## 2 Fundamentals
### Classification of the Present Method  
Dimensionless numbers were introduced to make the results of experimental investigations by several authors comparable and to reduce the experimental scope. They are based on the general principle that the solution of a physical problem is independent of the chosen metric system and can be expressed by dimensionless parameters. In the context of heat transfer problems, the Nusselt number \(Nu\) was introduced according to Equation (8) [9]:  
\[Nu=\frac{h\cdot L}{\lambda} \tag{8}\]  
with  
\(L\)  
as the characteristic length in m;  
\(\lambda\)  
as the thermal conductivity in W/(mK). The Nusselt number is also dependent on the properties of the fluid being used, including its velocity, density, viscosity and heat capacity. These properties can also be summarised in dimensionless groups of numbers, specifically the Prandtl number \(Pr\) and the Reynolds number \(Re\) in case of forced convection. The local Nusselt number also depends on an empirical constant \(K\) based on the nozzle geometry. For forced convection, the local Nusselt number follows the dependence described in Equation (9) for a defined geometry. \[Nu=f(K,Re,Pr) \tag{9}\]The dimensionless Reynolds number, defined in Equation (10), characterises the existing flow by measuring the ratio of inertial and viscous forces. It is important for comparing different nozzles with varying flow characteristics. \[Re=\frac{\rho\cdot\cdot u\cdot L}{\mu} \tag{10}\]  
with  
\(\rho\) as the fluid density in kg/m\({}^{3}\);  
\(\mu\) as the kinematic viscosity kg/ms. Initial studies of the heat transfer coefficient on an unmoved flat plate using an impingement jet were conducted in the 1970s. Since then, several further investigations have been carried out by various authors. A selection of investigated slot nozzles is listed in Table 1, while Table 2 lists a collection of investigated round nozzle systems. The studies presented were all conducted using different but comparable measurement principles and have different ranges of validity. The coefficients and their respective range of validity can be used to compare the different measurement methods used in these studies. The first coefficient for validity is the ratio between the nozzle-to-strip distance \(H\) and the width of the slot nozzle \(W\), called the _H/W_ ratio. The second coefficient for validity, _s/W_, describes the ratio between the nozzle-to-nozzle distance \(s\) and the width of the slot nozzle \(W\). The third coefficient is the range for the Reynolds number \(Re\) for the measurements. For round nozzle systems, the coefficients change. The first coefficient _H/D_ is the ratio between the nozzle-to-strip distance \(H\) and the hydraulic diameter of the round nozzle \(D\). The second coefficient _s/D_ describes the ratio between the nozzle-to-nozzle distance \(s\) and the hydraulic diameter \(D\). There are three main measurement principles as shown in Tables 1 and 2: vaporisation by a heated flow, the use of liquid crystal techniques and the determination of the heated surface temperature by thermocouples or, newly, by IR-cameras. [PERSON] (1977) experimental setup is based on a test method that measures a change in the water column. The integral heat transfer coefficient is determined from the measured integral mass transfer coefficient. Air flows onto a flat plate with concentric circles or individual rectangular elements consisting of a porous stone. It is important that each element on the plate is separate and has its own water chamber. A burette with an additional water supply is connected to the water chamber. To determine mass transport, the inlet tube of the water supply was closed and the water column in the burette was observed using a stopwatch. Investigating different nozzle geometries and fields require significant effort as it involves manufacturing a new porous plate and adapting the water supply.