum value of THPP was 2.43. Promvonge and Skullon [89] studied the effect of V-shaped flap-baffle and chamfered-grove vortex generators (VG) on the performance of a roughened duct, as shown in Figure 22. Both the flap baffle and VG were at α equal to 45°, and the experiment was performed in both the apex-up and apex-down pattern of a V-shaped flap baffle in the range of Re = 5290–22,600. The apex-up pattern had better performance in comparison with the apex-down pattern of V-shaped flap baffles. Nu and the friction factor were enhanced remarkably by using this type of roughness. They reported that the maximum value of TEF was 2.68 at Re = 5290.

#### 5.5. Arc-Shaped Ribs

_{h}= 0.03. Sahu and Prasad et al. [90] investigated effect of an arc-shaped wire type of roughness on the performance of the SAH by using exergy efficiency analysis, as shown in Figure 24. The maximum augmentation in the exergetic efficiency corresponding to e/D

_{h}equaled 0.0422, which was 56% as that of the smooth-plate SAH. The exergetic efficiency strongly depends on the various roughness parameters and Re. Gill et al. [91,92] investigated the effect of a broken-arc rib combined with staggered rib pieces on the performance of the SAH. The experimental parameters encompassed r/g = 1 to 6, α/90 = 0.333, p’/p = 0.4, W1/w = 0.65, e/D

_{h}= 0.043, and Re = 2000 to 16,000. The f and Nu were augmented 2.50 and 3.06 times as that of the smooth duct and 2.77 and 2.60 times over the broken-arc-type-rib roughened duct. The highest value of THPP was achieved at r/g = 4. On the same type of roughness, Hans et al. [33] further studied the effect of broken-arc-shaped artificial roughness (Figure 25) on the thermohydraulic performance of the SAH. The study encompassed parameters of p/e equal to 4–12, g/e equal to 0.5–2.5, e/D

_{h}equal to 0.022–0.043, d/x equal to 0.2–0.8, α’ equal to 15°–75°, and Re varying from 2000 to 16,000.

_{h}= 0.0395. The highest efficiency of the apex-up pattern was achieved at 73.2%, and for the apex-down pattern, it was 69.2%. The apex-up pattern performed 33.2% better in comparison with the apex-down arrangement. The thermal performance of the apex-up pattern was better as compared with the apex-down pattern of an arc-shaped artificially roughened duct. Yadav and Prasad [94] theoretically studied the effect of arc-shaped wire roughness on the performance of a parallel-flow SAH. The thermal efficiency of a roughened parallel-flow SAH was 8% to 10% higher in comparison with a smooth SAH. Ambade and Lanjewar [95] experimentally studied the effect of a symmetrical gap with arc-shaped roughness and a staggered element on the performance of the SAH at Re equal to 3000–15,000 and p/e equal to 6–14. The fixed parameters were p’/p = 3, g/e = 4, r/e equal to 4, Ng equal to 3, and α’ equal to 30°. They compared this geometry with the smooth duct and the duct having broken-arc-shaped rib roughness with staggered elements. The arc-shaped roughness with a new symmetrical gap augmented the friction factor and Nu up to 4.15 and 2.04 times, respectively, over the broken-arc-shaped roughness with a staggered element, while augmentation in Nusselt number and friction factor were 2.18 and 3.88 times, respectively with corresponding smooth duct. Azad et al. [96] investigated the effect of a discrete-symmetrical arc type of rib roughness on the performance of the SAH. The values of the experimental parameters covered in the study were e/D

_{h}= 0.045, g/e = 2–5, Ng = 3, p/e = 10, α’ = 30°, and Re = 3000 to 14,000. The value of g/e had a remarkable effect on the performance. The highest enhancement reported in Nu was equal to 3.88 over the smooth duct at g/e = 4. The value of THPP ranged from 1.4 to 1.68 at g/e = 4, and the best value of THPP was 1.68 at Re equal to 14,000. Gill et al. [97] analyzed the effect of staggered broken-arc hybrid-rib roughness on the thermohydraulic performance of the SAH. The parameters of the study ranged as e/D

_{h}= 0.022–0.043, α’ = 15–75°, p/e = 4–12, and Re = 2000–16,000. The f and Nu were augmented 2.57 and 3.16 times over the broken-arc roughened duct. The highest value of THPP was reported to be 2.33. Sureandhar et al. [98] studied the effect of arc-rib fin-type roughness on the performance of the SAH. The experimental parameters of the study varied as e/D

_{h}= 0.04222–0.0541, α/90 = 0.3333, and p/e = 10. Nu and THPP increased as the mass flow rate increased, while the friction factor decreased.

#### 5.6. Multi-Arc-Shaped Ribs

_{h}= 0.027, and Re = 3010. The friction factor at α’ = 60°, e/D

_{h}= 0.027, and Re = 3010 was 0.0342. Hassan et al. [103] studied the effect of a multiarc dimple-shaped roughness (Figure 26) on the performance of the SAH. They covered experimental parameters of p/e equal to 4–16, W/w equal to 1–5, e/D

_{h}equal to 0.018–0.036, α’ equal to 30°–75°, and Re equal to 2000–18,000. They reported that the highest value of Nu was 3.19 to 5.56 times that of the smooth duct at p/e equal to 12. The value of Nu increased up to e/D

_{h}equal to 0.036; after that, it decreased. The enhancement in the friction factor equaled 1.36 to 2.27 times in comparison with the smooth duct at e/D

_{h}equal to 0.045. Agrawal et al. [104] experimentally investigated the effect of a double-arc reverse rib with even gaps on the performance of a solar collector. The values of the fixed parameters were e/D

_{h}= 0.027, W/H = 8, and I = 1000 W/m2. The value of the variable parameter varied as p/e equal to 10, α equal to 30°–75°, and Re equal to 3000–14,000. The maximum augmentations in f and Nu were found to be 2.42 and 2.85 times over the smooth surface. The highest value of THPP equal to 2.41 was noticed at p/e = 10 and e/D

_{h}= 0.0270.

#### 5.7. W-Shaped Ribs

_{h}equal to 0.03375, Re range of 2300–14,000, and p/e equal to 10. The ranges of THPP were 1.21 to 1.73 and 1.46 to 1.95, respectively, for top-up and top-down patterns. The W-down pattern of artificial roughness had better performance in comparison with the W-up pattern. Kumar et al. [38] studied the effects of a discrete-W-shaped rib (Figure 27) on the performance of the SAH in the Re range of 3000 to 15,000. The value of the parameter p/e was fixed at 10, e/D

_{h}varied from 0.0168 to 0.0338, and α varied from 30° to 75° during the experiment. The highest augmentations in the friction factor and Nu were found to be 2.75 and 2.16 at e/D

_{h}= 0.0338 and α = 60°. Kumar et al. [105] investigated the effect of W-shaped ribs with a booster mirror on the performance of the SAH. The combination of W-shaped roughness with a booster mirror enhanced Nu, St, and the friction factor by 29–38%, 31–39%, and 23–29% in comparison with that without a booster mirror.

#### 5.8. L-Shaped Ribs

_{h}was fixed at 0.042. The highest enhancement in Nu was found up to 2.827 times as that of the smooth duct at p/e = 7.14 and Re = 15,000. The highest augmentation in the friction factor was found up to 3.424 times over the smooth duct at e/D

_{h}= 0.042, Re = 3800, and p/e = 7.14. THPP was found to be in the range of 1.92 to 1.90 by using this repeated roughness.

#### 5.9. S-Shaped Ribs

_{h}= 0.022–0.054, p/e = 4–16, W/w = 1–4, α = 30°–75°, and Re = 2400–20,000. The utilization of arc-shaped roughness in an ‘S’ type of pattern augmented the friction factor and Nu 2.71 and 4.64 times, respectively, in comparison with a smooth duct at the parameter’s p/e, W/w, and α at 8, 3, and 60° respectively. Wang et al. [107] analyzed the effect of an S-shaped rib with gaps (Figure 30) on the performance of the SAH. The various parameters varied as Re = 2000 to 20,000, p/e = 20 to 30, e/D

_{h}= 0.023 to 0.036, W/w = 3 to 5, and g/e = 1 to 2. The highest increase in Nu was found 5.42 times as that of the smooth duct at the parameters p/e = 20, W/w = 4, and Re = 19,258. The highest increase in f was 5.87 times over the smooth duct.

