A parametric study of wind chill equivalent temperatures by a dimensionless steady-state analysis

A first order analytical approximation of steady-state heat conduction in a hollow cylinder exchanging heat at its external surface by convection with a cold and windy environment is presented. The model depicts the thermal behavior of certain body elements, e.g., head/face, when exposed to such environments. The results are presented by dimensionless parameters and facilitate the estimation of wind chill equivalent temperatures (WCETs). The effects of several variables on determining WCETs were studied using specific examples, leading to the following generalizations: (1) the conditions assumed for "calm" wind speed appear to be a dominant factor in determining WCET; (2) the effects, on both (skin) surface temperature and on WCET, of a 1°C change in environmental temperature appear to be more pronounced than those of a 1 m/s change in wind speed; (3) similarly, predicted WCETs are more sensitive to the geometrical dimensions assumed for the modeled entity than they are to wind speeds; and (4) tissue thermal conductivity, the angle at which the convective heat transfer coefficient is measured relative to wind direction, and the factor used to establish "effective" wind speeds in the domain occupied by humans relative to reported values, all seem to have relatively small effects on the determination of WCET. These conclusions strongly suggest, among other things, that for any given combination of environmental conditions, wind chill indices may best be presented as ranges rather than as single values. This seems to apply even when worst-case scenarios are considered. Also emphasized is the need for careful and realistic selection of all the parameter values used in the determination of WCETs.