**3. Model assumptions and development**

*Noise and Environment*

**No. Material Density (kg/**

**m3 )**

 Artificial stone 1760 1.14 0.88 Asbestos cement sheet 1520 0.25 4.00 Asphalt 2240 1.05 0.95 Cement concrete (1:2:4) 2240 to 2480 1.24 0.80 Compressed straw slab 368 0.074 13.51 Fiberboard 240 to 400 0.046 to 0.056 21.74 to 17.86 Glass 2510 0.905 1.10 Glass cellular 168 0.061 16.40 Glass fiber 48 0.029 34.50 Granite 2640 2.52 0.40 Hair felt 80 0.034 29.40 Limestone 2180 1.32 0.76 Ordinary bricks 1760 0.7 to 1.44 1.43 to 0.70 Plastering 1280 to 1600 0.50 2.00 Sand-lime bricks 1840 0.93 1.07 Sandstone 2000 1.12 0.90 Saw dust 192 0.051 19.60 Terrazzo 2430 1.363 0.73 Timber 480 to 270 0.124 8.00 Wood-wool slab 400 0.071 14.08

**Thermal conductivity K (kcal/m h °C)**

**Thermal resistivity (1/K)**

cement sheets or corrugated galvanized iron sheets on bricks. (iv) Flat roofs may be kept cool by water which may either be stored or sprayed at regular intervals. The surface temperature of the roof is reduced by this method. (v) Thermal insulation of flat roof may also be provided by putting a layer of about 25 mm thickness of coconut pith cement concrete. For this purpose, coconut pith and cement are mixed in dry state and then the mix is transferred to concrete mixer. Water in required quantity is added so as to obtain concrete of workable consistency. It is then conveyed and laid in suitable thickness on the roof. Wet coconut pith may also be used with due care and hard mixing may be adopted for small quantity of work. To avoid loss of water from concrete surface, it is covered by an impermeable layer and then it is allowed to dry in air for a period of 20 days to 1 month. Any cracks which are seen during drying period are filled up by the pith concrete. When the pith concrete layer has fully dried, water-proofing treatment

*Density, thermal conductivity and thermal resistivity of some common building and insulating materials.*

Following methods may be adopted for thermal insulation of exposed walls: (i) suitable thickness of wall may be provided. (ii) Hollow wall or cavity wall construction may be adopted. (iii) For partitions, an air space may be created by fixing hard boards on battens. (iv) The inside and outside surfaces of exposed wall

**110**

**Table 2.**

may be given in the usual manner.

*2.4.3 Thermal insulation of exposed walls*

The assumptions used in the development of the model for a building integrated photovoltaic airflow window (BIPV-AW) system as depicted in **Figure 1** are: (i) fully developed heat transfer has been assumed for mixed convection heat transfer assuming a parallel plate wide channel at low air velocities ~0.5 m/s; (ii) temperature variation only along y-axis with lumped temperature distribution along x and z-axes; (iii) applicability of first law of thermodynamics at the surface; (iv) clear sky is applicable; (v) quasi steady state heat transfer analysis has been performed assuming a vertical channel; (vi) uniform average air velocity distribution; (vii) temperature variation only in y-direction (vertical), being taken as lumped in other directions (x-axis and z-axis); (viii) air properties are evaluated at film temperature of 300 K; (ix) negligible heat transfer from side walls/insulation panel and room air zone; (x) conduction (diffusion) equation for performing energy balance on air nodes is not taken into consideration; (xi) negligible thermal storage capacity of duct wall; (xii) no infiltration or air leakage sources from the test section; and (xiii) ambient air and room air temperatures are specified.

