Definitions of room temperature

Abstract

The loss of heat from a room to ambient at T o is normally taken to be proportional to T i− T o, where T i is an index of the room temperature. It has not been clear in the past however how the various measurable temperatures of the surfaces and the air, possibly with considerations of heat input, should be combined with measures of convective and radiant transfer to form the index. Neither the ‘air temperature’ nor ‘environmental temperature’ are satisfactory formulations for T i. It will be shown that such an index can in fact be derived in a manner that is rigorous from the point of view of logic, but includes some approximations. Certain features novel to room heat transfer theory are needed. (i) Radiant output from an internal heat source falling on, say, the floor is strictly handled as though totally absorbed at the floor black-body equivalent node. (ii) Radiant exchange between surfaces can be estimated using a star-based network, and the network can be optimally designed using least squares methods. (iii) It is necessary to have two global measures of radiant temperature: a fictitious one T rs deriving from the star network, and one based on observational concepts T rv. The radiant input is assumed to act at T rs. T rs serves as an estimate of T rv. (iv) The unlike mechanisms of radiation and convection can be formally merged through use of a simple circuit theorem: the combined flux from the room as a whole to one of its bounding surfaces (and on through the room walls to ambient) is taken to be driven by the new index, the ‘rad-air’ temperature T ra of the room. The rad-air temperature serves exactly the same function indoors as sol-air temperature outdoors. (v) Dry resultant or comfort temperature is also a room index temperature, but unlike rad-air temperature is not associated with large heat flows and must be modelled as a very ‘high impedance’ node. By contrast, T ra must be modelled as a low impedance node. Simple expressions describing various measures of room temperature are given.