**3.3 Experimental uncertainty and errors**

The used instruments were well calibrated, and the margin of error and uncertainty of each instrument were evaluated.

**4. Computational methods**

**4.2 Boundary conditions**

for the simulation:

set to zero.

**4.3 Grid generation**

**33**

**4.1 Numerical simulation and conditions**

*DOI: http://dx.doi.org/10.5772/intechopen.93359*

which enhances the accuracy of swirling flows.

all cases with *q*̿= 30,000 W/m<sup>2</sup>

300 K, as in **Tables 2** and **3**.

The numerical analyses included single phase flow based on steady and three dimensional continuity; momentum and energy equations were performed using the ANSYS-Fluent commercial code. RNG *k-ε* model was chosen to solve the considered cases because the effect of swirl on turbulence is included in this model,

*Applications of Compound Nanotechnology and Twisted Inserts for Enhanced Heat Transfer*

The thermo-fluid process in the current simulated was solved as steady, incompressible, and 3D flow. The following was adopted to set the boundary conditions

• The flow was considered as internal flow under uniform heat flux condition for

.

• Results are considered only at the fully developed region (*L* > 10*D*p).

• Water and 0.1 vol.% TiO2/water are considered as the working fluids, and calculations for the thermal properties are done at the inlet temperature of

• The nanofluid was considered as a single-phase fluid with changed physical parameters as density, thermal capability, thermal conductivity, and viscosity.

• All cases were investigated within the turbulent flow regime studied with a

• At the outlet, a pressure outlet condition was used, and the gauge pressure is

• Turbulence intensity obtained from the expression recommended by [28].

*<sup>T</sup>:I:* <sup>¼</sup> <sup>0</sup>*:*<sup>16</sup> *Re* �0*:*<sup>125</sup>

Other flow quantities are extrapolated from the interior domain by the solver in Fluent software. The SIMPLE (Semi-Implicit Pressure Linked Equations) algorithm were chosen as solver method. In addition, a convergence criterion of 10�<sup>5</sup> was used

To avoid blurred curved areas, tetrahedral cells are used for meshing the computational domains, as shown in **Figure 4**. Mesh, with around 3,000,000 elements,

*Dp* (20)

• The hydraulic diameter at each inlet and outlet has the same value.

• No slip condition was also applied to the tube wall.

range for Reynolds number of 5000–20,000.

for energy and mass conservation of the calculated parameters.

was decided to represent the domains for the current simulation.


The possible error in the prediction of Re and Nu was estimated. The uncertainty in Re values was estimated by Eqs. (16)–(18) using the uncertainties of the measuring instruments used for measurements of relevant variables in Re:

$$Re \;= \frac{4\,\dot{m}}{\pi\mu d} = \frac{4\rho\dot{V}}{\pi\mu d} \tag{16}$$

$$
\Delta Re = \left[ \left[ \left( \frac{\sigma Re}{\sigma \dot{V}} \right) \bullet \dot{V} \right]^2 + \left[ \left( \frac{\sigma Re}{\sigma d} \right) \bullet d \right]^2 \right]^{0.5} \tag{17}
$$

Getting,

$$
\Delta \text{Re} / \text{Re} = \left[ \left[ \left( \frac{\Delta \dot{V}}{\dot{V}} \right) \right]^2 + \left[ \left( \frac{\Delta d}{d} \right) \right]^2 \right]^{0.5} \tag{18}
$$

= 0.0665 or 6.65%.

Uncertainty in Nu values was estimated by Eq. (19) using the uncertainties of the measuring instruments used for measurements of relevant variables in Nu, as

$$
\Delta \mathbf{N} \boldsymbol{\mu} / \mathbf{N} \boldsymbol{\mu} = \left[ \left[ \left( \frac{\Delta \mathbf{h}}{h} \right) \right]^2 + \left[ \left( \frac{\Delta d}{d} \right) \right]^2 \right]^{0.5} \tag{19}
$$

= 0.0625 or 6.25%

*Applications of Compound Nanotechnology and Twisted Inserts for Enhanced Heat Transfer DOI: http://dx.doi.org/10.5772/intechopen.93359*