The system is discretized into network of two adjacent stacks of control volumes common to surface and air nodes (see **Figure 2**). The energy balances are performed on both surface and air nodes with aid of constitutive relations for noise fields due to solar intensity, sound intensity, airflow power intensity, electric power intensity and heat power intensity. The energy conversion and noise characterization is important, for example, in modeling airflow window and PV solar wall building structures. The resultant noise field due to composite wave elements (of heat, fluid, electricity, sound and sun) is a function of solar irradiation, sound intensity, air gap width, mass flow rate and pressure, wall and air temperatures of the double wall building structure. The integrated noise insulation due to thermal and sound

**Figure 2.** *Grid size in the duct: distribution of nodes and control volumes.*

fields is modeled. Noise characterization equations are devised, which calculate noise fields due to ventilation, heat transport and sound transmission of integrated building insulation through a double wall structure.

In writing nodal equations in matrix form, sign notation is adopted for automatic formulation of conductance matrix (U-matrix) with unknown temperatures and heat source elements. The sum of all incoming heat source elements and U-matrix conductances multiplied with temperature difference with respect to the unknown temperatures at other nodes are equal to zero. The energy balance is written in equation form for any general node (m,n):

$$\sum\_{\mathbf{n}=\mathbf{n}}^{N} \left( \mathbf{U}\_{\mathbf{m},\mathbf{n}} \times \Delta \mathbf{T}\_{\mathbf{m},\mathbf{n}} \right) + \sum\_{\mathbf{n}=\mathbf{n}}^{N} \mathbf{Q}\_{\mathbf{m},\mathbf{n}} = \mathbf{o} \tag{1}$$

where Um,n is the conductance at node (m,n), ∆Tm,n is the difference between unknown temperature at the node (m,n) and unknown temperature at surrounding heat exchange node. Qm,n is heat source term at the node (m,n).

#### **3.1 Noise characterization**

A unified theory for stresses and oscillations is proposed by Dehra [12]. The following standard measurement equations are derived and adopted from the standard definitions for sources of noise interference [1–60].

**Noise of sol:** for a pack of solar energy wave, the multiplication of solar power storage and the velocity of light gives solar power intensity I. On taking logarithm of two intensities of solar power, I1 and I2, provides intensity difference. It is mathematically expressed as:

$$Sol = \log\left(I\_{\mathbf{e}\_{\mathbf{e}}}\right) \left(I\_{\mathbf{e}\_{\mathbf{e}}}\right)^{-\iota} \tag{2}$$

where logarithmic unit ratio for noise of sol is expressed as *Sol*. The oncisol (oS) is more convenient for solar power systems. The mathematical expression by the following equality gives an oncisol (oS), which is 1/11th unit of a *Sol*:

$$
\rho \mathbf{S} = \pm \mathbf{n} \mathbf{1} \, \log \left( I\_{\mathbf{s}} \right) \left( I\_{\mathbf{s}} \right)^{\mathrm{-} \mathrm{i}} \, \tag{3}
$$

**113**

noise [37]:

tive units:

*Noise Transmission Losses in Integrated Acoustic and Thermo-Fluid Insulation Panels*

( )( ) −

> ( )( ) −

1 2 *Sip I I* log (4)

1 2 *oS I I* 11 log (5)

= <sup>1</sup>

where logarithmic unit ratio for noise of scattering is *Sip*. The oncisip (oS) is

The mathematical expression by the following equality gives an oncisip (oS),

= ± <sup>1</sup>

For energy area determination for a fluid wave, the water with a specific gravity of 1.0 is the standard fluid considered with power of ±1 Wm−2 for a reference

**Noise of scattering and lightning:** for a pack of fire wave, the intensity, I, of fire flash with power of light, is the multiplication of total power storage and the velocity of light. Whereas for a pack of fire wave, the intensity, I, of fire flash with power of fluid, is the multiplication of total power storage capacity and velocity of fluid.

• For a noise due to fire flash, the collective effect of scattering and lightning is

• For same intensity I, the pack of solar energy wave and a fire flash with light power have same energy areas; therefore, their units of noise are same as *Sol*. The therm power may also be included in fire flash with power of light.

