## 1 Introduction  
Heat exchangers consisting of a heated tube bank are widely used in practice to transfer heat from one medium to another. Typically, one fluid flows over the tube bank, while another fluid of a different temperature passes through the tubes. The tubes are arranged as a bank in an inline or staggered manner to heat the surroundings, dissipate excessive heat, or recover waste heat. Tube banks in crossflow are used in many fields, such as industry, biomedicine, mechanisms for heat transfer increase, and nanofluid applications. They can be found in the economizer and evaporator of an air conditioning system [1]. Moreover, they are parts of processes such as biological systems, filtration flow, fibrous media encountered in polymer processing, and in insulation materials [2]. [PERSON] and [PERSON] [3] discussed the inline tube bank heat exchanger installed on a gas porous burner, using the air as a working fluid and LPG as a fuel. [PERSON] and [PERSON] [4] investigated the thermal-hydraulic characteristics of the bare tube bank and plain finned tube heat exchangers used to cool the compressor bleed air in an aero turbine engine. [PERSON] et al. [5] performed an analysis and optimization of metal-foam tube banks for waste heat recovery from the engine's exhaust gas. [PERSON] et al. [6] investigated the heat transfer and pressure drop of sodium-to-air heat exchanger tube banks on a sodium-cooled fast reactor. A steam reactor powered by a propane fuel consisting of a shell and tube heat exchanger was investigated by [PERSON] et al. [7]. Some authors use the nanofluid to improve the heat transfer parameters [8; 9; 10]. To evaluate the heat transfer in a tube bank, the Nusselt number is used as one of the basic criteria. It is defined as a ratio of convective to conductive heat transfer across a boundary. In other words, the Nusselt number is a dimensionless heat transfer coefficient. The purpose of using dimensionless numbers is to compare the results of the used quantitiesindependently. There are two well-known ways to obtain the Nusselt number. The first one is based on the heat transfer coefficient, characteristic length, and thermal conductivity; the other one uses the empirical correlations based on the Reynolds and Prandtl numbers. The latter approach is usually mentioned in literature dealing with experimental results. Some authors have created more difficult and complex formulas where other variables are used as well. They are related to the manner in which fluid properties are evaluated. The base is either the free-stream temperature, the film temperature, which is the average of the free-stream and surface temperatures, or the base is the average of the inlet and outlet temperatures, which is not easy to determine without a calculation or experiment. Due to the lack of computational technology, the first studies of heat transfer were conducted only experimentally and reported the tube spacing effect for banks in crossflow. [PERSON] [11] and [PERSON] [12] created the correlations for various tube bank arrangements in the Reynolds number range of 2 \(\times\) 10\({}^{3}\) and 4 \(\times\) 10\({}^{4}\), while [PERSON] [13] tested different tube diameters at Reynolds numbers ranging from 2 \(\times\) 10\({}^{3}\) to 7 \(\times\) 10\({}^{4}\). He confirmed the similarity principle applied to the tube banks, despite some departure from the true geometric similarity in the ratio of length to the diameter or to the intertube space. [PERSON] and [PERSON] [14] detailed the flow conditions in a bank of 20 staggered circular tubes with a Reynolds numbers of over 2 \(\times\) 10\({}^{4}\). [PERSON] [15] discussed the effect of the Prandtl number and large differences in temperature-dependent properties in a wide range of the Reynolds numbers from laminar to turbulent flow. The most extensive and precise measurement of the local heat transfer coefficient around a cylinder was carried out by [PERSON] and [PERSON] [16].