In this lecture the student is introduced to the essential concepts in the transfer of radiative heat energy and light energy in the building context.
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Extract from text book:
"Energy Simulation in Building Design"
J A Clarke, 1985
With the liberal use of lightweight building materials and, in many 'passive' solar applications, large glazing areas, excessive solar gain can be an important design consideration even in countries with modest solar incidence. It is therefore necessary to have reliable and accurate means of predicting this gain, especially under elevated solar conditions. Section 5.3 covers solar prediction methodologies.
Since the solar energy absorbed by one of a group of buildings is often greatly influence by the extent to which that particular building is shaded by other members of the group and by self-associated facade obstructions, a prerequisite of solar modelling is the ability to predict shading and insolation patches as a function of solar position and obstruction geometry. Indeed it is often an early design stage strategy to alter design parameters such as orientation, shape or obstruction geometry in an attempt to so modify the shading/insolation patterns, at some critical time, that environmental performance is improved without recourse to plant intervention.
Essential information for energy modelling purposes include a time-series knowledge of the magnitude and position of:
These data are summarised in figure 5.3: the former data are required in the prediction of external opaque surface solar absorption/reflection and transparent surface absorption/transmission/reflection; and the latter data are required to track the window transmitted shortwave energy to its firstly incident internal surface (section 5.3 discusses the treatment of the then reflected portion).
Figure 5.3 Shading / insolation data required at each time_row. (a) External opaque and transparent surface shading . (b) Internal opaque and transparent surface insolation.
In essence there are two extant methods for the computation of insolation information on the basis of geometrical and solar position information:
The former method involves the 'clipping' of surface polygons - one against the other - until only those polygon portions remain that will be viewed from some chosen viewpoint (taken as the sun for insolation prediction). The technique is rigorous and can be designed to produce, in addition to insolation data, a polygon set which represents an entire scene. Indeed techniques are now available which can apply colour and texture to these viewed polygons as a function of ambient or artificial lightings conditions. The computer models that result [Stearn 1983] allow the generation of realistic and extremely accurate [Purdie 1983] images of future reality at an early design stage. Sutherland et al [1974] have produced characterisations of several hidden surface algorithms and so detailed descriptions are omitted here.
The point projection technique is used to quantify the insolation patch and has less potential for visualisation. Given some collection of target and obstruction objects, each defined relative to some site cartesian coordinate system, then the procedure is to relocate the X-Z plane of the coordinate system in the plane of each face (in turn) of the target body. Each obstruction object can now be projected, parallel to the sun's rays, onto the face and the projected image expressed relative to the local face coordinate system. A simple grid can then be superimposed on each opaque and transparent surface allowing grid point containment testing against each individual shadow polygon. Prediction accuracy is controlled simply by adjusting the number of elemental subdivisions of the homogeneous face in question.
A detailed discussion regarding insolation transformation equations is found in section 5.2.1. These transformation equations can now be utilised as the basis of an algorithm to determine external and internal surface (opaque and transparent) insolation as a function of building geometry, obstructions geometry and solar position.
For external surfaces, one possible algorithm involves the following computational procedure. Each face of the target building is processed in turn and the surrounding obstructions, including other obstructing parts of the target building, projected onto the plane of each face. For any solar position and target face this is achieved by:
in equations (5.7, sec. 5.2.1)
The point to emerge (xTR, yTR,zTR)
can then be re-expressed as angles 
as shown in figure 5.7.
For internal surfaces, insolation patch position and magnitude can be assessed by applying a grid to each window so that each grid point can be projected onto internal surfaces (by equation 5.8, sec. 5.2.1) to establish, again by point containment tests, the grid point/receiving surface pairings.
It is usual to express the position of the sun in terms of its altitude and azimuth angles which in turn depend on site latitude, solar declination and local solar time. Figure 5.9 illustrates these angles which are discussed in detail and established as mathematical expressions in a number of texts [for example: IHVE 1973, ASHRAE 1981, Duffie et al 1980]. For this reason only cursary treatment is given here.
The total radiation incident on an exposed opaque or transparent surface of arbitrary inclination beta and with azimuth alpha has three potential components: direct beam, ground reflected and sky diffuse (it is usual to disregard reflections from surrounding buildings).
The direct component is relatively straightforward to assess since it involves only angular operations on the known horizontal direct intensity. To determine the ground reflected component it is normal practice to treat the ground as a diffuse reflector and so the combined horizontal direct and diffuse radiation is treated isotropically and reflected onto the inclined surface as a function of some representative view factor.