#### 5.10. Delta Winglet-Shaped Ribs

_{h}= 0.8, and α = 45°. The friction factor and Nu were augmented 45.83 and 6.94 times in comparison with a smooth duct. The best value of TEF was equal to 2.26 at Re = 11,382. Kumar and Layek [109,110] analyzed the performance of a SAH duct with the help of winglet types of vortex generators (Figure 31). The experimental parameters covered the ranges of parameters as p/e = 5–12, α = 30°–75°, W/w = 3–7, and Re = 3000–22,000. The optimum value of Nu was achieved at α = 60° and p/e = 8. Kumar et al. [111] analyzed the performance of the SAH by using delta-shaped winglets with perforation. The thermohydraulic performance had a maximum value of 3.14 at Re = 12,000 and with a zero spacer length. The f and Nu were augmented 4.52 and 5.17 times, respectively, as that of the smooth duct. Promvonge et al. [112] analyzed the effect of a punched delta-shaped winglet type of roughness in the duct of the SAH. The experimental parameters covered the ranges of parameters as P

_{R}varying from 1 to 2, d

_{R}varying from 0 to 0.583, Re varying from 4000 to 24,000, and angle of attack equal to 30°. Nu was enhanced in the range of 17.1 to 78.21, and the friction factor was augmented in the range of 3.92 to 5.9 in comparison with a smooth duct.

#### 5.11. Quarter Circular-Shaped Ribs

_{h}= 0.042. Nu and f were augmented 2.7816 and 3.4355 times at Re equal to 15,000 and 3800 and p/e equal to 7.14, respectively. The thermal augmentation ratio had a maximum value of 1.88 at e/D

_{h}equal to 0.042, Re equal to 15,000, and p/e equal to 7.14.

#### 5.12. Dimple/Protrusion-Shaped Roughness

_{h}= 0.03, W/H = 10, d’/D = 0.147–0.367, and Re = 4000 to 20,000. The protruded duct surface had a higher value of convection coefficient in comparison with a smooth duct. The highest values of f and Nu were 2.2 and 3.8 times as that of the smooth duct. The highest augmentation in convection coefficient occurred at L/e = 31.25 and d/D = 0. 294. Gilani et al. [114] experimentally investigated the effect of pin-type protrusions of conical shape on the performance of the SAH. The staggered arrangement pattern of protrusion was much more effective compared with the inline pattern arrangement by up to 15% at Ra = 50,000 to 75,000. They tested three types of conical pin protrusions of 2, 3, and 4-mm height. The experiment was performed at pith values of 16, 32, and 48 mm. The highest value of Nu was achieved at p = 16 mm, and the efficiency was enhanced by 26.5% at this pith value. Perwez and Kumar [115] analyzed the thermal performance of the SAH with spherical dimple-shaped roughness at the absorber plate at Re varying from 1900 to 6000. The maximum value of convection coefficient was 20.23 W/m

^{2}K, and the instantaneous thermal efficiency was 23.45–35.50% higher in comparison with a smooth duct.

#### 5.13. Pentagonal Shape Ribs

_{h}= 0.045–0.084, and p/e = 6.43–8. The optimum configurations of various parameters were found as e/D

_{h}equal to 0.045 and Re equal to 38,414. The augmentations in the friction factor and Nu at optimum configuration were 67.2% and 70%, respectively, over the smooth duct.

#### 5.14. Stepped Cylinder Ribs

#### 5.15. NACA Profile Ribs

#### 5.16. C-Type Rib Roughness

_{h}were 2 mm, 10, and 0.02, respectively. The highest value of Nu was found to be 415 at Re = 15,000 and p/e = 24. The value of THPP was equal to 3.48. Saravanan et al. [120] studied the effect of the staggered multi-C-shape finned surface of the absorber on the performance of the SAH. They investigated both perforated and nonperforated surfaces of the absorber. The experimental parameters varied as p/g = 3.4–3.8 and Re = 3000–27,000. The secondary flow generated along the surface of the fin and the mixing of the secondary flow developed in the duct with the mainstream of flow enhanced the level of turbulence remarkably. In the case of perforated surface, the friction factor Nu was augmented 5.34 and 2.67 times as that of the smooth duct at p/g = 3.8. In the case of a nonperforated surface, the friction factor and Nu were augmented 5.93 and 2.61 times over the smooth duct.

#### 5.17. Twisted Tapes

#### 5.18. Hyperbolic-Shaped Ribs

#### 5.19. Wedge-Shaped Rib

_{h}= 0.015–0.033, Re = 3000–18,000, p/e = 60.17ϕ

^{−1.0264}< p/e < 12.12, and α = 8°–15°. The friction factor and Nu were augmented 5.3 and 2.4 times, respectively. The highest heat transfer performance was achieved at ϕ about 10° and p/e = 7.57. Nu decreased on both sides of this wedge angle.

#### 5.20. Spherical-Ball-Type Roughness

_{b}= 0.5 to 2, and Re = 2500 to 18,500. They reported that the highest thermal efficiency achieved was 81.30% at α = 55°, e/d

_{b}= 1, and p/e = 15. The lowest thermal efficiency was achieved at p/e = 9.

#### 5.21. Combination of Different Types of Ribs

_{h}= 0.055, α = 90°, Re = 4000–16,000, and p/e = 10. Rib arrangement in a roughened duct had a remarkable effect on the performance of the SAH. Case 1 of rib arrangement showed the highest augmentation in average Nu equal to 49.28. Case 4 showed the highest augmentation in friction factor equal to 2.88 to 7.18 over the smooth duct.

_{h}= 0.04, and α = 60°. The augmentations in f and Nu were reported as 1.58 and 2.88 times as that of the smooth duct. The highest value of THPP was equal to 3.66 at p/e = 25. Luo et al. [130] numerically studied the effect of a delta winglet vortex generator combined with a dimple type of roughness on the performance of the SAH. Re ranged from 4000 to 40,000. The f and heat transfer were enhanced by 36.29% and 36.23%, respectively. Skullong et al. [131] experimentally studied the effect of wavy-rib-grove turbulators (Figure 38) on the heat transfer performance of the SAH. The experimental parameter varied as e/H = 0.25, p/H = 0.5 to 2, and Re = 4000 to 21,000. The wavy rib was at α = 45° with respect to the flow stream. The rib-grove pattern on the upper and lower walls of the duct showed the highest performance at p/H = 0.5. Kumar et al. [132] numerically studied the effect of polygon- and trapezoid-shaped ribs on the performance of the SAH. The value of the parameter e/D

_{h}ranged from 3.33 to 20, p/e from 0.03 to 0.09, and Re from 3800 to 18,000. The highest augmentation in Nu equal to 2.483 was achieved in comparison with a smooth surface. The highest value of THPP equal to 1.89 was achieved at e/D

_{h}= 0.06 and p/e = 10. Tanda and Satta et al. [133] analyzed the effect of 45° angled and intersecting rib roughness on the performance of a rectangular duct as shown in Figure 39. The intersecting ribs were parallel to the stream of flow. The intersecting ribs enhanced the turbulence level in the duct due to which the thermohydraulic performance improved. The augmentation in Nu was slightly larger when two intersecting ribs were used instead of one intersecting rib. Farhan et al. [134] numerically studied the effect of a V-shape rib corrugated surface integrated with a twisted tape type of roughness (Figure 40) on the exergetic and energetic efficiency of the SAH. The thermal performance with twisted tape inserts in the channels had a remarkable increase in comparison with that without a twisted tape insert. It was 74.42% at Re = 12,000 and 68% in the case of that without a twisted tape insert.

#### 5.22. Other Roughnesses

_{h}= 0.043 was fixed. The highest augmentations in friction factor and Nu were found to be 3.55 and 2.14 times that of the smooth duct at Re = 15,000. They reported the highest value of THPP as 1.43 at Re = 12,000 and p/e = 10. Ansari and Bazargan [136] investigated the effect of L/H, e/Dh, p/e, and W/H on the heat transfer performance of the SAH. They reported that the optimum value of e/D

_{h}incremented as the value of the rate of flow decreased. The overall efficiency of the SAH was enhanced by more than 9% with the help of a ribbed surface. Alfarawi et al. [137] analyzed the effect of hybrid-rib roughness of rectangular and semicircular cross sections on the performance of the SAH. The study parameters encompassed p/e = 6.6 to 53.3 and Re = 12,500 to 86,500. The enhancements in the friction factor and Nu were 1.8 to 4.2 and 1.3 to 2.14, respectively. The highest increase in heat transfer was achieved at p/e = 6.6 in the case of hybrid ribs. Alam and Kim [138] numerically investigated the effect of a semi-elliptical-shaped obstacle type of roughness in a V-down pattern on the performance of the SAH. The parameter varied as α = 30°–90° and Re = 6000–18,000. The pattern of obstacles on the duct surface and α had a remarkable impact on thermal performance due to a high level of turbulence. The highest augmentations in f and Nu were 6.93 and 2.05, respectively, at α = 75° for a staggered pattern. Xiao et al. [139] numerically investigated the effect of inclined trapezoid-shape turbulators on the thermohydraulic performance of the SAH. Nu increased significantly, and energy efficiency was augmented by 24% and exergy efficiency was augmented by 31% over the smooth duct.

