**4. Performance of solar heating system on the liquid**

In the section herein the specifications of the solar heating system, shown in **Figure 1** will have been analyzed applying F-diagram method, solar energy monthly fraction (monthly solar energy contribution), thermal load and annual solar energy contribution. Correlation X, Y and f in the equation form equals to [1].

$$f = 1029Y - 0.065X - 0.245Y^2 + 0.0018X^2 + 0.0215Y^3 \tag{11}$$

where 0 < *Y* < 3 и 0 < *X* < 18.

At dimensions of accumulators, commonly used in the solar water supply systems, the difference Δ*U* is small comparing to Q, *Q <sup>h</sup>:ws* and *E* and can be adopted as

where f is the fraction of the monthly thermal load, provided at the solar energy

Straightforwardly, Eq. (2) cannot be used for computing f, as the value Q is the function of the falling radiation, environmental temperature and thermal loads. However, consideration of the parameters, the Q is dependent on, allows supposing, that the replacement rate of it can be empirically linked with two dimensionless

<sup>¼</sup> *<sup>Q</sup> Q <sup>h</sup>:ws*

> Δ*t Q <sup>h</sup>:ws*

*,* (4)

(2)

(3)

*<sup>f</sup>* <sup>¼</sup> *<sup>Q</sup> <sup>h</sup>:ws* � *<sup>E</sup> Q <sup>h</sup>:ws*

*X* ¼ *FkKk*ð Þ *Ta* � *Tb*

*<sup>Y</sup>* <sup>¼</sup> *Fkη*0*Eknd Q <sup>h</sup>:ws*

where *Ta* is basic temperature, accepted as equal to 100°С, *Tb* is the average monthly temperature of outside air, °С, Δ*t* is the time change, and *Ek* is the average monthly daily incoming of the total solar radiation falling onto the flat collector's

F-diagram method is based on correlation of many simulations in terms of easily

corresponding ranges of the system's practical constructions parameters. Resulting correlations give to f the fraction of monthly heating load (in the case herein—the premises heating and hot water), provided with the solar energy, as the function of two dimensionless parameters. One of them is linked with the ratio of collector losses to the thermal loads (X), another—the ratio of the absorbed solar radiation to the thermal loads Y. Proceeding from the systems simulation, where was used the F-diagram, it has become possible to develop the correlation between dimensionless variables and f–monthly load fraction, transmitted by the solar energy. Dimension-

<sup>X</sup> <sup>¼</sup> *Collector energy loss during a month*

<sup>Y</sup> <sup>¼</sup> *Absorber solar radiation*

Parameters X and Y can be recorded as in Eqs. (3) and (4), respectively.

*UL*ð*Tref* � *Ta*ÞΔ*τ*

*R*ð Þ *τα HN*

To simplify the computations the dimensionless parameters values X and Y in Eqs. (3) and (4) are usually placed as in the equations [1], respectively. The reason for the arrangement thereof consists in the fact that coefficients values (LR UF and

<sup>X</sup> <sup>¼</sup> *ACF<sup>=</sup>*

<sup>Y</sup> <sup>¼</sup> *ACF<sup>=</sup>*

*Total heating load during a month* (5)

*Total heating load during a month* (6)

*<sup>L</sup>* (7)

*<sup>L</sup>* (8)

computed dimensionless variables. Modeling conditions varied in the

equal to zero. Then Eq. (1) can be presented in the form of [1].

*Thermodynamics and Energy Engineering*

expense.

complexes [1].

inclined surface, J/(m2

**56**

\*day).

less parameters X and Y are defined as follows [1]:

Due to the equation nature (11) it should not be used beyond the ranges, shown with curves in **Figure 4**. In case a reference point is out of the range, the chart might be used for extrapolation with satisfactory results [1]. For simplicity, the common method "degree-day" is used for calculating the monthly average load for premises heating necessary for the system in the framework of the research herein. The method of premise heating extent assessment in degrees-days is based on the principle that the need in energy to heat the premises, first and foremost, depends on the temperatures difference: in the premise and outside. It is assumed that monthly load for heating the buildings, premises, in which the temperature is maintained at 24°С is proportional to degree-days amount in a month DD [1].

$$\mathbf{L}\_{\\$} = (\mathbf{U}\mathbf{A})\mathbf{h} \ast \mathbf{D}\mathbf{D} \tag{12}$$

where Ls is the load for premises heating, and (UA)h is the multiplication of losses by the building square. For the research the building with (UA)h 467 W/m2 °C has been taken from the building project. Days amount in degrees (DD) in one

**Figure 4.** *Average monthly daily solar radiation for Almaty city.*

day is the difference between 18.3°С and average daily atmospheric temperature (average of maximum and minimum atmospheric daily temperature). In case the average daily environmental temperature exceeds 18°С, the number of days in degrees is accepted being equal to zero [5]. For Almaty city the amount of days with a heating degree, monthly average daily solar radiation and environmental temperature are given in **Table 2**.

