## 3 Limitations of Mathematical Models  
Although mathematical models constitute a convenient means of assessing various heat-stress scenarios and then making recommendations, they are not easily applicable to the complicated thermal environment inside an incubator. The mathematical equations that describe body heat exchanges cannot be easily calculated from known physical laws, and are based on various empirical determinations. The problem is to find appropriate values for the parameters when a model is used for developing organisms (as opposed to adults) because the relative surface areas of the different body segments vary with body mass. The assumptions used to determine values of \(\mathrm{h_{c}}\) from theory (for standing adults, and restricted to either natural or forced convection) lead to errors. For example, neonates have larger convective heat transfer coefficients than adults. Air speed in the incubator (which determines whether convection is free or forced or mixed) is also relevant. The results of three-dimensional computational fluid mechanical studies of air flow in incubators [17; 18] have shown that air flow is not uniform; this non-uniformity, therefore, interferes with the determination of convective and evaporative heat transfer coefficients. The presence of eddies (i.e., small air vortices at the neonate's skin surface) leads to mixed-mode convection. Under these conditions, the equations used to calculate the combined heat transfer coefficient are not satisfactory. As mentioned above, clothing reduces radiant, convective and evaporative heat exchanges. There are no quantitative guidelines on the use of clothing for neonates. In the mathematical equations, the values of the reduction factors \(\mathrm{F_{cl}}\) and \(\mathrm{F_{pcl}}\) have been assessed with reference to the ISO 9920:1995 (F) standard [19] for adults by taking account of the percentage of the skin surface area covered by the fabric and the latter's thickness. As also mentioned above, the marked skin temperature differences between body segments mean that the conventional method for calculating \(\overline{\mathrm{T}}_{\mathrm{sk}}\) (i.e., spot measurements of several local skin temperatures) is not entirely suitable. Given that each body site has a specific weighting factor (i.e., the site's surface area relative to the total body surface area, which varies with body mass), the equations for calculating \(\overline{\mathrm{T}}_{\mathrm{sk}}\) should differ from one neonate to another. None of the incubators currently on the market feature a device for measuring \(\overline{\mathrm{T}}_{\mathrm{r}}\); hence, this parameter warrants more detailed investigation with regard to the geometric aspects of a neonate's posture, and the neonate's location in the incubator. \(\overline{\mathrm{T}}_{\mathrm{r}}\) is unlikely to be equal to the air temperature [20] or to a mean value calculated from the temperatures of the incubator inner walls and the mattress surface [15] or from the incubator and room air temperatures [21]. As reported by [PERSON] et al. [22] for a single-walled incubator, \(\overline{\mathrm{T}}_{\mathrm{r}}\) can be 4.0 to 5.5 \({}^{\circ}\)C lower than the incubator air temperature. When studying a single-wall incubator with a double-wall roof panel (the Satis\({}^{+}\) from Mediprema, Tauxigny, France), [PERSON] et al. [23] found a difference of 2.7 \({}^{\circ}\)C; this is similar to the value of 3.1 \({}^{\circ}\)C determined by [PERSON] [21] for the Vickers 79 closed incubator (Vickers Medical, UK) and the value of 3.5 \({}^{\circ}\)C determined by [PERSON] [24] for the Isolette closed incubator, Air-Shields Vickers, UK. \(\overline{\mathrm{T}}_{\mathrm{r}}\) can be measured using (i) matt-black copper globe thermometers, (ii) thermopile transducers in the mattress, (iii) a radiometer with two heat flow sensors, and (iv) a copper ellipsoid heated to simulate the neonate's convective and radiant heat losses.