_{h}= 0.17–0.34, Re = 3000–16,000, and p/e = 8–15. The highest value of Nu = 142.4 was achieved at e/D

_{h}= 0.34, p/e = 8, and Re = 16,000 as that of a smooth duct. The highest value of f equaled 0.167 reported at p/e = 8, e/D

_{h}= 0.34, and Re = 3500. The heat transfer performance was augmented by 192.2%. Dong et al. [142] numerically investigated the effect of an incline-grove ripple type of roughness on the performance of the SAH at Re in the range of 12,000–24,000. The incline-grove on the ripple surface enhanced the level of turbulence remarkably. The optimum value of α was near 45° to 60°.

_{h}= 0.02 to 0.044 and p/e = 6 to 12. The conical protrusion type of artificial rib roughness had a remarkable effect on the effective efficiency of the SAH. They reported the maximum value of effective efficiency as 70.92% at e/D

_{h}= 0.0289 and p/e = 10. Kumar and Goel [145,146] analyzed the effects of a distinct type of rib roughness on the thermohydraulic performance of the SAH by using a triangular cross-section channel. The performance of the SAH strongly depended on the cross section of artificial roughness and also the cross section of a flow passage. A rectangular cross-section rib with forwarding chamfering showed the highest THPP at 2.75. Further, Goel et al. [147] analyzed the effect of the hemispherical dimple cavity type of roughness on the performance of the SAH by using a triangular cross-section channel. The leading edge of the dimple-cavity-type roughness showed lower heat transfer than that of a trailing edge. The highest augmentation value of Nu equal to 5.33 was achieved at Re = 2160. The value of THPP was equal to 3.48. Xi et al. [148] numerically studied a ribbed channel for Re ranging from 10,000 to 90,000. The study parameter ranged as e/D varying from 0.05 to 0.15 and rib angle varying from 30° to 90°.

## 6. Performance Evaluation Parameters

## 7. Methodology and Formation of MATLAB Code for Calculating Thermal Efficiency

## 8. Thermal Performance of Roughened SAH

_{s}and THPP change from 0.75 to 14.20 and 0.39 to 5.58 in the Re range of 3000 to 24,000, respectively. The least values of Nu/Nu

_{s}are recognized for the metal grit type of roughness and the highest value in the case of staggered broken-arc hybrid-rib roughness. The least values of THPP are recognized for the combination of inclined and transverse rib pattern and the highest value in case of S-type of the rib. The multiple V-rib with gaps, continuous multiribs, and multiarc ribs with a gap also show a higher value of THPP. However, the performance of S-type of the rib is not considerable at low RE, but at a higher Re performance it increases tremendously. The creation of gaps in the continuous ribs has shown remarkable improvement in the performance as compared with continuous ribs. The gap in ribs introduces a secondary flow in the stream of flow, which is generated due to vortices on the upstream side of the roughness. The secondary flow augments the level of turbulence remarkably due to its mixing with the main flow. The improvement in Nu due to the creation of gaps in the continuous ribs ranges from 1.1 to 1.3 times, and the corresponding increase in pumping power requirement ranges from 1.0 to 1.4 times.

## 9. Conclusions

- The shape and size of artificial roughness and their pattern of arrangements on the duct surface are the most important factors for the performance optimization of the SAH.
- The thermohydraulic characteristics of a large number of rib geometries have been investigated by many researchers. For most of the rib roughness geometries, the optimum performance has been achieved at the following parameters: p/e = 10, W/w = 6, α = 60°, and e/D
_{h}= 0.043. - THPP and thermal efficiency show the highest values in the case of staggered broken-arc type of hybrid rib and least values in the case of metal grit, twisted tape, and delta-shaped vortex generator type of roughness.
- The multi-V and multiarc-shaped roughnesses show higher thermohydraulic performance over other roughness geometries. The introducing gaps in the limb of multi-V-ribs enhance the level of turbulence significantly.
- The multi-V-shaped ribs show a higher value of the friction factor, and arc-shaped circular dimples show a lower value of the friction factor.
- The broken-arc-shaped rib combined with a staggered-arc rib piece has better performance than broken-arc-shaped and arc-shaped rib roughness.
- The creation of gaps in the continuous ribs has shown remarkable improvement in thermohydraulic performance over the continuous ribs. The improvement in Nu due to the creation of gaps in the continuous ribs ranges from 1.1 to 1.3 times, and corresponding increase in pumping power requirement ranges from 1.0 to 1.4 times.
- THPP shows higher values in the case of an S-shape rib, multi-V ribs, and arc-shaped roughnesses with gaps. However, the performance of an S-shaped rib is not considerable at low Re, but the performance increases remarkably with the increase in Re.
- The arc arrangement of rib roughness shows lower value pressure losses over the V-shaped arrangement due to the curved nature of the induced secondary flow along with the roughness.
- In general, higher roughnesses’ height has a higher Nusselt number; however, higher roughnesses’ height contributes to higher pressure drop. Therefore, the thermohydraulic performance of roughnesses needs to be optimized. In this regard, net effective efficiency is the best tool to analyze roughnesses. On the basis of net effective efficiency, a multiarc rib with gaps is found to be best around 79% in comparison with other rib configurations, which is recommended for overall better performance.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Symbol | Title | Unit |

b | Roughness width | m |

c | Characteristic separation length | m |

d’ | Diameter of dimples | m |

d/x | Relative gap position | - |

d_{R} | Relative punched hole size | - |

D | Pipe inside diameter (to base of ribs) | m |

D_{e} | Equivalent diameter of annulus (d_{1} − d_{2}) | m |

D_{h} | Hydraulic diameter of duct | m |

e | Height of roughness element | m |

e^{+} | Roughness Reynolds number | - |

e/D_{h} | Relative roughness height | - |

e/H | Blockage ratio | - |

f_{s} | Smooth surface friction factor | - |

f | Friction factor of roughened surface | - |

F_{R} | Heat removal factor | - |

g | Roughness function of heat transfer | - |

g/e | Relative gap width | - |

H | Duct height | m |

I | Insolation | W/m^{2} |

L | Length of test section | m |

Nu | Nusselt number | - |

N_{g} | Number of gaps on half arc | - |

p/g | Relative pitch-to-gap ratio | - |

p’/p | Relative staggered rib pitch | - |

p/H | Rib-pitch-to-channel-height ratio | - |

P_{t}/b | Relative longitudinal length of obstacles | - |

P_{t}/e | Relative transversal length of obstacles | - |

P_{R} | Relative winglet pitch | - |

Q_{u} | Heat gain | W |

Qe^{+} | Heat transfer function | - |

r/e | Relative staggered rib size | - |

R | Momentum transfer roughness function | - |

Ra | Rayleigh number | - |

Re | Reynolds number | - |

S | Short way length between dimples | m |

s’/s | Relative gap position | - |

St | Stanton number | - |

T_{a} | Ambient temperature | K |

T_{i} | Air inlet temperature | K |

T_{f} | Mean air temperature | K |

T_{p} | Plate temperature | K |

T_{w} | Wall temperature | K |

ΔP | Pressure drops | N/m^{2} |

U_{O} | Overall heat loss coefficient | W/m^{2}·K |

V | Velocity of air in the SAH duct | m/s |

w/e | Staggered rib length to rib height | - |

W/e | Width-to-height ratio | - |

W/H | Width-to-duct-height ratio | - |

W/w | Relative roughness width | - |

W_{1}/w | Relative gap position | - |

x | Distance from starting | m |

η | Thermohydraulic performance parameter | - |

η_{th} | Thermal efficiency of solar collectors | - |

Ρ | Density | kg/m^{3} |

$\psi $ | Temperature factor T_{w}/T_{f} | - |

α | Angle of attack | degree |

α’ | Arc angle | degree |

α/90 | Relative arc angle | - |

$\phi $ | Chamfering angle of rib | degree |

β | Slope | degree |

β’ | Thermal expansion coefficient of air | 1/K |

ε_{g} | Glass cover emissivity | |

ε_{p} | Absorber plate emissivity | |

υ | Kinematic viscosity | m^{2}/s |

τ | Transmissivity | |

σ | Stefan–Boltzmann constant | W/m^{2}·K^{4} |

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**Figure 2.**Flow patterns due to distinct relative rib height [13].