Another load, included into the research by F-diagram method is the load for water heating for household consumption (amount of energy, necessary for domestic water heating). It much depends on the building inhabitants life style. Average assumed water need and its consumption in Almaty constitutes 300 l per a person per day [1]. Monthly load for water heating, Lw.

$$\mathbf{L\_w = N \* N\_p \* V \* (T\_w - T\_m) \* \rho \* C\_p} \tag{13}$$

where N is the days number in a month; Np is the people number in the family; Tw is the minimal hot water permissible temperature: it is �60°C [1], V is the daily water consumption per a person in m<sup>3</sup> , Tm is the temperature of the main feed water (°C), *ρ* is the water density in kg/m<sup>3</sup> , and Cp is the water specific heat capacity (4190 J/kg\*°C). Monthly total load (L) represents the total load for the building heating (LS) and loads for household water heating (Lw), as in the work [1].

$$\mathbf{L} = \mathbf{L\_S} + \mathbf{L\_w} \tag{14}$$

of solar energy monthly contribution, divided by the annual load, as in the follow-

*F-diagram Research Method for Double Circuit Solar System with Thermosyphon Circulation*

<sup>P</sup>*fi* P *Li Li*

(15)

(16)

(17)

F ¼

*Xc <sup>X</sup>* <sup>¼</sup> *<sup>M</sup>*

*<sup>Y</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>39</sup> <sup>þ</sup> <sup>0</sup>*:*65*<sup>e</sup>*

*YC*

<sup>75</sup> � ��0*:*<sup>25</sup>

37*:*5 < М < 300*:*

<sup>0</sup>*:*5 < *<sup>ε</sup>LCmin* ð Þ *UA h* � �

In this section we discuss the demanded thermal load, fraction of the load, supplied by the solar energy system for various collector zones and parametric

**Figure 5** shows that the chart of monthly values from correction factor by means of F-diagram method shows that the heating extent, monthly average daily temperature and direct solar radiation lower dependent on the weather conditions. It is clearly seen from **Figure 6** that changed correction factor Yc/Y from environmental temperature has an exponential function, which according to a correction factor, increases the annual fraction of the load, provided by the solar energy. It can be seen from **Figure 7** that the monthly load fraction increases along with the increase of a collector square. It also shows that the monthly fraction is higher in

Capacity of the systems with other values can be assessed from F-chart, changing Y applying the correction factor of the loading heat exchanger Yc/Y, as denoted

> ð�0*:*<sup>139</sup> ð Þ *UA <sup>h</sup> εCmin*

Let us consider the solar system's heat supply computation method for the conditions, when the hot water supply load is prevailing or the only. Both the pipe water temperature *Т*х.в, and minimal permissible hot water temperature *Т*г. influence at the system's characteristics. As the average working temperature in the system, and consequently, the heat losses from the collector depend on *Т*х.в and *Т*г.в, it is worth to suppose that expression of *X complex*, characterizing the heat loss from the collector, might be updated in the way, to account the impact of *Т*х. and *Т*г.в. If to multiply monthly X values by correction factor, defined by the expression given below, then the F-method of solar heating and hot water supply liquid systems computation can be used for defining the monthly F-values, achieved in the solar hot water supply systems. Correction factor for the hot water supply

ing equation:

*DOI: http://dx.doi.org/10.5772/intechopen.88045*

systems [1].

at

at

researches.

**59**

in Eq. (17) or in **Figure 4** [1].