• For same intensity I, the pack of fluid energy wave and a fire flash with fluid power have same energy areas; therefore, their units of noise are same as *Sip*. In determining the areas of energy for the case of fluids other than water, a

**Noise of elasticity:** for a pack of sound energy wave, the product of total power storage and the velocity of sound gives sound power intensity I. On taking logarithm of two intensities of sound power, I1 and I2, provides intensity difference. It is

> ( )( ) −

> > ( )( ) −

= ± <sup>1</sup>

Reference value used for I2 is −1 W m−2 on positive scale of noise and 1 W m−2 on negative scale of noise. In a power cycle, all types of wave form one positive power cycle and one negative power cycle [15]. Positive scale of noise has 10 positive units and 1 negative unit, whereas negative scale of noise has 1 positive unit and 10 nega-

There are following elaborative points on choosing an *onci* as 1/11th unit of

1 2 *Bel I I* log (6)

1 2 *oB I I* 11 log (7)

= <sup>1</sup>

where logarithmic unit ratio for noise of elasticity is *Bel*. The oncibel (oB) is more convenient for sound power systems. The mathematical expression by the

multiplication factor in specific gravity has to be evaluated.

following equality gives an oncibel (oB), which is 1/11th unit of a *Bel*:

*DOI: http://dx.doi.org/10.5772/intechopen.93296*

more convenient for fluid power systems.

obtained by superimposition principle.

which is 1/11th unit of a *Sip*:

mathematically expressed as:

intensity I2.

**Noise of therm:** for a pack of heat energy wave, the multiplication of total power storage and the velocity of light gives heat power intensity I. The pack of solar energy wave and heat energy wave (for same intensity I), have same energy areas, therefore their units of noise are same as *Sol*.

**Noise of photons:** for a pack of light energy beam, the multiplication of total power storage and the velocity of light gives light power intensity I. The pack of solar energy wave and light energy beam (for same intensity I), have same energy areas, therefore their units of noise are same as *Sol*.

**Noise of electrons:** for a pack of electricity wave, the multiplication of total electrical storage and the velocity of light gives electrical power intensity I. The pack of solar energy wave and electricity wave (for same intensity I), have same energy areas, therefore their units of noise are same as *Sol*.

**Noise of scattering:** for a pack of fluid energy wave, the multiplication of total power storage and the velocity of fluid gives fluid power intensity I. On taking logarithm of two intensities of fluid power, I1 and I2, provides intensity difference. It is mathematically expressed as:

*Noise Transmission Losses in Integrated Acoustic and Thermo-Fluid Insulation Panels DOI: http://dx.doi.org/10.5772/intechopen.93296*

$$\text{Sip} = \log\left(I\_{\text{\tiny\text{\tiny\text{\tiny}}}}\right) \left(I\_{\text{\tiny\text{\tiny}}}\right)^{\text{-}1} \tag{4}$$

where logarithmic unit ratio for noise of scattering is *Sip*. The oncisip (oS) is more convenient for fluid power systems.

The mathematical expression by the following equality gives an oncisip (oS), which is 1/11th unit of a *Sip*:

$$
\rho \mathbf{S} = \pm \mathbf{n} \mathbf{1} \mathbf{n} \log \left( I\_{\mathbf{n}} \right) \left( I\_{\mathbf{n}} \right)^{\mathbf{n}} \tag{5}
$$

For energy area determination for a fluid wave, the water with a specific gravity of 1.0 is the standard fluid considered with power of ±1 Wm−2 for a reference intensity I2.

**Noise of scattering and lightning:** for a pack of fire wave, the intensity, I, of fire flash with power of light, is the multiplication of total power storage and the velocity of light. Whereas for a pack of fire wave, the intensity, I, of fire flash with power of fluid, is the multiplication of total power storage capacity and velocity of fluid.