**Figure 4.**Nu vs. Re for various cross sections of rib roughness [16].

**Figure 5.**Vortices due to 45° angled rib [51].

**Figure 6.**Flow pattern of inclined discrete–continuous ribs [54].

**Figure 7.**Chamfered transverse rib roughness [61].

**Figure 8.**Transverse broken ribs [54].

**Figure 9.**Inclined repeated ribs [65].

**Figure 10.**Inclined continuous repeated ribs with a gap [17].

**Figure 11.**Flow over inclined ribs [66].

**Figure 12.**V-shaped type of rib roughness [24].

**Figure 13.**V-down discrete rib [19].

**Figure 14.**Multi-V-rib roughness [28].

**Figure 15.**V-shaped rib with multiple symmetrical gaps [25].

**Figure 16.**Multiple-gap V-shapes down-rib combined with a staggered rib [26].

**Figure 17.**V-shaped broken rib combined with staggered ribs [82].

**Figure 18.**V-shaped rib with multiple gaps and turbulators [74].

**Figure 19.**V-shaped roughness geometry with staggered elements [76].

**Figure 20.**V-shaped perforated blocks [80].

**Figure 21.**Multi-V-shaped rib with gap [29].

**Figure 22.**V-shaped flap-baffle and chamfered-grove vortex generators [89].

**Figure 23.**Arc-shaped protrusions as artificial roughness [32].

**Figure 24.**Arc-shaped artificial roughness [90].

**Figure 25.**Brocken-arc-shaped roughness [33].

**Figure 26.**Multiarc dimple-shaped roughness [103].

**Figure 27.**W-shaped artificial roughness [106].

**Figure 28.**L-shaped artificial roughness [39].

**Figure 29.**Arc-shaped wire ribs arranged in an ‘S’ type of pattern [40].

**Figure 30.**S-shaped ribs with gaps [107].

**Figure 31.**Winglet types of vortex generator [109].

**Figure 32.**Protrusion-type roughness [41].

**Figure 33.**Multi-C-type rib roughness [119].

**Figure 34.**Hyperbolic-shaped ribs [124].

**Figure 35.**Wedge-shaped roughness [46].

**Figure 36.**Spherical turbulators [125].

**Figure 37.**Spherical ball type of roughness in an inclined pattern [126].

**Figure 38.**Wavy-rib-grove turbulators [135].

**Figure 39.**45° angled and intersecting rib roughness [133].

**Figure 40.**V-shaped rib corrugated surface integrated with twisted tape [134].

**Figure 41.**Transverse rib with square wave type of profile [42].

**Table 1.**Values of e/D

_{h}at which the highest rate of heat transfer for distinct roughness geometries is investigated in the SAH duct.

S. No. | Researchers | Geometry of Artificial Roughness | Value of e/Dh |
---|---|---|---|

1 | Prasad and Saini [13] | Continuous transverse rib | 0.0333 |

2 | Singh et al. [16] | Nonuniform saw-tooth-shaped rib | 0.043 |

3 | Aharwal et al. [17] | Inclined rib with gap | 0.0377 |

4 | Singh et al. [18,19] | V-shaped with gap | 0.043 |

5 | Sahu and Bhagoria [20] | Broken transverse rib | 0.0338 |

6 | Yadav and Bhagoria [21] | Triangular-shaped rib | 0.042 |

7 | Yadav and Bhagoria [22] | Square-shaped rib | 0.042 |

8 | Gupta et al. [23] | Continuous inclined rib | 0.033 |

9 | Momin et al. [24] | V-shaped continuous rib | 0.034 |

10 | Maithani and Saini [25] | V-shaped rib with symmetrical gap | 0.043 |

11 | Deo et al. [26] | Multi-V-shaped rib with gap combined with staggered rib | 0.044 |

12 | Patil et al. [27] | V-rib with gaps combined with staggered rib | 0.0433 |

13 | Hans et al. [28] | Continuous multi-V-rib | 0.043 |

14 | Kumar et al. [29] | Multi-V-rib with gap | 0.043 |

15 | Saini and Saini [30] | Arc rib | 0.0422 |

16 | Sethi et al. [31] | Dimple rib in arc pattern | 0.036 |

17 | Yadav et al. [32] | Dimple rib in arc pattern | 0.030 |

18 | Hans et al. [33] | Brocken arc rib | 0.043 |

19 | Pandey et al. [34] | Multiarc rib with gaps | 0.044 |

20 | Singh et al. [35] | Multiarc rib | 0.045 |

21 | Lanjewar et al. [36,37] | Continuous W-rib | 0.03375 |

22 | Kumar et al. [38] | Discrete W-rib | 0.03375 |

23 | Gawande et al. [39] | L-shaped rib | 0.042 |

24 | Kumar et al. [40] | S-shaped rib | 0.043 |

25 | Bhushan and Singh [41] | Protrusion roughness | 0.030 |

26 | Singh I and Singh S [42] | Transverse rib with square wave profile | 0.043 |

27 | Saini and Saini [43] | Expanded metal mesh | 0.039 |

28 | Karmare and Tikekar [44] | Metal grit | 0.044 |

**Table 2.**Values of p/e at which the highest rate of heat transfer for distinct roughness geometries is investigated in the SAH duct.

S. No. | Investigators | Type of Roughness | p/e |
---|---|---|---|

1 | Prasad and Saini [13] | Continuous transverse rib | 10 |

2 | Singh et al. [16] | Nonuniform saw-tooth-shaped rib | 8 |

3 | Aharwal et al. [17] | Inclined rib with gap | 10 |

4 | Singh et al. [18,19] | V-shaped with gap | 8 |

6 | Yadav and Bhagoria [21] | Triangular-shaped rib | 7.14 |

7 | Yadav and Bhagoria [22] | Square-shaped rib | 7.14 |

8 | Gupta et al. [23] | Continuous inclined rib | 10 |

9 | Momin et al. [24] | V-shaped continuous rib | 10 |

10 | Karwa [45] | Transverse rib | 10 |

11 | Maithani and Saini [25] | V-shaped rib with symmetrical gap | 10 |

12 | Deo et al. [26] | Multi-V-shaped rib with gap combined with staggered rib | 12 |

13 | Patil et al. [27] | V-shaped rib with gap combined with staggered rib | 10 |

14 | Saini and Verma [46] | Dimple-shaped | 10 |

15 | Hans et al. [28] | Continuous multi-V-rib | 8 |

16 | Kumar et al. [29] | Multi-V-ribs with gap | 10 |

17 | Saini and Saini [30] | Arc ribs | 10 |

18 | Sethi et al. [31] | Dimple rib in arc pattern | 10 |

19 | Yadav et al. [32] | Dimple rib in arc pattern | 12 |

20 | Hans et al. [33] | Brocken arc rib | 8 |

21 | Pandey et al. [34] | Multiarc rib with gaps | 8 |

22 | Singh et al. [35] | Multiarc rib | 8 |

23 | Lanjewar et al. [36,37] | Continuous W-rib | 10 |

24 | Kumar et al. [38] | Discrete W-rib | 10 |

25 | Gawande et al. [39] | L-shaped rib | 7.14 |

26 | Kumar et al. [40] | S-shaped rib | 8 |

27 | Bhagoria et al. [47] | Wedge-shaped rib | 7.57 |

28 | Karmare and Tikekar [44] | Metal grit | 17.5 |

29 | Layek et al. [48] | Chamfered rib combined with groove | 6 |

**Table 3.**Values of α at which the highest heat transfer rate for distinct geometries of roughness is investigated in the SAH duct.

