Solar radiation (opaque surface)#

The Solar radiation (opaque surface) block describes the heat exchangeby radiation as it falls on an opaque surface. The calculation takes into account the angles of surface inclination and radiation.

Flux density of solar radiation falling to the surface taking intoaccount angles of inclination (1):

(1)#\[ q_{\mathrm{с}\mathrm{о}\mathrm{л}\mathrm{н}}^{\mathrm{'}}=q_{\mathrm{с}\mathrm{о}\mathrm{л}\mathrm{н}}\cdot \cos\theta \]

where:

\(q_{sun}\) - solar radiation flux density [W/m\(^2\)];

\(\cos\theta\) - cosine of the angle between solar radiation and the normal to the surface.

The heat flux of solar radiation is calculated using the following formula: (2):

(2)#\[ Q_{\mathrm{с}\mathrm{о}\mathrm{л}\mathrm{н}}=q_{\mathrm{с}\mathrm{о}\mathrm{л}\mathrm{н}}^{\mathrm{'}}\cdot F \]

where \(F\) - surface area, [m\(^2\)].

Heat flux according to the Stefan-Boltzmann law (3) :

(3)#\[ Q_{\mathrm{и}\mathrm{з}\mathrm{л}}=\sigma \cdot \epsilon \cdot F \cdot \left(T_{1}^{4}-T_{2}^{4}\right) \]

\(\sigma\) – Stefan-Boltzmann constant, [W/(m\(^2\cdot K^4\))];

\(\epsilon\) - degree of surface emissivity;

\(F\) - surface area, [m\(^2\)];

T\(_1\) - ambient temperature, [℃];

T\(_2\) - surface temperature, [℃].

Heat flux transferred to the surface (4) :

(4)#\[Q_{пов}=A \cdot Q_{солн}+ Q_{изл}\]

where \(A\) - absorption factor.

Reflected heat flux (5) :

(5)#\[ Q_{\mathrm{о}\mathrm{т}\mathrm{р}}=\left(1-A\right)\cdot Q_{\mathrm{с}\mathrm{о}\mathrm{л}\mathrm{н}}- Q_{\mathrm{и}\mathrm{з}\mathrm{л}} \]

Surface geometry

Geometry of the surface arrangementAll angles required for the calculation are shown below Fig. 1 :

\(\theta_z\) - angle of inclination between the radiation direction and the vertical, °;

\(\gamma_s\) - angle between the projection of the radiation direction on the horizontal plane and the meridian of the point, °;

\(\gamma\) - angle between the projection of the normal to the surface on the horizontal plane and the meridian of the point, °;

\(\beta\) - angle of inclination of the surface relative to the horizontal plane, °.

\(*\) - Displacements east of south are negative, west of south are positive.

\[ \mathrm{c}\mathrm{o}\mathrm{s}\theta =\mathrm{c}\mathrm{o}\mathrm{s}\theta _{z}\cdot \mathrm{c}\mathrm{o}\mathrm{s}\beta +\mathrm{s}\mathrm{i}\mathrm{n}\theta _{z}\cdot \mathrm{s}\mathrm{i}\mathrm{n}\beta \cdot \mathrm{c}\mathrm{o}\mathrm{s}\left(\gamma _{s}-\gamma \right) \]

[1]

1. Properties#

Property	Default value	Description	Units of measurement
Surface area	10	–	m\(^2\)
Absorption factor	0.5	–	–
Emissivity factor	0.5	–	–
Solar radiation flux density	800	–	\(\frac{W}{m^2}\)
Slope, β	60	see Fig. 1	°
Angle between the projection of the normal to the surface on the horizontal plane and the meridian of the point, \(\gamma\)	0	see Fig. 1	°
Angle of inclination between the radiation direction and the vertical, \(\theta_z\)	20	see Fig. 1	°
Angle between the projection of the radiation direction on the horizontal plane and the meridian of the point, \(\gamma_s\)	0	see Fig. 1	°

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Input	Input	Preceding block temperature	-	Heat exchange
Reflected heat flow	Output	–	W	Heat exchange
Output	Output	–	–	Heat exchange

In order to see the connection capabilities of the block, you need to go to page Description of block ports

Solar radiation (opaque surface)#

1. Properties#

2. Inputs and outputs#

3. Sources#