3. Results

where <sup>r</sup><sup>0</sup> is the reference density of the water flow (kg/m<sup>3</sup>

136 Heat and Mass Transfer - Advances in Modelling and Experimental Study for Industrial Applications

difference in the domain is large.

2.3. Boundary conditions and settings

2.4. Grid dependence and computer storage

Table 2. Various settings used during the calculations.

Table 3. Boundary conditions used during the calculations.

Battery module outside dimensions Cooling pipe radius (rinnerÞ

Coolant Final mesh size

Cylinder outer wall Coolant/solid interface Cooling pipe inlet Cooling pipe outlet Cell initial temperatures

2.2.2. Solid section

and, Eq. (37) is obtained by the Boussinesq approximation <sup>r</sup> <sup>¼</sup> <sup>r</sup><sup>0</sup> <sup>1</sup> � <sup>β</sup>Δ<sup>T</sup> to replace the buoyancy terms. This approximation is acceptable so long as changes in actual density are small. Specifically, it is valid when βð Þ T � T<sup>0</sup> ≪ 1, and should not be used if the temperature

The solid section in this work consists of three components, namely, the aluminium block, the wall of the helix coil and the battery module. When the velocity is set to zero in Eq. (20), the

> Γφ ∂φ ∂xi

The cooling fluid is modelled using the material properties of water calculated using the inlet

The requirements set out in two recent guidelines referring to good CFD practice [35, 36] were followed in the present work. Non-uniform structured Cartesian grids were used throughout this work with extensive tests for independence of grid size checked by increasing the grid numbers until further refinement was shown not to be of significance. Close to solid surfaces, the grid was refined using geometric progression with an expansion ratio from the solid surfaces of less than 1.1 and with the Y<sup>þ</sup> values adjacent to a solid boundary held around a

equation governing pure conductive heat transfer by diffusion is obtained, that is,

∂ ∂xi

ð Þ¼ rφ

Conjugate heat transfer was used between the solid domain and fluid domain.

temperature. The settings and boundary conditions are set out in Tables 2 and 3.

∂ ∂t ); T<sup>0</sup> is the reference temperature (K);

þ S<sup>φ</sup> (37)

Radius = 130 mm, height = 360 mm

Conjugate heat transfer uin ¼ 0:005 � 0:1 m/s Tin ¼ 293:15 K 101,325 Pa Tinit ¼ 313:15 K Tinit ¼ 349:15 K

5–15 mm H2O 107

293.15 K