S. No. | Investigators | Type of Roughness | Value of α |
---|---|---|---|

1 | Aharwal et al. [17] | Inclined rib with gaps | 60 |

2 | Gupta et al. [23] | Continuous inclined rib | 60 |

3 | Momin et al. [24] | V-shaped continuous rib | 60 |

4 | Maithani and Saini [25] | V-shaped rib with symmetrical gaps | 60 |

5 | Deo et al. [26] | Multi-V-shaped rib with gaps combined with staggered rib | 60 |

6 | Patil et al. [27] | V-shaped rib with gaps combined with staggered rib | 60 |

7 | Hans et al. [28] | Continuous multi-V-rib | 60 |

8 | Kumar et al. [29] | Multi-V-shaped rib with gap | 60 |

9 | Sethi et al. [31] | Dimple rib in arc pattern | 60 |

10 | Yadav et al. [32] | Dimple rib in arc pattern | 60 |

11 | Pandey et al. [34] | Multiarc rib with gap | 60 |

12 | Singh et al. [35] | Multiarc rib | 60 |

13 | Lanjewar et al. [36,37] | Continuous W-rib | 60 |

14 | Kumar et al. [38] | Discrete W-rib | 60 |

15 | Kumar et al. [40] | S-shaped rib | 60 |

16 | Saini and Saini [43] | Expanded metal mesh | 61.9 |

Investigators | Type of Roughness | Parameter Used | Augmentation |
---|---|---|---|

Prasad and Saini [13] | Continuous transverse rib | e/D = 0.02–0.033 p/e = 10–20 | Nu/Nu_{s} = 2.35f/f _{s} = 4.25 |

Singh et al. [16] | Nonuniform saw-tooth-shaped rib | e/D_{h} = 0.043, p/e = 8Re = 3000–15,000 | Nu/Nu_{s} = 1.78f/f _{s} = 2.49 |

Aharwal et al. [17] | Inclined rib with gaps | g/e = 0.5–2 e/D _{h} = 0.018–0.0377α = 30°–90° d/W = 0.16–0.67 p/e = 4–10 | Nu/Nu_{s} = 2.83f/f _{s} = 3.60 |

Singh et al. [18,19] | V-shape with gap | e/D_{h} = 0.015–0.043d/w = 0.2–0.8 g/e = 0.5–2.0 p/e = 4–12 α = 30°–75° | Nu/Nu_{s} = 3.04f/f _{s} = 3.11 |

Sahu and Bhagoria [20] | Broken transvers ribs | p = 10–30 mm e/D = 0.0338 | h/h_{s} = 1.25–1.4 |

Yadav and Bhagoria [21] | Triangular-shaped ribs | Re = 800–18,000 p/e = 7.14–35.71 | Nu/Nu_{s} = 3.07f/f _{s} = 3.35 |

Yadav and Bhagoria [22] | Square shape ribs | e/D_{h} = 0.021–0.042, Re = 000–18,000, p/e = 7.14–35.71 | Nu/Nu_{s} = 2.86f/f _{s} = 3.84 |

Gupta et al. [23] | Continuous inclined ribs | W/H = 6.8–11.5 e/D = 0.023–0.050 α = 60° | η/η_{s} = 1.16–1.25 |

Momin et al. [24] | V-shaped continuous rib | p/e = 4–10 e/D _{h} = 0.02–0.034α = 30°–90° | Nu/Nu_{s} = 2.30f/f _{s} = 2.89 |

Maithani and Saini [25] | V-rib with symmetrical gaps | α = 30°–75° N _{g} = 1–5g/e = 1–5 p/e = 6–12 | Nu/Nu_{s} = 3.6f/f _{s} = 3.67 |

Deo et al. [26] | Multiple V-rib with gaps combined with staggered rib | n = 2 e/D _{h} = 0.026–0.057w/e = 4.5 p/e = 4–14 p/P = 4.5 g/e = 1 α = 60° | Nu/Nu_{s} = 3.34f/f _{s} = 2.45 |

Patil et al. [27] | V-ribs with gap combined with staggered rib | e/D = 0.0433 p’/p = 0.2–0.8 s’/s = 0.2–0.8 p/e = 10 r/e = 1–2.5 α = 60° | Nu/Nu_{s} = 3.18 |

Hans et al. [28] | Continuous multiple V-rib | W/w = 1–10, e/D = 0.019–0.043 α = 30°–75°, p/e = 6–12 | Nu/Nu_{s} ~ 6f/f _{s} ~ 4.3 |

Kumar et al. [29] | Multi-V-ribs with gaps | g/e = 0.5–1.5 G _{d}/L_{v} = 0.24–0.80e/D = 0.019–0.043 W/w = 1–10, p/e = 6–12 α = 30°–75° | Nu/Nu_{s} = 6.74f/f _{s} = 6.37 |

Jin et al. [86] | Multiple V-shaped ribs | p/e = 3–20, e/Dh = 0.03–0.11 α = 30°–75°, Re = 8000–20,000 | THPP_{max} = 1.93 |

Saini and Saini [30] | Arc rib | e/D = 0.0213–0.0422 α/90 = 0.333–0.666 p/e = 10 | Nu/Nu_{s} = 3.8f/f _{s} = 1.75 |

Sethi et al. [31] | Dimple rib in arc fashion | e/d = 0.5 e/Dh = 0.021–0.036 α = 45°–75° p/e = 10–20 | η = 1.10–1.887 |

Yadav et al. [32] | Dimple rib in arc pattern | α = 45°–75° e/D _{h} = 0.015–0.030p/e = 12–24 | Nu/Nu_{s} = 2.89,f/f _{s} = 2.93 |

Hans et al. [33] | Brocken arc rib | e/D_{h} = 0.022–0.043d/w = 0.2–0.8 g/e = 0.5–2.5 p/e = 4–12 Re = 2000–16,000 | Nu/Nu_{s} = 2.63f/f _{s} = 2.44 |

Pandey et al. [34] | Multiple-arc rib with gaps | W/w = 1–7 e/D = 0.016–0.044 d/x = 0.25–0.85 g/e = 0.5–2 p/e = 4–16 α = 30°–75° | Nu/Nu_{s} = 5.85f/f _{s} = 4.96 |

Singh et al. [35] | Multiple-arc rib | e/D = 0.018–0.045 p/e = 4–16 W/w = 1–7 α = 30°–75° | Nu/Nu_{s} = 5.07f/f _{s} = 3.71 |

Lanjewar et al. [36,37] | Continuous W-rib | e/D_{h} = 0.018–0.03375α = 30°–75° p/e = 10 | Nu/Nu_{s} = 2.36f/f _{s} = 2.01 |

Kumar et al. [38] | Discrete W-rib | e/D_{h} = 0.018–0.03375α = 30°–75°, p/e = 10 | Nu/Nu_{s} = 2.16f/f _{s} = 2.75 |

Gawande et al. [39] | L-shaped rib | e/D = 0.042 p/e = 7.14–17.86 | Nu/Nu_{s} = 2.827f/f _{s} = 2.434 |

Kumar et al. [40] | S-shaped rib | e/D_{h} = 0.022–0.054α = 30°–75° W/w = 1–4 p/e = 4–16 Re = 2400–20,000 | Nu/Nu_{s} = 4.64f/f _{s} = 2.71 |

Bhushan and Singh [41] | Protrusion roughness | e/D = 0.03 L/e = 25–37.5 S/e = 18.75–37.5 d/D = 0.0147–0.0367 | Nu/Nu_{s} = 3.8f/f _{s} = 2.2 |

Bhagoria et al. [47] | Wedge-shaped ribs | e/D_{h} = 0.015–0.033ϕ = 8°–15°, p/e = 4.7–12.12 | Nu/Nu_{s} = 2.4f/f _{s} = 5.3 |

Singh I and Singh S [42] | Transverse rib with square wave profile | p/e = 4–30, e/Dh = 0.043, Re = 3000–15,000 | Nu/Nu_{s} = 2.14f/f _{s} = 3.55 |

Alam and Kim [137] | Semiellipse-shaped obstacle | p/e = 3.5, α = 30°–90°, Re = 6000–18,000 | Nu/Nu_{s} = 2.05f/f _{s} = 5.3 |

Karmare and Tikekar [44] | Metal grit | e/D_{h} = 0.035–0.044l/s = 1–1.72, p/e = 12.5–36 | Nu/Nu_{s} =1.87f/f _{s} = 6.93 |

Layek et al. [48] | Chamfered rib combined with groove | g/p = 0.3–0.6 e/D _{h} = 0.022–0.04ϕ = 5°–30° p/e = 4.5–10 | Nu/Nu_{s} = 3.24f/f _{s} = 3.74 |

Investigators | Roughness | Correlations |
---|---|---|

Aharwal et al. [17] (2009) | Inclined rib with gap | $Nu=0.0102{(e/{D}_{h})}^{0.51}{\mathrm{Re}}^{1.148}\left[\left\{1-{(0.25-d/w)}^{2}\left\{0.01{(1-g/e)}^{2}\right\}\right\}\right]$ $f=0.5{(e/{D}_{h})}^{0.72}{\mathrm{Re}}^{-0.0836}$ |

Verma and Prasad [60] (2000) | Wire roughness | $Nu=0.0731{P}_{r}^{0.4}{f}_{s}^{0.5}{\mathrm{Re}}^{0.918}$ $f=0.245{(e/{D}_{h})}^{0.243}{(p/e)}^{-0.206}{\mathrm{Re}}^{-1.25}$ |

Ebrahim-Momin et al. [24] (2002) | V-shaped continuous ribs | $Nu=0.067{\mathrm{Re}}^{0.888}{(\alpha /60)}^{-0.077}{(e/{D}_{h})}^{0.424}\mathrm{exp}\left[-0.728{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]$ $f=6.266{\mathrm{Re}}^{-0.425}{(\alpha /60)}^{-0.093}{(e/{D}_{h})}^{0.565}\mathrm{exp}\left[-0.719{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]$ |

