Lumping radiant and convective exchange in a room

Abstract

The convective heat exchange between the air in a room and one of its bounding surfaces at Tw can be described in terms of mean air temperature Tai, (which can be estimated from a single observation), together with the convective heat transfer coefficient hc. A radiation heat transfer coefficient hr can be written down for a simple system, but the transfer of heat by radiation from the several surfaces of a room to one of them cannot be described exactly in terms of a single temperature (to be estimated from a single observation), and hr as it stands. Yet for design purposes it is useful to postulate the existence of such a mean surface or radiant temperature Ts and to treat a weighted mean of Ts and Tai as a room index temperature, Ti. The heat flux from the room as a whole to a bounding surface at Tw is then computed in a design context as (Ti—Tw)hi, where hi is an equivalent heat transfer coefficient based on hc and hr. An account is given of the development of the ideas relating to this heat flow. The earliest work simply considered the mechanisms separately. Later the heat flow was treated as driven by the air temperature Tai but with a coefficient hi = hc + ∊hr. (∊ is surface emittance). The workers at the UK Building Research Establishment, on the basis of a simple model of radiant heat exchange, generalised this so that Ti became 1/3 Tai + 2/3 Ts and hi became hc + 6/5 Ehr. (E is a function of emittance). In the CIBS 1970 Guide, hi appears as hc + Ehr. The present author, using the full expression for radiant exchange, has demonstrated optimal versions for this expression; they are based on solutions which minimise the differences between the consequences of the exact model for radiant exchange, and the simplified model needed for design calculations. The emittance for each surface is introduced explicitly. Attention is drawn to the temperature node at which longwave radiation from a hot body heat source is introduced, and also to the difference in concept of an index temperature and a mean observable temperature.