| Abstract: | A system of algorithms is developed for calculation of the frequency- and time-domain responses of the heat transfer equations for a dwelling. Conduction through the walls, considered as multi-layered slabs, as well as convection to the inside air, infiltration, solar radiation deposition in the space, and radiative interaction between the walls is included in the calculation. The first part of this system of algorithms provides a means whereby a set of frequency responses of the dwelling as a whole may be calculated, one frequency response for each input-output pair, considering internal temperature or heat flow as the output, and the sol-air temperatures on each surface, infiltration, and the solar heat gain to the interior as inputs. The second part of the system of algorithms is then used to obtain from these frequency responses sets of digital transfer function coefficients of the type presented in the ASHRAE Handbook of Fundamentals, but relating the total dwelling heat gain, rather than that for a single wall, with specified internal temperatures, or internal temperature with specified heat gains, to the sol-air temperatures on each surface, infiltration, and solar heat deposited in the interior. The method is shown to produce rapidly calculatable, accurate results in the time-domain. Further the plots of the frequency responses themselves are expected to prove useful in seeking optimal thermal designs. |
