# On the Svelteness as an Engineering Tool in Constructal Design: A Critical Review
## 1 Introduction  
Constructal theory highlights the role of configuration in the survival of flow systems. It presents the generation of the architecture, and its evolution, as a universal physical phenomenon, in both natural and engineered systems [1]. Following a different approach to developing engineering systems, Constructal Design includes the flow architecture as a design input instead of a result. Moreover, describing the flow architecture and assessing its evolutionary path implies linking its survival to greater efficiency and performance. Therefore, measuring the significance of the flow configuration requires a parameter to express it. [PERSON] and [PERSON] [1] introduced a way to characterize a flow configuration by comparing an external length scale with an internal one, resulting in a global geometric property of the system designated as Svelteness (Sv).  
\[\text{Sv}=\frac{\mathcal{L}_{e}}{\mathcal{L}_{i}} \tag{1}\]  
According to [PERSON] [2], the properties of a flow system include two global sizes, an external and an internal one; at least one global measure of performance; configuration; and freedom to morph. Svelteness is the parameter able to connect the flow system characteristics, emerging as a global property associated with the flow architecture andindependent of the flow operating conditions and their type. When applied in Constructal Design, the results highlight its role in the overall performance and survival of flow systems and allow assessing the evolutionary direction of the flow configuration towards vascularization expressed through higher Sv values [1; 2].  
The application of Svelteness should be as broad as Constructal theory. However, its discussion remains restricted to applications regarding fluid flow, disregarding energy flows or any other type. According to [PERSON] and [PERSON] [3], configurations evolve toward the simplest form that still captures their meaning. For example, from one point to an area, flows evolve toward dendritic configurations visualized in the similarity between tree branches and river basins. Therefore, a higher Svelteness in a configuration indicates originality and a more effective way of conveying meaning.  
In engineering applications, this meaning equals greater performance. Therefore, Constructal Design should guide engineers toward designing the flow architectures that, in time, continuously promote greater global performance.  
After this Introductory Section, the next section synthesizes how researchers have considered Svelteness (Sv) as a design criterion, applying it in three main approaches to fluid flow configurations, namely a parallel flow [4; 5; 6; 7; 8], the tree flow [8; 9; 10; 11; 12; 13; 14; 15; 16; 17], and the radial tree flow [18; 19; 20; 21]. In most research works, Sv is mentioned, but not explored or developed; instead, its role in the flow is assumed through criteria. However, some works explore Sv to assess its impact, and the following section reviews the reasoning underlying the use of the flow configuration of Svelteness as a design criterion. Afterward, in Section 3, we review several examples exploring Svelteness as a design tool, followed by Section 4, dedicated to the definition of the appropriate length scale with special emphasis on the external one. In this section, we use two configurations to suggest an essential criterion for choosing the external length scale. Finally, before the Conclusions, in Section 5 of this review, for the aforementioned configurations, we explore the implications of a validated Svelteness as a design tool to assess the evolution of technological flow configurations.