b. **Orientation of photovoltaic system**

Adjusting the system to an optimum angle of inclination, a significant increase of radiation can be achieved, which can be used, instead of positioning the panels on horizontal or at a random angle in general, to place latitude.

*Assessment of Solar Energy Potential Limits within Solids on Heating-Melting Interval DOI: http://dx.doi.org/10.5772/intechopen.104847*

**Figure 9.** *On–off adjustment of furnace temperature.*

If a tracking system is used, an increased quantity with approximately 40% will be achieved, as shown in **Figure 10**, where system losses are also considered.

The use of sensors for orientation can lead to delicate situations in case of sunclouds alternations, if the system is not properly calibrated and has high energy consumptions.

Taking into account of these considerations, the variant that uses a mathematical algorithm is chosen for solar panel positioning. The orientation makes after the two directions, namely E-V and S-N.


#### **Figure 10.**

*Comparison between a fixed system at an optimum angle of 37°and tracking system.*

#### **2.5 Characterization of metallic materials heating process within solar furnaces**

#### *2.5.1 Materials heating within a furnace*

Equation of energetic balance for the furnace can be written as:

$$dQ\_2 = dQ\_u + dQ\_a + dQ\_{pd} + dQ\_x \tag{4}$$

where:

dQ2 is the elementary heat quantity transmitted toward furnace interior by the heating element:

$$dQ\_2 = P\_2 \cdot dt = a \cdot A\_1 \cdot (\theta - \theta\_0) \cdot dt \tag{5}$$

dQu is the elementary heat quantity that leads to the heating of the useful material within the furnace (absorbed heat):

$$dQ\_u = c\_u \cdot m\_u \cdot d\theta \tag{6}$$

dQa is theheat quantity that leads to heating the attached pieces (stands, supports, etc):

$$dQ\_a = c\_a \cdot m\_a \cdot d\theta \tag{7}$$

dQpd is the elementary thermal losses through furnace walls, opening, leakiness, etc.;

dQz is the elementary heat quantity that gathers in furnaces walls:

$$dQ\_u = c\_x \cdot m\_x \cdot d\theta \tag{8}$$

where:

P2 – thermal energy (thermal flow) transmitted by photovoltaic systems;

α – heat exchange superficial coefficient;

Al – area of the total lateral surface of heating elements;

θ –the temperature of heating elements;

θ<sup>0</sup> � the temperature inside the furnace;

dt – interval of elementary time;

cu, ca, cz � mass heats (temperature-dependant) of the heated materials, attached elements, and crucible;

mu, ma, mz � pieces weight, attached elements, and crucible;

dθ � elementary interval of temperature.

## *2.5.2 The achievement for a design algorithm for a solar furnace used in metallic material heating*

Solar panel positioning by implementing the mathematical model needs the astronomic considerations.

In order to determine the real position of the sun on the sky, the following angles are important; θ<sup>z</sup> – Zenith angle and γ<sup>s</sup> Azimuth angle, as shown in **Figure 11**.

*Assessment of Solar Energy Potential Limits within Solids on Heating-Melting Interval DOI: http://dx.doi.org/10.5772/intechopen.104847*

#### **Figure 11.**

*Sun's trajectory on the sky – Important angles.*

The calculus of these angles is made with mathematical formulas. Calculus formula for Zenith angle can be calculated by the relation:

cos *θ<sup>z</sup>* ¼ sin *φ* � sin *δ* þ cos *φ* � cos *δ* � cos*ω*

where **ϕ** is the latitude and is constant for the place where the solar tracker is positioned, for example, for Brasov, it is 45°39<sup>0</sup> , and δ is a declination and ω is an hour angle.

#### *2.5.3 Virtual design of a heating solar furnace*

In order to determine the minimum dimensions of the solar panel, a concave mirror is used as shown in **Figure 12**. The calculi are made on shading intervals as well

**Figure 12.** *The minimum dimensions of the solar panel.*

**Figure 13.**

*The mirror position to create maximum thermal flow toward the furnace's crucible.*

as on illumination optimum of the mirror in order to create maximum thermal flow toward the furnace's crucible (**Figure 13**).

### **Determination of minimum dimensions of the solar panel.**

AC = Φ concave mirror. *C*^ = 90–21.34 = 68.26. AC = sin *<sup>B</sup>*^ <sup>∙</sup> BC ! BC <sup>¼</sup> AC sin *<sup>B</sup>*^ ! BC <sup>¼</sup> AC 0*:*363 AB <sup>¼</sup> sin*C*^ � BC ! AB <sup>¼</sup> <sup>0</sup>*:*<sup>928</sup> � AC <sup>0</sup>*:*<sup>363</sup> ! AB ¼ 2*:*558 � AC AB minim ð Þ BD = AC BD <sup>¼</sup> BE � sin *<sup>E</sup>*^ BE <sup>¼</sup> BD sin *<sup>E</sup>*^ <sup>¼</sup> AC <sup>0</sup>*:*<sup>98</sup> ¼ AC � 1*:*0183 BE max 45<sup>∘</sup> ð Þ <sup>¼</sup> AC � ffiffi 2 <sup>p</sup> � <sup>1</sup>*:*15; 1ð Þ *:*<sup>15</sup> <sup>¼</sup> const*:* BEmin ¼ AC � 1*:*0183
