**2.4 Boundary conditions**

The present study is the optimization of EATHE performance. This study is performed for the desert climate of western Bikaner Rajasthan India. The Bikaner has *Earth Air Tunnel Heat Exchanger for Building Cooling and Heating DOI: http://dx.doi.org/10.5772/intechopen.99348*

**Figure 5.** *Model of spiral pipe EATHE.*

**Figure 6.** *Helical pipe heat exchanger for earth to air.*

**Figure 7.** *Model of helical pipe EATHE [8].*

**2.3 Meshing**

*Spiral pipe heat exchanger for earth to air.*

**Figure 4.**

**268**

**Figure 3.**

*Model of straight pipe EATHE.*

*Heat Transfer - Design, Experimentation and Applications*

**2.4 Boundary conditions**

The next step of the pre-processing stage is the generation of mesh to be used in the ANSYS ICEM is used for generating the mesh of the geometry. The tetrahedral meshing

is used to mesh the heat exchanger for the earth-to-air model which is shown in **Figure 8**. Since air enters from the one end of the pipe this is the 'inlet' and leaves from the 'outlet' created in the model. In the present analysis, CFD simulations performed using an unstructured grid. The mesh is used proximity and curvature-based. One of the geometry meshing algorithms picks a different mesh method by default. The sizing parameters are selected based on the size of the model. The 'relevance centre' and 'smoothing'specification of each mesh is set to fine. The minimum element size and

maximum element size both are set to 0.011 mm and 0.15 mm respectively.

The present study is the optimization of EATHE performance. This study is performed for the desert climate of western Bikaner Rajasthan India. The Bikaner has

Where.

tion law is written as

can be written as:

momentum equation:

*m*\_ = mass flow rate (kg/sec). *Cp* = specific heat (W/m-K).

*DOI: http://dx.doi.org/10.5772/intechopen.99348*

*u ∂T ∂x* þ *v ∂T ∂y* þ *w ∂T <sup>∂</sup><sup>z</sup>* <sup>¼</sup> *<sup>α</sup> <sup>∂</sup>*<sup>2</sup>

Momentum equation in X-direction:

Momentum equation in Y-direction:

Momentum equation in Z-direction:

*u ∂u ∂x* þ *v ∂u ∂y* þ *w ∂u <sup>∂</sup><sup>z</sup>* <sup>¼</sup> <sup>1</sup> *ρ ∂p ∂x* þ *v ∂*2 *u <sup>∂</sup>x*<sup>2</sup> <sup>þ</sup>

*u ∂v ∂x* þ *v ∂v ∂y* þ *w ∂v <sup>∂</sup><sup>z</sup>* <sup>¼</sup> <sup>1</sup> *ρ ∂p ∂y* þ *v ∂*2 *v <sup>∂</sup>x*<sup>2</sup> <sup>þ</sup>

*u ∂w ∂x* þ *v ∂w ∂y* þ *w ∂w <sup>∂</sup><sup>z</sup>* <sup>¼</sup> <sup>1</sup> *ρ ∂p ∂z* þ *v ∂*2 *w <sup>∂</sup>x*<sup>2</sup> <sup>þ</sup>

shown in **Table 1**.

Density (ρs) (kg/m<sup>3</sup>

**Table 1.** *Soil properties.*

**271**

*Tout* = Temperature of air at the outlet EATHE. *Tin* = Temperature of air at the inlet EATHE.

*Earth Air Tunnel Heat Exchanger for Building Cooling and Heating*

*∂u ∂x* þ *∂v ∂y* þ *∂w*

Q = heat extract or released by the soil to surrounding soil via pipe material (W).

Mass conservation Law: The equation for continuity equation or mass conserva-

Conservation Law of energy: neither the energy can be created nor destroyed, it only changes its form which stated by the law of energy conservation. The equation

(Newton's second law also known asNavier–Stokes equation): the flowing is

In Eqs. (2)–(6) the velocity components in *x*-, *y*-, and *z*-directions are *u*, *v*, and *w*

Thermal properties of sandy and sandy soil used tor CFD EATHE which is

**Property Sandy Loam Soil** Thermal Conductivity (κ) W/m-K 1.26

Specific heat (Cs) J/kg-K) 1260

) 2215

and temperature and pressure are *T* and *p* of the flowing air [13].

*T <sup>∂</sup>x*<sup>2</sup> <sup>þ</sup> *∂*2 *T <sup>∂</sup>y*<sup>2</sup> <sup>þ</sup>

*∂*2 *T ∂z*<sup>2</sup> (3)

> *∂*2 *u <sup>∂</sup>y*<sup>2</sup> <sup>þ</sup>

*∂*2 *v <sup>∂</sup>y*<sup>2</sup> <sup>þ</sup>

*∂*2 *w <sup>∂</sup>y*<sup>2</sup> <sup>þ</sup>

*∂*2 *u ∂z*<sup>2</sup> (4)

*∂*2 *v ∂z*<sup>2</sup> (5)

*∂*2 *w ∂z*<sup>2</sup> (6)

*<sup>∂</sup><sup>z</sup>* <sup>¼</sup> *<sup>o</sup>* (2)

a geological area of East Longitude 28 01<sup>0</sup> and North Latitude 73 019<sup>0</sup> . Arranged at a normal elevation of 797 Feet, Bikaner has extraordinary temperatures. As the region lies in the betray region, outrageous warmth in summer and frosty in winter is normal for forsaking. Both day and night temperature increments bit by bit and achieves their most extreme esteems in April, May, and June. The temperature fluctuates from 47°C in summer to around 0°C in winter. Climate is for the most part dry and hot except amid the storm time frame. The dampness is most noteworthy in August with mean day by day relative moistness is 71% in the morning and 52% at night. The EATHE is displayed as two coupled warmth exchange forms, to be specific, convection warm exchange among air streaming in the tube and the tube inner surface, and conduction warm exchange between the pipe external surface and the dirt condition. The external distance across the dirt barrel encompassing the EATHE pipe is taken as four times the pipe width. The external distance across the dirt barrel encompassing the EATHE pipe is taken as four times the pipe width to restrict the emphasis time. To analyze the EAHE system, the following assumptions are made.