Istanto et al. [152] (2016) | V-shaped rib | $Nu=0.016{\mathrm{Re}}^{0.891}{(\alpha /90)}^{-1.123}\mathrm{exp}\left[-1.107{\left\{\mathrm{ln}(\alpha /90)\right\}}^{2}\right]$ $f=31.589{\mathrm{Re}}^{-0.759}{(\alpha /90)}^{-1.385}\mathrm{exp}\left[-1.318{\left\{\mathrm{ln}(\alpha /90)\right\}}^{2}\right]$ |

Singh et al. [19] (2011) | V-shape with gap | $\begin{array}{l}Nu=2.36\times {10}^{-3}{(p/e)}^{3.50}{\mathrm{Re}}^{0.90}{(e/{D}_{h})}^{0.47}{(d/w)}^{-0.043}{(\alpha /60)}^{-0.023}\\ {(g/e)}^{-0.014}\mathrm{exp}\left[-0.84{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.05{\left\{\mathrm{ln}(d/w)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.72{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.15{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=4.13\times {10}^{-2}{\mathrm{Re}}^{-0.126}{(e/{D}_{h})}^{0.7}{(p/e)}^{2.74}{(d/w)}^{-0.058}{(\alpha /60)}^{-0.034}\\ {(g/e)}^{0.31}\mathrm{exp}\left[-0.685{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.058{\left\{\mathrm{ln}(d/w)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.93{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.21{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\end{array}$ |

Maithani and Saini [25] (2016) | V-ribs with symmetrical gap | $\begin{array}{l}Nu=1.8\times {10}^{-6}{\mathrm{Re}}^{0.9635}{(g/e)}^{0.111}{({N}_{g})}^{0.126}{(\alpha /60)}^{0.1307}\\ {(p/e)}^{5.7419}\times \mathrm{exp}\left[-0.055{\left\{\mathrm{ln}({N}_{g})\right\}}^{2}\right]\times \mathrm{exp}\left[-0.0401{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-1.299{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.895{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=3.6\times {10}^{-7}{\mathrm{Re}}^{-0.1512}{(\alpha /60)}^{0.07}{(g/e)}^{0.072}{({N}_{g})}^{0.1484}\\ {(p/e)}^{9.24}\times \mathrm{exp}\left[-0.0763{\left\{\mathrm{ln}({N}_{g})\right\}}^{2}\right]\times \mathrm{exp}\left[-0.0249{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-2.08{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.3364{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ |

Deo et al. [26] (2016) | Multi-gap-V-down rib | $Nu=0.02253{\mathrm{Re}}^{0.98}{(e/{D}_{h})}^{0.18}{(p/e)}^{-0.06}{(\alpha /60)}^{0.04}$ $f=0.3715{\mathrm{Re}}^{-0.15}{(e/{D}_{h})}^{0.65}{(p/e)}^{0.21}{(\alpha /60)}^{0.57}$ |

Saini and Verma [46] (2008) | Dimple shape | $\begin{array}{l}Nu=5.2\times {10}^{-4}{(p/e)}^{3.15}{(e/{D}_{h})}^{0.033}{(\mathrm{Re})}^{1.27}\\ \times \mathrm{exp}\left[-1.30{\left\{\mathrm{ln}(e/{D}_{h})\right\}}^{2}\right]\times \mathrm{exp}\left[-2.12{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=0.642{(\mathrm{Re})}^{-0.423}{(e/{D}_{h})}^{-0.0214}{(p/e)}^{-0.465}\\ \times \mathrm{exp}\left[0.840{\left\{\mathrm{ln}(e/{D}_{h})\right\}}^{2}\right]\times \mathrm{exp}\left[0.054{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\end{array}$ |

Hans et al. [28] (2010) | Continuous multi-V-ribs | $\begin{array}{l}Nu=3.35\times {10}^{-5}{\mathrm{Re}}^{0.92}{(e/{D}_{h})}^{0.77}{(p/e)}^{8.54}{(\alpha /90)}^{-0.49}\\ {(W/w)}^{0.043}\times \mathrm{exp}\left[-0.61{\left\{\mathrm{ln}(\alpha /90)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-2.0407{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.1177{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=4.47\times {10}^{-4}{\mathrm{Re}}^{-0.3188}{(p/e)}^{8.9}{(e/{D}_{h})}^{0.73}{(\alpha /90)}^{-0.39}\\ {(W/w)}^{0.22}\times \mathrm{exp}\left[-0.52{\left\{\mathrm{ln}(\alpha /90)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-2.133{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.1177{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\end{array}$ |

Singh et al. [83] (2021) | Multi-V-ribs with uniform gap | $\begin{array}{l}Nu=0.0187{\mathrm{Re}}^{1.176}\times {(p/e)}^{-0.6586}\times {(e/{D}_{h})}^{0.4927}\\ \times {(e/w)}^{0.033}\times {(W/w)}^{0.0659}\times {(g/e)}^{0.1753}\times {(x/w)}^{0.1147}\\ \times \mathrm{exp}\left[-0.011{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\times \mathrm{exp}\left[0.1837{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[0.0775{\left\{\mathrm{ln}(x/w\right\}}^{2}\right]\times \mathrm{exp}\left[0.0869{\left\{\mathrm{ln}(e/w)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[0.2413{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=1.3601{\mathrm{Re}}^{-0.434}\times {(p/e)}^{-0.7032}\times {(e/{D}_{h})}^{0.0863}\\ \times {(e/w)}^{0.0229}\times {(W/w)}^{0.0858}\times {(g/e)}^{0.1436}\times {(x/w)}^{-1.3003}\\ \times \mathrm{exp}\left[0.0098{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\times \mathrm{exp}\left[0.1925{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.4762{\left\{\mathrm{ln}(x/w\right\}}^{2}\right]\times \mathrm{exp}\left[-0.0556{\left\{\mathrm{ln}(e/w)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[0.0455{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\end{array}$ |

Kumar et al. [85] (2013) | Multi-V-ribs with gap | $\begin{array}{l}Nu=8.532\times {10}^{-3}{\mathrm{Re}}^{0.932}{(e/{D}_{h})}^{0.175}{(p/e)}^{1.196}{(\alpha /60)}^{-0.0239}\\ {(g/e)}^{-0.0708}{(W/w)}^{0.506}{({G}_{d}/{L}_{v})}^{-0.0348}\mathrm{exp}\left[-0.2805{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.0753{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.1153{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.0653{\left\{\mathrm{ln}({G}_{d}/{L}_{v})\right\}}^{2}\right]\times \mathrm{exp}\left[-0.223{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=3.1934{\mathrm{Re}}^{-0.3151}{(e/{D}_{h})}^{0.268}{(\alpha /60)}^{0.1553}{(p/e)}^{-0.7941}\\ {(g/e)}^{-0.1769}{(W/w)}^{0.1132}{({G}_{d}/{L}_{v})}^{0.0610}\mathrm{exp}\left[0.1486{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[0.0974{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.1527{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.1065{\left\{\mathrm{ln}({G}_{d}/{L}_{v})\right\}}^{2}\right]\times \mathrm{exp}\left[-0.6349{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\end{array}$ |

Saini and Saini [30] (2008) | Arc ribs | $Nu=0.001047{\mathrm{Re}}^{1.3186}{(\alpha /90)}^{-0.1198}{(e/{D}_{h})}^{0.3772}$ $f=0.14408{(\mathrm{Re})}^{-0.17103}{(\alpha /90)}^{0.1185}{(e/{D}_{h})}^{0.1765}$ |

Sethi et al. [31] (2012) | Dimple shape | $\begin{array}{l}Nu=7.1\times {10}^{-3}{\mathrm{Re}}^{1.1386}{(\alpha /60)}^{-0.0048}{(p/e)}^{-0.47}{(e/{D}_{h})}^{0.3629}\\ \times \mathrm{exp}\left[-0.7792{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=4.869\times {10}^{-1}{\mathrm{Re}}^{-0.223}{(\alpha /60)}^{0.0042}{(p/e)}^{-0.059}{(e/{D}_{h})}^{0.2663}\\ \times \mathrm{exp}\left[-0.4801{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ |

Yadav et al. [32] (2013) | Dimple ribs in arc arrangement | $\begin{array}{l}Nu=0.154{\mathrm{Re}}^{1.017}{(e/{D}_{h})}^{0.521}{(p/e)}^{-0.38}{(\alpha /60)}^{-0.213}\\ \times \mathrm{exp}\left[-2.023{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=7.207{\mathrm{Re}}^{-0.56}{(e/{D}_{h})}^{0.176}{(p/e)}^{-0.18}{(\alpha /60)}^{-0.038}\\ \times \mathrm{exp}\left[-1.412{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ |

