3157 -- Design Models to Handle Radiative and Convective Exchange in a Room PDF

The traditional method of handling heat exchange in a room for design purposes was to suppose that all heat from the plant, radiative as well as convective, was input at a so called "air temperature". This is an evident misnomer, since air temperature as such cannot drive longwave radiation as the model actually assumed. The "environmental temperature" concept has been introduced in the UK to get round the difficulty, This paper presents an analysis of when an approach along these lines may be logically acceptable. The surface-to-surface system of radiant exchange is first reduced to a surface-to-star point (T_r) exchange by a least squares fit. It is then shown that the space-averaged observable radiant temperature T_avr can be approximated by the value of the temperature generated at Tr when the radiant output from heating appliances and casual gains is taken to act at T_r. (Strictly speaking, this is not possible, since T_r is only a convenient fiction.) Now it is normally assumed that convective gains can be treated as though input at the space averaged air temperature, T_a. Thus we can set up a "binary star" model, formed from the radiant star pattern centred on T_r and the convective star pattern centred on T_a. It provides an attractive model for the internal exchange of heat in a room. An equivalence theorem can be demonstrated, and it serves to show that the binary star system, based on T_r and T_a can, in certain well-defined conditions, be replaced by a single star system, centered on an index temperature, T_ra, (the "rad-air" temperature), Tra in fact serves the same function as did as "air temperature" in the old fashioned sense, The model based on T_ra is workable but it is physically unattractive, and a model that handles convection and radiation separately may provide a better design procedure, Environmental temperature (t_ei) is in fact a form of T_ra but the logic of setting it up is seriously flawed.