**2.5 Computational fluid dynamics (CFD)**

The numerical simulation was performed by the software ANSYS Fluent. The mathematical model κ-ε solved the three balances: mass, energy and momentum.

Conservation of mass:

$$\nabla \cdot (\rho \nu) = \mathbf{0} \nabla \tag{20}$$

Conservation of momentum:

$$\nabla \cdot (\rho v v) = -\nabla P + \nabla \cdot (\mu \nabla v) \tag{21}$$

Conservation of energy:

$$\nabla \cdot (\rho v c p T) = \nabla \cdot (k \nabla T) \tag{22}$$

where k is the thermal conductivity, ρ is the density, μ is the dynamic viscosity, cp is the specific heat, v is the velocity, T is the temperature and P is the pressure (**Table 4**).

**Figure 3.** *Mesh of the spiral plate heat exchanger.*


A suggested car cooling system performance must cool down the hot fluid 10°C or maximum 20°C. The results were achieved by implementing the thermal and hydraulic model, where one of the fundamental variables to measure was the hot outlet temperature. The difference between hot inlet and hot outlet was 6.4°C. The thermal and hydraulic method is an option to design heat exchangers. One of its goals is to find the lowest heat transfer area because the permissible pressure drop was fixed as a parameter to use completely. Then, from this value, the method seeks for some geometrical configuration to satisfy the required pressure drop. The method determined the heat transfer area, and the numeric value was of 2.04 m<sup>2</sup>

*Designing Spiral Plate Heat Exchangers to Extend Its Service and Enhance the Thermal…*

The permissible pressure drop was set by 1 psi for the two passages. The simulation calculated a value of 0.975 psi for the hot channel. The value for cold channel was 0.00013 psi because the cold channel has a length of 0.15 m. This flow section was considered as an open channel. This hydraulic behaviour was determined by the spiral diameter of 0.387 m, a plate length of 6.7 m, 10 spiral turns and the plate

Flow (kg/s) 1 0.38 Inlet temperatures (°C) 15 42.14 *T*out (C) 31.33 33.65 Viscosity (cp) 1.1 0.175 Maximum pressure drop (kPa) 150 950 Thermal conductivity (k, W/m K) 0.61 0.0763 Heat capacity (J/kg K) 4528.02 1563.76

Channel spacing (m) 0.00254 0.00635

Tout (°C) 6.72 60.7 Pressure drop (kPa) 0.975 0.00068

HTC (W/m<sup>2</sup> K) 12227.62 305

Plate length (m) 6.7 6.7

) 2.04

Diameter (m) 0.378

U (W/m<sup>2</sup> K) 52.41 Effectiveness 0.52 Number of rounds 10

Thermal conductivity of steel (W/m K) 13 Plate width (m) 0.0762 Core diameter (m) 0.508 Specific gravity 0.97

Plate thickness (m) 0.003175

**Water R134a**

**Water Air**

(**Tables 6** and **7**).

*DOI: http://dx.doi.org/10.5772/intechopen.85345*

**Table 6.**

*Second case study [13].*

Area (m<sup>2</sup>

**Table 7.**

**215**

*Results for case study 1.*

#### **Table 5.**

*Second case study.*

**Figure 3** shows the virtual spiral plate heat exchanger designed by the software workbench, the mesh was structured with 97,250 control volumes and the geometrical features (plate width, plate spacing, plate length, thickness, etc.) are shown in **Tables 5** and **8**.

The boundary conditions such as the inlet velocity, inlet temperatures, fluid properties, flow rates and metal properties were considered from the results shown in **Tables 5** and **8**.
