# Solar Radiation and Sol Air Temperature on Building Surfaces

Figure 2.9 shows a schematic view of a building with a single sloped roof and a horizontal roof (dotted line) with dimensions of walls and roofs for Jaipur. In order to determine the total solar radiation on building cover, it is necessary to determine the total solar radiation on each of the walls and roof of the building by using Eq. (2.12). There are four vertical walls and one roof (i = 5). The roof is also made horizontal for some cases, as shown by the dotted line in Figure 2.9. Hence, the total solar radiation on building surfaces can be obtained by using the following expression:

i=5

Total Solar Radiation = AiIi (2.12)

i=1

where Ai and I,- are an area of the ith section, and total solar radiation available on the ith section are shown in Figures 2.10a and b. Figure 2.9 Schematic views of single slope and horizontal roof building. Figure 2.10a Solar radiation on different building surfaces in June. Figure 2.10b Solar radiation on different building surfaces in December.

In this section, Tsa is a sol air temperature and an expression for this can be written as,

Tsa = I(t) + Ta — for bare surface of wall or roof

ho ho

where a is the absorptivity of the wall or the roof surface, is the ambient air temperature and Ta is the solar radiation on the building surface.

The term eAR represents longwave radiation from the roof or wall surface of the building and its value for a vertical wall is taken as 60 W/m2 and 0 W/m2 for a horizontal roof. The longwave radiation for inclined roof shown in Figure 2.9 is taken as

eAR x cos b

where b = slope of inclined surface = j

ho — hr T hc,

ho — Outside heat transfer coefficient of building hr — Radiative heat transfer coefficient of building hc — Convective heat transfer coefficient of building The variation of sol air temperature on outside building surfaces are plotted and shown in Figures 2.11. The value of sol air is found to be directly dependent on the solar radiation falling on the outside surface of a building.   Sol air Temperature of various Building Surfaces in December at Jaipur

♦ Inclined_Roof ■ Horizontal_Roof – Д – East Wall – X-West Wall – Ж – South Wall —•—North Wall

0

Figure 2.11b Sol air temperatures on different building surfaces in December.

The program for evaluating solar radiation and sol air temperature on a building surface is given in Table 2.6, which is used for obtaining Figures 2.10 and 2.11.

Table 2.6 Calculation of Solar Radiation and Sol air Temperatures on Building Surfaces in Matlab.

%Jaipur

phi = 26.916*(pi/180);

Isc = 1367;

omega = [-75 -60 -45 -30 -15 0 15 30 45 60 75 105 105 105 105 105 105 105 105 105 105 105 105 105]*pi/180;; % 7:00 AM to 6:00 AM t = 7:1:17;

n = 173; %nth day of the year (June 22, 2010, n = 173, December 21, 2010, n = 355)

rho = 0.2; % Reflectivity of surface

TR = 3.1; % Turbidity of surface TR = 3.1 in June,

TR = 2.7 in December

delta = (23.45*sin((360/365)*(n + 284)*pi/180))*pi/180;

Iext = Isc*(1 +0.033*cos(2*pi*n/365)); for j = 1:1:24

CThz(1,j) = cos(phi)*cos(delta).*cos(omega(1,j)) + sin(delta)*sin(phi); if CThz(1,j)<0;

CThz(1,j) = 0; end

if omega(1,j)>90;

CThz(1,j) = 0;

end

end

CThz1 = repmat(CThz,24,1); for j = 1:1:24

In(1,j) = Iext.*exp(-TR/((0.9 + 9.4.*CThz(1,j))));

Ib(1,j) = In(1,j).*CThz1(j, j);

Id(1,j) = (1/3)*(Iext-In(1,j)).*CThz1(j, j); end

Ib1 = repmat(Ib,24,1);

Id1 = repmat(Id,24,1);

Ta = [28.5 28.7 29.3 30.4 31.9 33.6 35.6 37.4 38.8 39.8 40.1 39.8 38.7 37.7 36.2 34.6 33.4 32.2 31.3 30.6 30 29.4 29 28.6] ;% Jaipur in June

%Ta = [9.5 9.8 10.6 11.9 13.9 16.1 18.7 21.1 22.9 24.1 24.6 24.1 23.1 21.4 19.5 17.5 15.8 14.3 13.1 12.2 11.5 10.7 10.1 9.7] ;% Jaipur in December gamma = [0 0 -90 90 0 -180]*pi/180;

%[InclinedRoof Horizontal_Roof East West South North]; beta = [26.916 0 90 90 90 90]*pi/180;

%[InclinedRoof Horizontal_Roof East West South North]; for k = 1:1:6 for j = 1:1:24

Thz(j, k) = cos(phi)*cos(delta).*cos(omega(j)) + sin(delta)*sin(phi);

Thi(j, k) = (cos(phi)*cos(beta(k)) + sin(phi)*sin(beta(k))*cos(gamma(k)))*cos(delta).*cos(omega(j)) + cos(delta).*sin (omega(j))*sin(beta(k))*sin(gamma(k)) + sin(delta)*(sin(phi)*cos(beta(k))-cos(phi)*sin(beta(k))*cos(gamma(k))); Rb(j, k) = Thi(j, k)./Thz(j, k); num = size(Rb(j, k)); for i = 1:1:num; if Rb(j, k)<0;

Rb(j, k) = 0; end

Rd(j, k) = (1 + cos(beta(k)))/2;

Rr(j, k) = rho*(1-cos(beta(k)))/2;

It(j, k) = Ib1(j, j).*Rb(j, k) + Id1(j, j).*Rd(j, k) + (Ib1(j, j) + Id1(j, j)).*Rr(j, k);

end

end

end

ho = 22.78; % Outside Heat Transfer Coefficient = 5.7 + 3.8v

Table 2.6 (Continued).

alpha = 0.6; % Absorptivity of surface em = 0.9; % emissivity of surface

DeltaR_H = 60; % radiative value for horizontal surface DeltaR_V = 60; % radiative value for verticle surface Taa(1:24) = transpose(Ta);

% Sol-Air temperature calculations

Tsr1(1:24) = (alpha*It(1:24,1))*(1/ho) + Taa(1:24,1)—(em*DeltaR_V)/ho; %InclinedRoof Surface Tsr(1:24) = (alpha*It(1:24,2))*(1/ho) + Taa(1:24,1)-(em*DeltaR_V)/ho;

%Horizontal Roof Surface

Tse(1:24) = (alpha*It(1:24,3))*(1/ho) + Taa(1:24,1)-(em*DeltaR_H)/ho;

%East wall

Tsw(1:24) = (alpha*It(1:24,4))*(1/ho) + Taa(1:24,1)-(em*DeltaR_H)/ho;

%West wall

Tss(1:24) = (alpha*It(1:24,5))*(1/ho) + Taa(1:24,1)-(em*DeltaR_H)/ho;

%South wall

Tsn(1:24) = (alpha*It(1:24,6))*(1/ho) + Taa(1:24,1)-(em*DeltaR_H)/ho;

%North wall

plot(t, Tsr) %Horizontal Roof Surface vs. Time plot(t, Tse) %East wall vs. Time plot(t, Tsw) %West wall vs. Time plot(t, Tss) %South wall vs. Time plot(t, Tsn) %North wall vs. Time

Updated: September 24, 2015 — 7:20 am