**Noise of elasticity:** for a pack of sound energy wave, the product of total power storage and the velocity of sound gives sound power intensity I. On taking logarithm of two intensities of sound power, I1 and I2, provides intensity difference. It is mathematically expressed as:

( )( ) − = <sup>1</sup> 1 2 *Bel I I* log (6)

where logarithmic unit ratio for noise of elasticity is *Bel*. The oncibel (oB) is more convenient for sound power systems. The mathematical expression by the following equality gives an oncibel (oB), which is 1/11th unit of a *Bel*:

$$
\rho B = \pm \mathbf{n} \mathbf{n} \log \left( I\_{\mathbf{n}} \right) \left( I\_{\mathbf{n}} \right)^{-4} \tag{7}
$$

There are following elaborative points on choosing an *onci* as 1/11th unit of noise [37]:

Reference value used for I2 is −1 W m−2 on positive scale of noise and 1 W m−2 on negative scale of noise. In a power cycle, all types of wave form one positive power cycle and one negative power cycle [15]. Positive scale of noise has 10 positive units and 1 negative unit, whereas negative scale of noise has 1 positive unit and 10 negative units:

*Noise and Environment*

**3.1 Noise characterization**

ematically expressed as:

fields is modeled. Noise characterization equations are devised, which calculate noise fields due to ventilation, heat transport and sound transmission of integrated

In writing nodal equations in matrix form, sign notation is adopted for automatic formulation of conductance matrix (U-matrix) with unknown temperatures and heat source elements. The sum of all incoming heat source elements and U-matrix conductances multiplied with temperature difference with respect to the unknown temperatures at other nodes are equal to zero. The energy balance is writ-

> ∑ ∑ ( ×∆ + = ) N N m,n m,n m,n

where Um,n is the conductance at node (m,n), ∆Tm,n is the difference between unknown temperature at the node (m,n) and unknown temperature at surrounding

A unified theory for stresses and oscillations is proposed by Dehra [12]. The following standard measurement equations are derived and adopted from the

**Noise of sol:** for a pack of solar energy wave, the multiplication of solar power storage and the velocity of light gives solar power intensity I. On taking logarithm of two intensities of solar power, I1 and I2, provides intensity difference. It is math-

> ( )( ) −

> > ( )( ) −

= <sup>1</sup>

where logarithmic unit ratio for noise of sol is expressed as *Sol*. The oncisol (oS) is more convenient for solar power systems. The mathematical expression by the

= ± <sup>1</sup>

**Noise of therm:** for a pack of heat energy wave, the multiplication of total power storage and the velocity of light gives heat power intensity I. The pack of solar energy wave and heat energy wave (for same intensity I), have same energy

**Noise of photons:** for a pack of light energy beam, the multiplication of total power storage and the velocity of light gives light power intensity I. The pack of solar energy wave and light energy beam (for same intensity I), have same energy

**Noise of electrons:** for a pack of electricity wave, the multiplication of total electrical storage and the velocity of light gives electrical power intensity I. The pack of solar energy wave and electricity wave (for same intensity I), have same energy

**Noise of scattering:** for a pack of fluid energy wave, the multiplication of total power storage and the velocity of fluid gives fluid power intensity I. On taking logarithm of two intensities of fluid power, I1 and I2, provides intensity difference. It

U T Q0 (1)

1 2 *Sol I I* log (2)

1 2 *oS I I* 11 log (3)

n=1 n=1

heat exchange node. Qm,n is heat source term at the node (m,n).

standard definitions for sources of noise interference [1–60].

following equality gives an oncisol (oS), which is 1/11th unit of a *Sol*:

areas, therefore their units of noise are same as *Sol*.

areas, therefore their units of noise are same as *Sol*.

areas, therefore their units of noise are same as *Sol*.

is mathematically expressed as:

building insulation through a double wall structure.

ten in equation form for any general node (m,n):

**112**


Reference value of I2 is −1 W m−2 with I1 on positive scale of noise, should be taken with negative noise measurement expression (see Eqs. 3, 5 and 7), therefore it gives positive values of noise;

Reference value of I2 is 1 W m−2 with I1 on negative scale of noise, should be taken with positive noise measurement expression (see Eqs. 3, 5 and 7), therefore it gives negative values of noise.

The choosing of *onci* in noise units is done so as to have separate market product and system of noise scales and their units distinguished from prevailing *decibel* units (which have its limitations) in the International System of Units. More discussions on energy conversion, noise characterization theory and choice of noise scales and its units are presented in many papers by the author [1–60].