**5. Result and discussion**

Monthly total load fraction, incoming from the solar heating system and water heating, shown in **Figure 1**, is given as a function of dimensionless parameters X and Y, defined in Eqs. (1) and (2) and in **Figure 3**. In order to define f, the heating load share, provided by the solar energy within a month, values X and Y are computed for collector and thermal load (**Table 3**). F-value is defined at X and Y junction point in **Figure 3**. It is done for every month of the year. Contribution of solar energy for a month is multiplication by total heating load L for a current month. Share of annual thermal load, provided by solar energy, represents the sum


#### **Table 3.**

*Heating degree and monthly average daily temperature and global radiation in Almaty city.*

*F-diagram Research Method for Double Circuit Solar System with Thermosyphon Circulation DOI: http://dx.doi.org/10.5772/intechopen.88045*

of solar energy monthly contribution, divided by the annual load, as in the following equation:

$$\mathbf{F} = \frac{\sum f\_i L\_i}{\sum L\_i} \tag{15}$$

Let us consider the solar system's heat supply computation method for the conditions, when the hot water supply load is prevailing or the only. Both the pipe water temperature *Т*х.в, and minimal permissible hot water temperature *Т*г. influence at the system's characteristics. As the average working temperature in the system, and consequently, the heat losses from the collector depend on *Т*х.в and *Т*г.в, it is worth to suppose that expression of *X complex*, characterizing the heat loss from the collector, might be updated in the way, to account the impact of *Т*х. and *Т*г.в. If to multiply monthly X values by correction factor, defined by the expression given below, then the F-method of solar heating and hot water supply liquid systems computation can be used for defining the monthly F-values, achieved in the solar hot water supply systems. Correction factor for the hot water supply systems [1].

$$\frac{X\_c}{X} = \left(\frac{\mathcal{M}}{75}\right)^{-0.25} \tag{16}$$

at

day is the difference between 18.3°С and average daily atmospheric temperature (average of maximum and minimum atmospheric daily temperature). In case the average daily environmental temperature exceeds 18°С, the number of days in degrees is accepted being equal to zero [5]. For Almaty city the amount of days with a heating degree, monthly average daily solar radiation and environmental temper-

Another load, included into the research by F-diagram method is the load for

where N is the days number in a month; Np is the people number in the family; Tw is the minimal hot water permissible temperature: it is �60°C [1], V is the daily

capacity (4190 J/kg\*°C). Monthly total load (L) represents the total load for the building heating (LS) and loads for household water heating (Lw), as in the

Monthly total load fraction, incoming from the solar heating system and water heating, shown in **Figure 1**, is given as a function of dimensionless parameters X and Y, defined in Eqs. (1) and (2) and in **Figure 3**. In order to define f, the heating load share, provided by the solar energy within a month, values X and Y are computed for collector and thermal load (**Table 3**). F-value is defined at X and Y junction point in **Figure 3**. It is done for every month of the year. Contribution of solar energy for a month is multiplication by total heating load L for a current month. Share of annual thermal load, provided by solar energy, represents the sum

**Month** *Ta* **(°C)** *H* **(MJ/m<sup>2</sup>**

January �17 �16.0 February �20 �18.63 March 7 6.2 April 12 10.5 May 18 18.4 June 25 19.0 July 30 20.0 August 28 19.12 September 22 17.00 October 15 13.0 November 7 6.2 December �10 �9.2

*Heating degree and monthly average daily temperature and global radiation in Almaty city.*

Lw ¼ N ∗ Np ∗ V ∗ ð Þ Tw � Tm ∗ *ρ* ∗*C*<sup>p</sup> (13)

, Tm is the temperature of the main feed

L ¼ LS þ Lw (14)

**\*day)**

, and Cp is the water specific heat

water heating for household consumption (amount of energy, necessary for domestic water heating). It much depends on the building inhabitants life style. Average assumed water need and its consumption in Almaty constitutes 300 l per a

person per day [1]. Monthly load for water heating, Lw.

ature are given in **Table 2**.

*Thermodynamics and Energy Engineering*

water consumption per a person in m<sup>3</sup>

work [1].

**Table 3.**

**58**

water (°C), *ρ* is the water density in kg/m<sup>3</sup>

$$37.5 < \text{M} < 300.$$

Capacity of the systems with other values can be assessed from F-chart, changing Y applying the correction factor of the loading heat exchanger Yc/Y, as denoted in Eq. (17) or in **Figure 4** [1].

$$\frac{Y\_C}{Y} = \mathbf{0.39} + \mathbf{0.65}e^{(-0.139)} \frac{(UA)\_h}{\varepsilon \mathbf{C}\_{min}} \tag{17}$$

at

$$0.5 < \left(\frac{\varepsilon LC\_{min}}{(UA)h}\right)$$
