LESSONS OF EASTER ISLAND
March 17th, 2016
To help visualize the results of this research, some formulas have been programmed by the authors in Matlab® computational language, which greatly enhances understanding of radiative exchange between emitting surfaces and receiving planes. 3D graphs have been produced for a generic semicircular emitter.
Figure 7 shows a generic semicircular emitter that gives energy to a perpendicular plane in its base. Thanks to this new configuration factor, several radiative properties for these shapes can be clarified. For instance, a semicircular emitter is not capable of transferring more than 50% of its energy to a perpendicular plane; this is particularly important in some engineering lighting applications, such as lighted vaults or tunnels.
Figure 7... 
Extending the previous deduction to a finite rectangle located at a certain distance to the sphere in a random position (figure 6), a new unknown factor has been deducted:
F = 1 A1A2 4p 
(56) 
7‘Jxf+yf+ 2 
■Jx 2 + yj2 + z 2 Zy]xl + y2 + z 2 
z x22 + y22 + z2 
Figure 6. Configuration factor between a sphere and a parallel plane 
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After analyzing the previous form factors for the circle, a new question can be deducted. A sphere can be considered, in terms of radiative transfer as a circle [7], as the viewed area of the said sphere from a distant point equals always a circle, because only half of the emitter is visible. Let us consider as emitting source a sphere of radius r, and a differential element, placed randomly in space at a distance (x, y,z), referenced to the three coordinate directions as shown in figure 5:


Being radiation a vector, the resolution for a third coordinate plane that obviously cuts the emitting circle in two halves is required; the outline of the integral in this case yields:
In this particular case, the limits of the integral cannot be extended to 2n, as the value would be nil. If (41) is integrated with respect to 0, in the numerator the derivatives of cos0, – sin0 could be found. Therefore by making this change:
t = cosQ dt = sin0d0 (42)
Integral (41) can therefore be expressed as:

Taking out all the constants, and integrating with respect to r, the primitive is just the quotient of the numerator:









3.1. Direct integration for a differential element to a circular disk on a plane parallel to that of the element
Let us consider the proposed figure. In order to determine the radiant interchange between an emitting circle, which lies in the plane ZX, and a point P situated in another parallel plane XY, the following coordinate system is proposed (Figure 2).
Terms depicted in figure 2 are:
d: vertical distance between the center of the emitting circle and the plane XY.
b: horizontal distance between differential element dAj and the plane ZX that contains the said circle.
r: Emitting surface radius.
S: Distance between differential elements (in the canonical equation (1) of the configuration factor, it is denoted as r, but in order to differentiate it from radius of the disk (emitting surfa...
Read MoreThe reciprocity principle enunciated by Lambert in his paramount book Photometria, written in Latin (Lambert, 1760), yields the following wellknown integral equation:
Relevant terms in equation (1) are depicted in figure 1.
From the times of Lambert to our days, researchers and scientists in the fields of Geometric Optics and Radiative Transfer have striven to provide solutions for the canonical equation 1. This is no minor feat, since the said equation will lead in most cases to a quadruple integration and to be sure the fourth degree primitive of even simple mathematical expressions implies lengthy calculations...
Read MoreJose M. CabezaLainez, Jesus A. Pulido Areas, Carlos Rubio Bellido, ManuelViggo Castilla and Luis GonzalezBoado
Additional information is available at the end of the chapter http://dx. doi. org/10.5772/60017
Many architectural examples rank among masterpieces for its beautiful and harmonious use of solar radiation. However, their creation had to rely solely on intuition because they possessed a curvilinear nature. As the necessary tools required for evaluating shapes derived from the sphere or the circle were not available, such forms could not be assessed.
Circular emitters represent an important issue not merely in architecture but in the field of configuration factors calculation...
Read MoreImproving the solar panel energy efficiency by cleaning the solar panel was undertaken to study the energy output efficiency for the noncrystalline, monocrystalline, and polycrystalline solar panel with and without the emulated rainfall. The weather in Taiwan is rather humid; the dust in the air is thus easily moistened, adhered to and accumulated on the solar panel, s surface to interfere with the solar panel’s energy efficiency. Onsite observations reveals that raindrops were somewhat effective in cleaning the solar panel surface. Hence, a water spraying system was installed above the solar panel and operated once every week to study the effectiveness of cleaning by rainwater. The results are shown in Figure 9.
Without the water spray cleaning system, the polycrystalline solar panel pr...
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