**3. F-chart method**

Solar heat supply system's energy balance for the month period can be presented as [1]:

$$Q = Q\_{h.ws} + E = \Delta U \tag{1}$$

where *Q* is the solar installation monthly heat production, *Q <sup>h</sup>:ws* is the hot water supply monthly load, Е is the energy total amount, obtained within a month, and ΔU is the energy amount change in the accumulating unit.

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

$$f = \frac{Q\_{h.ws} - E}{Q\_{h.ws}} = \frac{Q}{Q\_{h.ws}}\tag{2}$$

n RF) are obtained from the results of the standard collector testing. The ratios F'R/ FR correct various temperature gradients between collector and storage tank and they are computed with the techniques, generalized in [1]. The ratio (τα)/(τα) n is

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

*Tref* � *Ta* Δ*τ*

<sup>∗</sup> ð Þ *τα* ð Þ *τα <sup>n</sup>* *AC*

<sup>∗</sup> *Ht* <sup>∗</sup> *<sup>N</sup>* <sup>∗</sup> *AC*

LS ¼ ð Þ UA h ∗ DD (12)

*<sup>L</sup>* (9)

*<sup>L</sup>* (10)

*F= R FR*

> *R FR*

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

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].

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

*<sup>f</sup>* <sup>¼</sup> <sup>1029</sup>*Y*–0*:*065*X*–0*:*245*Y*<sup>2</sup> <sup>þ</sup> <sup>0</sup>*:*0018*X*<sup>2</sup> <sup>þ</sup> <sup>0</sup>*:*0215*Y*<sup>3</sup> (11)

contribution. Correlation X, Y and f in the equation form equals to [1].

as well assessed with the techniques, given in [1].

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

where 0 < *Y* < 3 и 0 < *X* < 18.

**Figure 4.**

**57**

*Average monthly daily solar radiation for Almaty city.*

X ¼ FRUL

<sup>Y</sup> <sup>¼</sup> FRð Þ *τα <sup>n</sup>* <sup>∗</sup> *<sup>F</sup><sup>=</sup>*

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

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

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 complexes [1].

$$X = F\_k K\_k (T\_a - T\_b) \frac{\Delta t}{Q\_{h.ws}} \tag{3}$$

$$Y = \frac{F\_k \eta\_0 E\_k n\_d}{Q\_{h.ws}},\tag{4}$$

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 inclined surface, J/(m2 \*day).

F-diagram method is based on correlation of many simulations in terms of easily computed dimensionless variables. Modeling conditions varied in the 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. Dimensionless parameters X and Y are defined as follows [1]:

$$\mathbf{X} = \frac{\text{Collection energy loss during a month}}{\text{Total heating load during a month}} \tag{5}$$

$$\text{Y} = \frac{\text{Absorbance} \cdot \text{solar radiation}}{\text{Total heating load during a month}} \tag{6}$$

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

$$\mathbf{X} = \frac{\mathbf{A}\_C \mathbf{F}^\dagger \mathbf{U}\_{L(T\_{\rm ref}} - T\_a)\Delta \mathbf{r}}{L} \tag{7}$$

$$\mathbf{Y} = \frac{A\_C F^/R(\ddagger a)\overline{H}\mathcal{N}}{L} \tag{8}$$

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

n RF) are obtained from the results of the standard collector testing. The ratios F'R/ FR correct various temperature gradients between collector and storage tank and they are computed with the techniques, generalized in [1]. The ratio (τα)/(τα) n is as well assessed with the techniques, given in [1].

$$\mathbf{X} = \mathbf{F}\_{\mathbb{R}} \mathbf{U}\_{\mathrm{L}} \frac{F^{\prime}\_{\cdot R}}{F\_{\mathbb{R}}} \left( T\_{\mathrm{ref}} - T\_a \right) \Delta \mathbf{z} \frac{A\_C}{L} \tag{9}$$

$$\mathbf{Y} = \mathbf{F}\_{\mathrm{R}}(\tau a) \boldsymbol{n} \* \frac{\boldsymbol{F}^{\prime}\_{\mathrm{R}}}{\boldsymbol{F}\_{\mathrm{R}}} \* \frac{\overline{(\tau a)}}{(\tau a)\_{n}} \* \overline{\overline{H}} \boldsymbol{t} \* \boldsymbol{N} \* \frac{A\_{\mathrm{C}}}{L} \tag{10}$$