In this EATHE CFD designed model, air as fluid supplied to the model with Maximum temperature of summer.

Heat gain/released by air to surroundings calculated by

$$Q = \dot{m}C\_p(T\_{out} - T\_{in}).\tag{1}$$

*Earth Air Tunnel Heat Exchanger for Building Cooling and Heating DOI: http://dx.doi.org/10.5772/intechopen.99348*

Where.

a geological area of East Longitude 28 01<sup>0</sup> and North Latitude 73 019<sup>0</sup>

*Heat Transfer - Design, Experimentation and Applications*

normal elevation of 797 Feet, Bikaner has extraordinary temperatures. As the region lies in the betray region, outrageous warmth in summer and frosty in winter is normal for forsaking. Both day and night temperature increments bit by bit and achieves their most extreme esteems in April, May, and June. The temperature fluctuates from 47°C in summer to around 0°C in winter. Climate is for the most part dry and hot except amid the storm time frame. The dampness is most noteworthy in August with mean day by day relative moistness is 71% in the morning and 52% at night. The EATHE is displayed as two coupled warmth exchange forms, to be specific, convection warm exchange among air streaming in the tube and the tube inner surface, and conduction warm exchange between the pipe external surface and the dirt condition. The external distance across the dirt barrel encompassing the EATHE pipe is taken as four times the pipe width. The external distance across the dirt barrel encompassing the EATHE pipe is taken as four times the pipe width to restrict the emphasis time. To analyze the EAHE system, the following assumptions are made.

1.The temperature of soil throughout the length and depth of pipe is constant.

2.Thermal properties and heat flux are considered to remain constant.

5.Engineering materials used are considered homogenous and isotropic.

In this EATHE CFD designed model, air as fluid supplied to the model with

*Q* ¼ m\_ *Cp*ð Þ *Tout* � *Tin :* (1)

3.Airflow throughout the EATHE is incompressible.

Maximum temperature of summer.

**270**

**Figure 8.** *Meshing model.*

4.Friction and joint losses during the air flow are neglected

Heat gain/released by air to surroundings calculated by

. Arranged at a

Q = heat extract or released by the soil to surrounding soil via pipe material (W).

*m*\_ = mass flow rate (kg/sec).

*Cp* = specific heat (W/m-K).

*Tout* = Temperature of air at the outlet EATHE.

*Tin* = Temperature of air at the inlet EATHE.

Mass conservation Law: The equation for continuity equation or mass conservation law is written as

$$\frac{\partial u}{\partial \mathbf{x}} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial \mathbf{z}} = \sigma \tag{2}$$

Conservation Law of energy: neither the energy can be created nor destroyed, it only changes its form which stated by the law of energy conservation. The equation can be written as:

$$a\frac{\partial T}{\partial \mathbf{x}} + v\frac{\partial T}{\partial \mathbf{y}} + w\frac{\partial T}{\partial \mathbf{z}} = a\left[\frac{\partial^2 T}{\partial \mathbf{x}^2} + \frac{\partial^2 T}{\partial \mathbf{y}^2} + \frac{\partial^2 T}{\partial \mathbf{z}^2}\right] \tag{3}$$

(Newton's second law also known asNavier–Stokes equation): the flowing is momentum equation:

Momentum equation in X-direction:

$$u\frac{\partial u}{\partial \mathbf{x}} + v\frac{\partial u}{\partial \mathbf{y}} + w\frac{\partial u}{\partial \mathbf{z}} = \frac{1}{\rho} \frac{\partial p}{\partial \mathbf{x}} + v \left[ \frac{\partial^2 u}{\partial \mathbf{x}^2} + \frac{\partial^2 u}{\partial \mathbf{y}^2} + \frac{\partial^2 u}{\partial \mathbf{z}^2} \right] \tag{4}$$

Momentum equation in Y-direction:

$$u\frac{\partial v}{\partial x} + v\frac{\partial v}{\partial y} + w\frac{\partial v}{\partial z} = \frac{1}{\rho} \frac{\partial p}{\partial y} + v \left[ \frac{\partial^2 v}{\partial x^2} + \frac{\partial^2 v}{\partial y^2} + \frac{\partial^2 v}{\partial z^2} \right] \tag{5}$$

Momentum equation in Z-direction:

$$u\frac{\partial w}{\partial x} + v\frac{\partial w}{\partial y} + w\frac{\partial w}{\partial z} = \frac{1}{\rho}\frac{\partial p}{\partial z} + v\left[\frac{\partial^2 w}{\partial x^2} + \frac{\partial^2 w}{\partial y^2} + \frac{\partial^2 w}{\partial z^2}\right] \tag{6}$$

In Eqs. (2)–(6) the velocity components in *x*-, *y*-, and *z*-directions are *u*, *v*, and *w* and temperature and pressure are *T* and *p* of the flowing air [13].

Thermal properties of sandy and sandy soil used tor CFD EATHE which is shown in **Table 1**.


**Table 1.** *Soil properties.*
