Abstract
Room temperature θ_i(t)_R caused by a heat source f_R(t), for example, out-door temperature or solar radiation, may be computed from following expression, [numerical formula] (1) where ψ_R(t) is the "weight function for thet heat source". The heat flow W_R(t) which enter into the room by the heat source f_R(t) will be called "equivalent heating of f_R(t)" because it reduces the heating load of the room so much. Using W_R(t), room temperature θ_i(t)_R depending on f_R(t) may be computed from following expression, too, [numerical formula] (2) where ψw(t) is the "weight function for heating" and W_R(t) is gained from [numerical formula] (3) And therefore, room temperature θ_i(t) and "total heating W_T(t)" which is the total of actual heating and all "equivalent heatings" are shown by following formulae, respectively; [numerical formula] [numerical formula] (4) [numerical formula] (5) where Q is "heat capacity of the room" and δ(t) is Dirac's "Delta function". Substituting [numerical formula] and n→∞ in these formulae, the solution in periodic case is gained. Formulae (4) and (5) show the relation between actual heating and room temperature under influences of out-door temperature and solar radiation and so on, then if one of the two quantities is arranged the other may by computed from either formula (4) or (5). ψw(t) and s_<im>(t) in (4) and (5) are gained from J_<im>(t). Though j_<im>(t) is the function consists of infinite series of exponential terms, it may be substituted in practical calculation dy j_<im>(t) which is the approximate function of j_<im> similary, in computing "equivalent heating W_R(t)", j_R(t) may be substituted by j_R(t) which is the finite series of exponential terms. Many solutions may be gained in accordance with substituting method of j_<im>(t). Prof. Maeda uses following substitution; j_<im>(t)→j_<im>(t)+Q_<im>・δ(t) (6) and Dr. Fujii, in addition to (6), uses j_0(t)→j_0(t)+Q_0・δ(t) (7) Suphixes in (6) and (7), im and 0 denote heating and out-door temperature, respectively, and Q_<im> and Q_0 are the quantities of instantaneous heating at t=0, and are calculated from [numerical formula] (8) where suphix R denotes im or 0. However, when Q_R≒0 there happen many inconveniences in calculation, so that the writer recommended Q_R=0. Using finite series of exponential terms as j_R(t), the writer shew the calculating method of heating which will form the required room temperature of any time range.