Hans et al. [33] (2017) | Broken-arc rib | $\begin{array}{l}Nu=1.014\times {10}^{-3}{(\mathrm{Re})}^{1.036}{(d/w)}^{-0.078}{(e/{D}_{h})}^{0.412}{(p/e)}^{2.522}{(\alpha /90)}^{-0.293}\\ {(g/e)}^{-0.016}\times \mathrm{exp}{\left[-0.114\left\{\mathrm{ln}(\alpha /90)\right\}\right]}^{2}\times \mathrm{exp}\left[-0.567{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \mathrm{exp}\left[-0.133{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.077{\left\{\mathrm{ln}(d/w)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=8.1921\times {10}^{-2}{(\mathrm{Re})}^{-0.147}{(e/{D}_{h})}^{0.528}{(\alpha /90)}^{-0.292}{(p/e)}^{1.191}{(d/w)}^{-0.067}\\ {(g/e)}^{-0.006}\times \mathrm{exp}{\left[-0.110\left\{\mathrm{ln}(\alpha /90)\right\}\right]}^{2}\times \mathrm{exp}\left[-0.255{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \mathrm{exp}\left[-0.158{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.063{\left\{\mathrm{ln}(d/w)\right\}}^{2}\right]\end{array}$ |

Ambade et al. [95] (2019) | L-shaped rib | $Nu=0.032{(p/e)}^{0.3479}{\mathrm{Re}}^{0.8332}\mathrm{exp}\left[-0.1004{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]$ $f=0.2805{(p/e)}^{0.3479}{\mathrm{Re}}^{\mathrm{0.0.0815}}\mathrm{exp}\left[-\mathrm{0.0.0319}{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]$ |

Gill et al. [97] (2021) | Hybrid rib | $\begin{array}{l}Nu=3.596\times {10}^{-3}{\mathrm{Re}}^{1.068}{\left(g/e\right)}^{-0.018}{\left(r/e\right)}^{-0.02}{\left({W}_{1}/w\right)}^{-0.073}\\ {\left(p/e\right)}^{1.403}{\left(\alpha /90\right)}^{-0.408}{\left(e/{D}_{h}\right)}^{0.56}\times \mathrm{exp}\left[-0.151{\left\{\mathrm{ln}\left(g/e\right)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=7.981\times {10}^{-2}{\mathrm{Re}}^{-0.157}{\left(g/e\right)}^{-0.021}{\left(r/e\right)}^{0.012}{\left({W}_{1}/w\right)}^{-0.104}{\left(p/e\right)}^{1.739}\\ {\left(\alpha /90\right)}^{-0.638}{\left(e/{D}_{h}\right)}^{0.783}\end{array}$ |

Pandey et al. [34] (2016) | Multiarc ribs with gap | $\begin{array}{l}Nu=1.39\times {10}^{-4}{\mathrm{Re}}^{1.3701}{(e/{D}_{h})}^{0.0931}{(p/e)}^{0.5858}{(\alpha /60)}^{-0.2235}\\ {(g/e)}^{-0.0292}{(W/w)}^{0.4017}{(d/x)}^{-0.4997}\mathrm{exp}\left[-0.142{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.129{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.5614{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.3989{\left\{\mathrm{ln}(d/x)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.2013{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=2.11\times {10}^{-1}{\mathrm{Re}}^{-0.25}{(e/{D}_{h})}^{0.145}{(\alpha /60)}^{-2.546}{(p/e)}^{0.643}\\ {(W/w)}^{0.032}{(g/e)}^{-0.079}{(d/x)}^{-0.888}\mathrm{exp}\left[-0.160{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.496{\left\{\mathrm{ln}(g/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-3.96{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.662{\left\{\mathrm{ln}(d/x)\right\}}^{2}\right]\end{array}$ |

Singh et al. [153] (2014) | Multiarc ribs | $\begin{array}{l}Nu=1.564\times {10}^{-4}{\mathrm{Re}}^{1.3343}{(e/{D}_{h})}^{0.048}{(\alpha /90)}^{-0.355}{(p/e)}^{0.572}\\ {(W/w)}^{0.407}\times \mathrm{exp}\left[-0.099{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.272{\left\{\mathrm{ln}(\alpha /90)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.148{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=0.063{\mathrm{Re}}^{-0.16}{(e/{D}_{h})}^{0.102}{(\alpha /90)}^{-0.023}{(p/e)}^{0.562}{(W/w)}^{0.277}\\ \times \mathrm{exp}\left[-0.013{\left\{\mathrm{ln}(\alpha /90)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.140{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\end{array}$ |

Hasan et al. [103] (2021) | Multiarc dimple shape | $\begin{array}{l}Nu=8.84\times {10}^{-6}{\mathrm{Re}}^{1.0623}\times {(p/e)}^{1.72}\times {(e/{D}_{h})}^{2.5259}\\ \times {(\alpha /60)}^{-0.087}\times \mathrm{exp}\left[2.43{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-5.24{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times {(W/w)}^{-0.328}\\ \times \mathrm{exp}\left[-0.77{\left\{\mathrm{ln}(e/{D}_{h}\right\}}^{2}\right]\times \mathrm{exp}\left[-1.243{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=4.46\times {\mathrm{Re}}^{-0.09257}\times {(p/e)}^{2.19}\times {(e/{D}_{h})}^{-0.0112}\\ \times {(\alpha /60)}^{0.452}\times \mathrm{exp}\left[3.345{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\\ \times {(W/w)}^{-0.0941}\times \mathrm{exp}\left[-0.0664{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.0828{\left\{\mathrm{ln}(e/{D}_{h}\right\}}^{2}\right]\times \mathrm{exp}\left[-9.494{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ |

Lanjewar et al. [36] (2011) | Continuous W-ribs | $\begin{array}{l}Nu=0.0613{\mathrm{Re}}^{0.9079}{(\alpha /60)}^{-0.1331}{(e/{D}_{h})}^{0.4487}\\ \times \mathrm{exp}\left[-0.5307{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=0.06182{\mathrm{Re}}^{-0.2554}{(\alpha /60)}^{0.0817}{(e/{D}_{h})}^{0.4682}\\ \times \mathrm{exp}\left[-0.28{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ |

Kumar et al. [38] (2009) | Discrete W-ribs | $\begin{array}{l}Nu=0.105{\mathrm{Re}}^{0.873}{(\alpha /60)}^{-0.081}{(e/{D}_{h})}^{0.453}\\ \times \mathrm{exp}\left[-0.59{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=5.86{\mathrm{Re}}^{-0.40}{(\alpha /60)}^{0.081}{(e/{D}_{h})}^{0.59}\\ \times \mathrm{exp}\left[-0.579{\left\{\mathrm{ln}(\alpha /60)\right\}}^{2}\right]\end{array}$ |

Gawande et al. [39] (2016) | S-shaped rib | $Nu=0.032{(p/e)}^{0.3479}{\mathrm{Re}}^{0.8332}\mathrm{exp}\left\{-0.1004\mathrm{ln}{(p/e)}^{2}\right\}$ $f=0.280{(p/e)}^{0.0815}{\mathrm{Re}}^{-0.2617}\mathrm{exp}\left\{-0.0319\mathrm{ln}{(p/e)}^{2}\right\}$ |

Kumar et al. [98] (2016) | S-shaped rib | $\begin{array}{l}Nu=1.4332\times {10}^{-4}{\mathrm{Re}}^{1.2764}\times {(W/w)}^{0.2748}\times \mathrm{exp}\left[-0.1107{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ \times {(p/e)}^{0.4876}\times {(\alpha /90)}^{-0.0468}\times \mathrm{exp}\left[-0.1084{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.0642{\left\{\mathrm{ln}(\alpha /90)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.1257{\left\{\mathrm{ln}(e/{D}_{h}\right\}}^{2}\right]\times {(e/{D}_{})}^{-0.7653}\end{array}$ $\begin{array}{l}f=1.430\times {10}^{-1}\times {\mathrm{Re}}^{-0.224}\times {(W/w)}^{0.1424}\times {(p/e)}^{0.7657}\\ \times \mathrm{exp}\left[-0.187{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times {(\alpha /90)}^{0.2129}\times {(e/{D}_{h})}^{0.2159}\end{array}$ |

