###### Abstract  
Heat transfer through tube walls can be promoted using a ribbed tube configuration. Most of the ribs used in previous reports have equal height along the tube length. In this numerical study, we investigate the heat transfer and pressure drop in a transverse ribbed tube where ribs of unequal heights are mounted such that the tops of the ribs form a zigzag shape. Four configurations were studied. Each configuration had a set of two neighboring ribs of different heights. The set was repeated along the tube length to form a zigzag shape. The rib height ratios, \(\mathrm{e_{2}/e_{1}}\), of the four sets were 0.25, 0.5, 0.75, and 1.0. The ratios of the height of the taller rib, pitch, and width to the tube diameter were kept constant at values of \(\mathrm{e_{1}/d}\) = 0.1, \(\mathrm{p/d}\) = 1.0, and \(\mathrm{w/d}\) = 0.05, respectively. The Reynolds number ranged from 10,000 to 60,000, while the Prandtl number ranged from 0.71 to 7.0. The results from the k-\(\varepsilon\) and k-\(\omega\) models were first validated and compared with the experimental results of smooth and ribbed tubes. The two models showed comparable results, with the k-\(\varepsilon\) showing slightly better performance and was thus selected to perform the current study. It was found that the average Nusselt number increases along with increases in the rib height ratio, Prandtl number, and Reynolds number. The friction factor changed exponentially with the rib height ratio, while the Reynolds number showed a minor effect. At the same pumping power, a maximum thermal performance enhancement of approximately 8% was achieved at rib height ratios of 0.25 and 0.5. The rib height ratio of 0.5 has an advantage over that of 0.25 as it has a higher average Nusselt number. Two correlations were introduced to estimate the Nusselt number and friction factor for the current ribbed tube of zigzag configurations. 202212573420222125734  
Ribs enhance heat transfer by separating the boundary layer upstream of the rib and then recirculating the fluid slightly downstream. The reattachment of the boundary layer occurs between the ribs, causing an increase in the heat transfer coefficient. One of the leading parameters affecting heat transfer and pressure drop is the rib height-to-diameter ratio, e/d. The heat transfer and pressure drop in transverse ribbed circular tubes have been investigated numerically and experimentally. [PERSON] and [PERSON] [20] investigated the problem experimentally, considering the effect of the entrance region. An isothermal surface condition was considered. The rib pitch-to-tube diameter ratio (p/d) and the rib height-to-tube diameter ratio (e/d) were in the ranges of 0.304-5.72 and 0.015-0.143, respectively. The Reynolds number (Re) range was 4608-12,936. It was found that the entrance has little effect on Nu. The effect of the e/d ratio on Nu is larger than that of the p/d ratio. For e/d < 0.057 and e/d > 0.057, the friction factor f is proportional to e/d and (e/d)\({}^{2.55}\), respectively. An experimental study of different grooved tubes at fully developed turbulent flow was performed by [PERSON] et al. [21]. Circular, trapezoidal, and rectangular geometries were investigated. Each groove has a depth of 3 mm, while the inner tube diameter is 36 mm. Heat transfer enhancements of 63%, 58%, and 47% for the circular, trapezoidal, and rectangular grooves, respectively, were obtained. [PERSON] et al. [22] studied the experimentally and numerically angled ribs mounted on the inner surface of a tube. Two pairs of vortices were induced, which enhanced the heat transfer compared with conventional transverse ribs. Another experimental and numerical study was conducted by [PERSON] et al. [23] to study the turbulent heat transfer and flow resistance in ribbed tubes. The e/d ranged from 0.01 to 0.05. The standard k-\(\varepsilon\) model was used. Both the numerical and experimental results showed good agreement. The most significant discrepancies were 10% for the Nusselt numbers and 15% for the friction factors.