Mathematical justification of thermosyphon effect main parameters for solar heating system

Figures & data

Figure 1. Principal schema of a double-circuit solar plant with thermosyphon circulation

Figure 2. Flat solar collector

(a) Principal schema of a flat solar collector. (b) Cross section of a flat solar collector.

Table 1. Technical specifications of flat-plate solar collector

Parameters	Value
Absorbing plate material	copper
Absorber plate dimensions	2 m × 1 m
Plate thickness	0.4 mm
Glazing material	Hardened glass
Glazing dimensions	2 m × 1 m
Glazing thickness	4 mm
Insulation	Foam plex (foam polyurethane)
Collector’s tilt angle	45°
Absorber’s thermal conductivity	401 W/(m K)
Insulation thermal conductivity	0.04 W/(m K)
Transmittance-absorption factor	0.855
Sun apparent temperature	4350 K
Atmospheric temperature	303 K
Radiation intensity	1000 W/m^2

Table 2. Values of coefficients ${\mathit{\alpha }}_1\dots {\mathit{\alpha }}_9$ for a flat solar collector

	Values of coefficients
	${\alpha }_1$	${\alpha }_2$	${\alpha }_3$	${\alpha }_4$	${\alpha }_5$	${\alpha }_6$	${\alpha }_7$	${\alpha }_8$	${\alpha }_9$
Flat collector	598.0	−75.0	−2.0	−1298.0	445.5	19.9	1875.0	−1067.0	23.0

Table 3. Values of coefficients ${\mathit{\beta }}_1\dots {\mathit{\beta }}_9$ for a flat solar collector

	Values of coefficients
	${\beta }_1$	${\beta }_2$	${\beta }_3$	${\beta }_4$	${\beta }_5$	${\beta }_6$	${\beta }_7$	${\beta }_8$	${\beta }_9$
Flat collector	1.1045	−0.256	0.099	−1.9	3.4	−0.878	3.345	−5.09	1.335

Table 4. Value of coefficients $\mathit{a}$ and $\mathit{b}$

	Values of coefficients
	$\mathrm{a}$	$\mathrm{b}$
Flat collector	226	0.65

Table 5. Value of coefficients $\mathit{a}$ and $\mathit{b}$

$H$ value, $kWh/m^2$	$\mathrm{\Delta }q$value, %
	$f=0.3$	$f=0.4$	$f=0.5$	$f=0.6$
Less than 1500	+15.7	+8.87	0	−9.87
More than 1500	+9	+7	0	−5.67

Figure 3. Pressure drop in flat solar collector element’s linear part

Figure 4. Total amount of the flat solar collector’s copper spiral elements

Figure 5. Distance between flat-plate solar collector copper spiral elements

Figure 6. Length of the arc of flat solar collector copper spiral non-linear part element

Figure 7. Length of the arc of flat solar collector copper spiral linear part element

Figure 8. Amount of heat q_к(J), entering a tank accumulator from the collector