# Cooling Effectiveness of the Sustainable Cooling Solution for Cattle: Case Study in Poland
## 2 Materials and Methods  
### Developed and Applied Cooling System  
The proposed cooling system consists of two main subsystems: an innovative cooling water mattress module and a chilled water production and distribution system. The design of the water mattress handling module was selected among four propositions analyzed in terms of heat transfer by applying the Computational Fluid Dynamics-based simulations in the Ansys Fluent environment. Furthermore, in the decision-making process authors considered also the influence of the design on animals' well-being and its technical challenges. The chosen and developed design in the present study is based on modifying the commercially available water mattress for cattle in a way that ensures a stable and even flow of coolant through its interior. For that purpose, the water distributor and channel structure were applied inside the mattress. The 3D geometry of the module developed in Autodesk Inventor Professional 2020 Software is presented in Figure 1. It was implemented in the Ansys Meshing Module, where tetrahedral mesh was generated. For the simulation, the inlet water temperature of 4.5 \({}^{\circ}\)C and mass flow of 0.85 kg/s were assumed. The model of heat transfer between the animal and mattress surface was simplified to the surface temperature boundary conditions and assumed as 35 \({}^{\circ}\)C, being the temperature of a cow's skin. In model calculations, for the fluid domain the k-\(\varepsilon\) realizable turbulence with enhanced wall treatment was employed. As a result, the 715 W/m\({}^{2}\) heat flux was achieved. More detailed information about the modeling process has been described by the authors in [24]. Implementation of the design into a prototype was achieved through the 10 rubber fenders shaping the channel structure inside the mattress. Each f  
Figure 1: Geometry of the innovative cooling water mattress [24]. wide, and 25 mm high, spaced every 45 mm from the edge. Water is supplied directly to the channel through a distributing collector with a diameter of 50 mm and 9 orifices with a 10 mm diameter. The collection of the returning water is realized through the 50 mm return collector. The water mattress is placed on a layer of 2.5 cm-thick plywood fixed to the steel frame. The water capacity of the mattress ensures proper cushioning for the cows' body weight. Figure 2 presents the innovative cooling water mattress and its supplying cooling system. The cooling water mattress is supplied with chilled water produced and distributed by the RadMAT system presented in Figure 3. It consists of two water circuits but can be expanded with another two in the future. The first water circuit is connected with the 200 L chilled water storage tank to accumulate cold water produced by the Frimec MGC-V5W/D2N1 chiller with a 5 kW cooling capacity (FRIMEC International, Meru, Selangor, Malaysia). It is coupled through the Alfa Lava CB30 heat exchanger (Alfa Laval Corporate AB, Lund, Sweden) with the cooling water mattress circuit. Each circuit is equipped with a water circulation pump (Ecocirc XL 32-80) (Xylem Inc. Washington, DC, USA) coupled with variable speed drivers. The temperature and water flow at the inlet to the water mattress are measured with a Vortex SV7204-SVR34 XXX50 KG/US-100 (ifm electronic gmbh, Essen, Germany) flow meter (accuracy rating \(\pm\)2%) equipped also with a temperature sensor (accuracy rating \(\pm\)1 K). The water mattress outlet temperature is recorded with an ifm TA2115 (ifm electronic gmbh, Essen, Germany) temperature sensor (accuracy rating \(\pm\)0.1%). Furthermore, an electric three-way valve enables supplying and returning water blending for temperature regulation. The operation of the system is controlled with Supervisory and Control Data Acquisition.