Abstract
This paper describes the research on the mathematical analysis to give the amount of transmitted solar radiation energy through louvers and glass into the room, by applying the theory of non-steady state heat transfer to the thermal distribution within the section of the louvers the upper surface of which is irradiated by the sun, and by considering the effects of the mutual radiation and reflection in a certain thermal system as the combination of the louvers, the glass and the adjoining air. Authours investigated the general solution in the form of Fourier's series and the numerical one using the equation of the relaxation treatment. As for the former, by solving the simultaneous equations, regarding the heat balance equations at the upper and lower surfaces of louvers and the outer surface of the glass as the boundary conditions, the temperature of each surface variant with the time is expressed as the function of various factors. Then the heat transmitted by temperature difference between the outer surface of the glass and the room is added to the direct and diffuse solar radiation transmitted through the glass section which is to be computed in usual way. Thus the total heat gain from the glass surface is obtained as the Fourier's series, if the outdoor temperature and the amount of solar radiation are expressed in the Fourier's series. As for the latter, by using the circulating equation shown as the eq. (28) with the similar boundary conditions, the temperature at each surface and the several points of internal section of louvers are obtained at every Δt hour, and the total amount of heat gain obtained by this method is also expressed as the respective value at every Δt hour, if the outdoor temperature and the amount of solar radiation are given at the corresponding Δt hour. Finally, the one example as the application of the latter method is shown in Table 2 and Fig. 6 about the horizontal louvers attached on the south surface of window, with the result that the heat gain involving the effects of the mutual radiation is 1.16〜1.18 times as much as the instantaneous rate of heat transmission from outdoor to indoor through the glass section.