Baissi et al. [108] (2019) | Delta-shaped tubulators | $\begin{array}{l}Nu=0.5884{\mathrm{Re}}^{0.4793}{({P}_{l}/e)}^{0.5943}{({P}_{t}/b)}^{-0.3201}\\ \times \mathrm{exp}\left[-0.5426{\left\{\mathrm{ln}({P}_{l}/e)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=0.338{\mathrm{Re}}^{-0.0996}\mathrm{exp}\left[-1.2539{\left\{\mathrm{ln}({P}_{l}/e)\right\}}^{2}\right]\\ \times {({P}_{l}/e)}^{2.1042}\times {({P}_{t}/b)}^{-0.56}\mathrm{exp}\left[-0.2375{\left\{\mathrm{ln}({P}_{t}/b)\right\}}^{2}\right]\end{array}$ |

Kumar and Layek [110] (2020) | Winglet turbulators | $\begin{array}{l}Nu=3.64\times {10}^{-5}{\mathrm{Re}}^{0.95}{(\alpha /75)}^{-0.91}{(p/e)}^{3.73}{(W/w)}^{2.37}\\ \times \mathrm{exp}\left[-0.90{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-1.22{\left\{\mathrm{ln}(\alpha /75)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.81{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=0.13{\mathrm{Re}}^{-0.37}{(W/w)}^{2.41}{(\alpha /75)}^{-0.45}{(p/e)}^{-0.12}\\ \times \mathrm{exp}\left[-0.77{\left\{\mathrm{ln}(W/w)\right\}}^{2}\right]\end{array}$ |

Bhushan and Singh [41] (2011) | Protrusions | $\begin{array}{l}Nu=2.1\times {10}^{-88}{(\mathrm{Re})}^{1.452}{(S/e)}^{12.94}{(d/D)}^{-3.9}{(L/e)}^{99.2}\\ \times \mathrm{exp}\left[-77.2{\left\{\mathrm{ln}(L/e\right\}}^{2}\right]\times \mathrm{exp}\left[-1.4{\left\{\mathrm{ln}(S/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-7.83{\left\{\mathrm{ln}(d/D\right\}}^{2}\right]\end{array}$ $f=2.32{(\mathrm{Re})}^{-0.201}{(S/e)}^{-0.383}{(L/e)}^{-0.484}{(d/D)}^{0.133}$ |

Patel et al. [118] (2020) | NACA 0040 profile rib | $Nu=0.009016{(e/{D}_{h})}^{-3.1354}\times {\mathrm{Re}}^{0.526}\mathrm{exp}\left[-0.5834{\left\{\mathrm{ln}(e/{D}_{h}{}_{})\right\}}^{2}\right]$ $\begin{array}{l}f=0.32449{\mathrm{Re}}^{1.3728}\times {(e/{D}_{h})}^{5.6236}\times \mathrm{exp}\left[0.943{\left\{\mathrm{ln}(e/{D}_{h})\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.0875{\left\{\mathrm{ln}(\mathrm{Re})\right\}}^{2}\right]\end{array}$ |

Gabhane and Patil [119] (2017) | Multi-C-shape rib | $Nu=0.20627{(\mathrm{Re})}^{0.8087}{(\alpha /90)}^{0.2735}{(p/e)}^{-0.03724}$ $f=0.9123{(\mathrm{Re})}^{-0.28379}{(\alpha /90)}^{-0.12127}{(p/e)}^{-0.14847}$ |

Kumar and Layek [123] (2019) | Twisted tape | $\begin{array}{l}Nu=3\times {10}^{-10}{\mathrm{Re}}^{1.043}{(y/e)}^{-0.17}{(p/e)}^{15.75}{(\alpha /60)}^{-0.84}\\ \times \mathrm{exp}\left[-3.75{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\times \mathrm{exp}\left[-0.85{\left\{\mathrm{ln}(\alpha /90)\right\}}^{2}\right]\end{array}$ $f=6.82{\mathrm{Re}}^{-0.58}{(y/e)}^{0.31}{(\alpha /60)}^{0.23}{(p/e)}^{-0.42}$ |

Bhagoria et al. [47] (2002) | Wedge-shaped rib | $\begin{array}{l}Nu=1.89\times {10}^{-4}{(\mathrm{Re})}^{1.21}{(e/{D}_{h})}^{0.426}\mathrm{exp}\left[-0.71{\left\{\mathrm{ln}(p/e)\right\}}^{2}\right]\\ {(\phi /10)}^{-0.018}\times \mathrm{exp}\left[-1.50{\left\{\mathrm{ln}(\phi /10)\right\}}^{2}\right]\end{array}$ $f=12.44{(\mathrm{Re})}^{-0.18}{(e/{D}_{h})}^{0.99}{(\phi /10)}^{0.49}$ |

Promvonge et al. [127] (2021) | Combination of V-shaped rib and delta groove | $Nu=1.48{\mathrm{Re}}^{0.537}{\mathrm{Pr}}^{0.4}{\left(p/H\right)}^{-0.269}{\left(e/H\right)}^{0.126}$ $f=6.8{\mathrm{Re}}^{0.127}{\mathrm{Pr}}^{0.4}{\left(p/H\right)}^{-0.521}{\left(e/H\right)}^{1.096}$ |

Alfarawi et al. [137] (2017) | Hybrid rib | $Nu=10.12{(p/e)}^{-0.107}{(\mathrm{Re})}^{-0.144}$ $f=15.23{(p/e)}^{-0.241}{(\mathrm{Re})}^{-0.093}$ |

Saini and Saini [43] (1997) | Expanded metal mesh | $\begin{array}{l}Nu=4\times {10}^{-4}{(e/{D}_{h})}^{0.625}{(L/10e)}^{2.66}{\mathrm{Re}}^{1.22}{(S/10e)}^{2.22}\\ \times \mathrm{exp}\left[-0.824{\left\{\mathrm{ln}(L/10e)\right\}}^{2}\right]\times \mathrm{exp}\left[-1.25{\left\{\mathrm{ln}(S/10e)\right\}}^{2}\right]\end{array}$ $f=0.815{(e/{D}_{h})}^{0.591}{(L/10e)}^{0.266}{\mathrm{Re}}^{-0.361}{(S/10e)}^{-0.19}$ |

Karmare and Tikekar [44] (2007) | Metal grit | $Nu=2.4\times {10}^{-3}{(e/{D}_{h})}^{0.42}{\mathrm{Re}}^{1.3}{(p/e)}^{-0.27}{(l/s)}^{-0.146}$ $f=15.55{(e/{D}_{h})}^{0.91}{\mathrm{Re}}^{-0.26}{(p/e)}^{-0.51}{(l/s)}^{-0.27}$ |

Layek et al. [48] (2007) | Chamfered rib combined with groove | $\begin{array}{l}Nu=0.00225{(e/{D}_{h})}^{0.52}{(g/p)}^{-1.21}{\mathrm{Re}}^{0.92}{\phi}^{1.24}{(p/e)}^{1.172}\\ \times \mathrm{exp}\left[-0.22{\left\{Ln(\phi )\right\}}^{2}\right]\times \mathrm{exp}\left[-0.46{\left\{Ln(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.74{\left\{Ln(g/p)\right\}}^{2}\right]\end{array}$ $\begin{array}{l}f=0.00245{(e/{D}_{h})}^{0.365}{(g/p)}^{-1.124}{\mathrm{Re}}^{-0.124}{(p/e)}^{4.32}\\ \times \mathrm{exp}\left[0.005\phi \right]\times \mathrm{exp}\left[-1.09{\left\{Ln(p/e)\right\}}^{2}\right]\\ \times \mathrm{exp}\left[-0.68{\left\{Ln(g/p)\right\}}^{2}\right]\end{array}$ |

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**MDPI and ACS Style**

Karmveer; Gupta, N.K.; Alam, T.; Cozzolino, R.; Bella, G.
A Descriptive Review to Access the Most Suitable Rib’s Configuration of Roughness for the Maximum Performance of Solar Air Heater. *Energies* **2022**, *15*, 2800.
https://doi.org/10.3390/en15082800

**AMA Style**

Karmveer, Gupta NK, Alam T, Cozzolino R, Bella G.
A Descriptive Review to Access the Most Suitable Rib’s Configuration of Roughness for the Maximum Performance of Solar Air Heater. *Energies*. 2022; 15(8):2800.
https://doi.org/10.3390/en15082800

**Chicago/Turabian Style**

Karmveer, Naveen Kumar Gupta, Tabish Alam, Raffaello Cozzolino, and Gino Bella.
2022. "A Descriptive Review to Access the Most Suitable Rib’s Configuration of Roughness for the Maximum Performance of Solar Air Heater" *Energies* 15, no. 8: 2800.
https://doi.org/10.3390/en15082800