###### Abstract
When e/d < 0.02, the Nusselt number ratio and the friction factor ratio were comparable. The friction factor increased rapidly as e/d increased above 0.03. A numerical investigation using k-\(\varepsilon\) was performed by [PERSON] et al. [24] to study the effects of different geometrical parameters on the thermal and flow fields through transversely corrugated circular ribs. The roughness height (e/d) was changed from 0.025 up to 0.1. The Nusselt number and friction factor increased as e/d increased, but the rate of increase in the friction factor was much higher than that in the Nusselt number. Another numerical investigation using the SST k-\(\omega\) model was performed by [PERSON] et al. [25]. The values of e/d increased from 0.025 to 0.15. It was found that rib height was the dominant factor in heat transfer and friction loss. The highest thermal performance was found when e/d ranged from 0.1 to 0.125, apart from the rib width and the rib pitch values. Circular cross-sectional rings inserted near the tube wall were investigated numerically by [PERSON] et al. [26]. Five pitches in the range of 0.5 d to 3.0 d were studied, whereas the Reynolds number was in the range of 4475-43,725. The best overall 18% enhancement was achieved at Re = 15,600. Another numerical investigation was conducted by [PERSON] et al. [27] using the LES method. The pipe insert was a helical rib shape. Two Re values and three Pr values were applied. There was a 190% heat transfer enhancement compared with a smooth pipe. It is also notable that while the enhancement in heat transfer was between 170% and 190%, the pressure loss was doubled compared with the results of the smooth tubes. A numerical and experimental study of heat transfer and pressure drop was performed by [PERSON] et al. [28] on a circumferential ribbed pipe using a nanofluid. The e/d ranged from 0.034 to 0.1. A realizable k-\(\varepsilon\) model was applied along with an enhanced wall treatment. Both the heat transfer and the friction coefficients increased as e/d increased. [PERSON] et al. [29] conducted a 3D numerical investigation of the turbulent flow inside spirally corrugated tubes. The tube diameter and length were 18 mm and 6 m, respectively. The corrugation depth was 0.43 mm, and the helical pitch was 15.86 mm. The k-\(\varepsilon\) turbulence model was used. The error in predicting the Nusselt number was within 17%. Some authors performed their investigation on one e/d value, such as [PERSON] et al. [30], who performed an experimental work using an e/d value of 0.055. In contrast, [PERSON] [31]used the LES numerical model to perform a study using e/d = 0.115. Helically finned and corrugated tubes with different geometric parameters were investigated by [PERSON] et al. [32], where the k-\(\varepsilon\) model was applied. The Reynolds numbers ranged from 12,000 to 57,000. It was found that helically finned tubes worked better regarding thermal performance than corrugated ones. Another experimental and numerical study was conducted by [PERSON] [33] on ribbed tubes of p/d = 0.225, e/d = 0.05, and a helix angle of 15\({}^{\circ}\) using Therminol-55 heat transfer fluid. The heat transfer increased 2.24-fold, while the friction factors increased by 2.4- and 2.8-fold compared with the smooth tube results. As previous work indicates, the heat transfer is enhanced as the rib height increases. The drawback of increasing the rib height is the increase in the friction factor and, hence, an increase in the working fluid's pumping power. Most of the previous research has focused on studying ribbed tubes comprising equal-height ribs along the tube length. In the present numerical work, the height of half of the transverse ribs was changed along the pipe length while the height of the other half remained unchanged. Thus, the ribs formed a zigzag shape configuration inside the tube. The effects of different rib height ratios as well as their effects on heat transfer and pressure drop were studied. The effects of the Prandtl number and the Reynolds numbers were also investigated.