Estimation of the sky diffuse component is more problematic since the known horizontal diffuse intensity exhibits a mix of true diffuse behaviour (caused by general atmospheric scatter) and directional qualities; the mix varying between totally overcast conditions (fully isotropic sky) and completely clear skies (fully anisotropic sky). One possibility is to assume isotropic sky conditions at all times and so simplify computation since diffuse radiation is then independent of direction. It has been estimated that such an assumption leads to an underestimation of inclined surface intensities [Ma et al 1983]. An alternative approach is to formulate an anisotropic model which accounts for the enhancement of diffuse radiation in the vicinity of the sun and at the horizon.
Direct Beam Component
This is given by:
where,
= direct intensity on
inclined surface (W/m2).
= direct intensity on
the horizontal (W/m2).
Ground Reflected Component
For an unobstructed vertical surface,
the view factor between the surface and the ground and between the
surface and the sky is in each case 0.5 and so the radiation intensity at the surface
due to isotropic ground reflection of the combined direct and diffuse radiation impinging
on the horizontal is given by:
where,
= ground reflected totalradiation incident on surface of inclination (W/m2).
= horizontal diffuse
radiation (W/m2).
= ground reflectivity
(albedo).
For a surface of non-vertical inclination a simple view factor modification is introduced so that:
where,
= ground reflected totalradiation incident on surface of inclination (W/m2).
Sky Diffuse Component
Two approaches are prominent in the treatment of anisotropic sky conditions.
In the first [Temps et al 1977, Klucher 1979] the sky diffuse component on an inclined surface is determined by an expression which increases the intensity of the diffuse flux due to circumsolar activity and horizon brightening:
where,
= sky diffuse radiation incident on the surface of 
inclination (W/m2).
= total radiation on
horizontal, 
(W/m2).
Thus, when the sky is completely overcast, 
, the expression reduces to the isotropic sky case.
In the second approach [Hay 1979] the known horizontal diffuse radiation is assumed to be composed of a uniform background diffuse component and a circumsolar component, with a weighting applied according to the degree of sky isotropy. The sky diffuse component is given by:
where,
= extraterrestrial
radiation incident on the horizontal (W/m2).
Again, as overcast sky conditions are approached so 
and the isotropic expression is obtained.
The foregoing equations allow the computation of direct and diffuse shortwave radiation impinging on exposed external surfaces. These flux quantities, when modified by representative surface absorptivities, are the shortwave nodal heat generation terms, qs1, of the simulation equations derived in chapter 3.
The formulations of sec. 5.3.2 will permit calculation of the direct and diffuse intensities impinging on external building surfaces. For opaque surfaces, intensity modification by surface absorptivity and shading factors will give the shortwave heat injection to be applied to surface nodes via the excitation matrix (C) of chapters 3 and 4. For a transparent system, the formulations of sec. 5.3.3 allow the assessment of internal element absorption for application, via the heat generation terms of equation (3.5), to intra-element nodes. The eventual heat exchange between surface nodes and the surrounding air (by convection) and other surfaces (by longwave radiation exchange) will then follow from the matrix equation solutions of chapter 4.
The formulations of sec. 5.3.3 also allow the assessment of overall system properties such as transmissivity, absorptivity and reflectivity. This section addresses the use of these properties, in conjunction with the shading and insolation time-series information discussed in sec. 5.2, to estimate the apportioning of shortwave energy between internal surfaces.
For a window system, the transmitted portion of the direct beam can be evaluated from:
Eq. 5.16 where,
= transmitted direct
beam flux (W)
= overall transmissivityfor the given incidence angle
= window shading factor
(proportion. of 1)
= apparent window
area (m )
The 
values can be
determined by the techniques of sec. 5.3.3 or, alternatively, by reference to published
data for different window arrangements and glass types [Pilkingtons 1973].
If, as is often the case, more than one internal surface will share this transmitted radiation then the flux defined by equation 5.16 can be applied to those internal surfaces defined by the insolation data determined by the technique of sec. 5.2. Any internal node will then receive a heat injection given by:
where,
= surface absorptivity
= surface area (m)
= proportion of window
direct beam transmission which strikes surface in question (proportion of 1)
And the first reflected flux is given by:
The accumulated flux reflections from each surface can now be further processed to give the final apportioning between all internal surfaces. If the usual assumption of diffuse reflections is made then apportionment can be decided on the basis of enclosure view factor information as described in the following section. For the case of specular reflections a recursive ray tracing technique will be required.
It is important to remember that an internal surface may be composed of opaque and transparent portions, with the latter allowing the onward transmission of incident shortwave flux to a connected zone or back to outside. The conservation of the integrity of multi zone systems will be important in building systems incorporating passive solar features. Application of equation 5.16 with the
term set to the incident flux value will then
give the re-transmitted flux.
The diffuse beam transmission can be determined from:
= overall
transmissivity corresponding to 51degrees incidence angle, representing the average approachangle for anisotropic sky conditions.
This flux quantity can now be processed by the technique described for the direct beam: internal surface smearing on the basis of specular or diffuse reflections as described in the following section concerned with the evaluation of longwave radiation exchanges.
