## 1 Introduction  
Heat exchangers are devices designed to allow the transfer of thermal energy between two or more fluids at different temperatures, without direct mixing between them. Various criteria can be considered to classify them [1]; when based on construction geometry, the acronym PHE (Plate Heat Exchanger) refers to a stack of metal plates with inlet and outlet ports, forming alternate channels through which substances flow. The primary feature of a PHE is the embossed pattern on the plate surfaces, which increases the heat exchange by promoting turbulence at low Reynolds numbers. The development of new corrugation designs, a passive enhancement technique, is the focus of extensive research [2, 3], as it promotes energy savings, reduces industrial costs, and improves the efficiency of process equipment, contributing to environmental benefits, as demanded by the IEA [4]. The most common PHE is recognized [2] to be the herringbone (or chevron) type, consisting of a wavy surface with a characteristic \(\beta\) angle. In a manner similar to the scope of this study, computational fluid dynamics (CFD) simulations have been conducted to understand the flow patterns and improve the generalized heat transfer and pressure-drop correlations. It is well established that, as described by [PERSON] et al. [5], two distinct structures, dependent on the Reynolds number \(Re\), influence the mass transfer between the top and bottom grooves inside a herringbone channel: a helical motion, primarily aligned with the longitudinal direction, at low \(Re\), and a cross-flow one, with the fluid following the corrugation until reaching the downstream end, at high \(Re\). In recent years, modifications to that design have been proposed to improve performance. [PERSON] et al. [6] analyzed a capsule-type PHE using CFD and compared it with chevron PHEs, demonstrating a higher Nusselt number \(Nu\) for \(Re\) below 3000, as well as a superior heat transfer performance index across all the examined \(Re\); this was attributed to the presence of concave and convex surface features, which generate longitudinal and transverse vortices. [PERSON] and [PERSON] [7; 8] introduced a PHE consisting of a basic unit constructed through a hyperbolic tangent function, finding an average \(Nu\) increase of 28% compared to herringbone PHEs and other new designs [7]. Additionally, they investigated the impact of various geometric parameters on flow characteristics [8]. [PERSON] et al. [9] considered three novel plates with anti-phase, in-phase, and full-wave rectified secondary corrugations, achieving a more uniform distribution of the Nusselt number with respect to the traditional sinusoidal surface, with benefits in reducing thermal stress and transverse heat conduction. The same authors [10] also conducted a design of experiment to optimize the first of the geometries mentioned, explaining the impact of the secondary corrugation amplitude on the flow pattern and turbulence behavior. [PERSON] et al. [11] studied a PHE featuring a lung pattern that replicates a branching system with bronchial trees and bronchioles, supplied with water in a countercurrent configuration: they illustrated that this shape achieved effectiveness comparable to a reference chevron plate while providing 71.3% more heat transfer with fewer plates, leading to a reduction in cost. In regard to alternative plate corrugations, a dimpled pattern, as shown in Figure 1, presents an undulated surface to enhance turbulence and create multiple contact points, thereby distributing pressure loads over a larger area. It is specifically employed for high-pressure applications, when the pack is assembled from plates that are brazed together in a vacuum oven to form a self-contained unit (BPHE), using brazing materials such as copper, stainless steel, or others, selected according to their compatibility with the operating fluid. The limited literature available on this type of design primarily focuses on the central portion of the heat plate (HP). [PERSON] et al.