**2. Numerical simulation**

And the heat transfer is obtained from Eq. (4):

198 Numerical Simulation - From Brain Imaging to Turbulent Flows

transferred by air which is absorbed by water *Q*<sup>2</sup> =*Q*1.

And the Reynolds number according to Eq. (8) is

o

*k*

<sup>1</sup> 1/4 2/3

where

*Q hA T* 2 2 2 2 *conv T C* = D( )

<sup>2</sup> 40 *A DL T i* = p

Now the mass coefficient is calculated based on the Nusselt number for air leaving the heat

4 *<sup>C</sup>*

As the air flows through the matrix or tube bank, the speed will remain unchanged because the volume of air flow will be lower in the area where this is in contact with the tubes, and to maintain flow mass, the speed increases accordingly. Then, it is interesting to know the maximum speed reached by the air; this is the type of arrangement of the tube bank, and this case is rectangular arrangement type and the equation for the maximum speed is defined as

*T*

*T o*

c

If the Reynolds number is the turbulent regime as in this case, the equation determined by

282,000 0.4 <sup>1</sup>

4/5 5/8 1/2 1/3

æ ö æ ö

Churchill and Bernstein can be applied, which is valid for all Reynolds numbers [6]:

0.62 0.3 <sup>1</sup>

*Pr*

è ø è ø

= =+ ç ÷ <sup>+</sup> ç ÷ æ ö è ø æ ö è ø ç ÷ <sup>+</sup> ç ÷

*hD Re Pr Re Nu*

*<sup>P</sup>* = = (11)

*<sup>S</sup> v v S D* <sup>=</sup> - (12)

= (13)

(14)

It is necessary to know the hydraulic diameter of the cross section that crosses in air:

*h c <sup>A</sup> D L*

*max*

2 *max v L Re µ* r

The geometry used for the analysis has exactly the same dimensions as that of the heat exchanger installed on the laboratory (1:1 scale) in order to obtain data and represent both volumes of fluid (water and air) within the domain. This geometry was formed using the Solid Works software. Once completed, it is exported to the ICEM CFD software that is used to discretize the domain and to assign the name of the frontiers or boundaries of the total domain.

The discretization of the model is the partition or geometry in small elements called control volumes, where the Navier-Stokes equations will be evaluated, which govern fluid dynamics. For discretization, it is necessary to define the existing volumetric bodies; in this case, there are total 41 bodies; 40 of them are tubes, which represent the total volume of water, and the remaining body represents the air passing through them.

The discretization or (or mesh) selected was unstructured. Then, the parameters for the partition of the total volume into smaller volumes are set; these parameters are set in order to have the maximum size and the minimum size that can have the volume or item in a specific area.

Once meshed, the next step is to establish the boundary conditions in the domain; these conditions are very important because the solution is based on them and must be known before carrying out numerical simulation as these represent the actual phenomenon being simulated; and if they are not representative, it is impossible to validate such a simulation.
