The equation of heat-transfer on the spherical thermometer bulb can be expresed in a dimentionless form:
Nu=β+KRen. ……(1)
where, β=(2Hr/k+2), H is the radiative heat-transfer coefficient, k the molecular heat conductivity of the air, r the radius of the thermometer bulb. The Nusselt number is usually written as
Nu=KRen. ……(2)
The time constants of two types of mercury thermometer were measured in a wind tunel, and the Nusselt number for each thermometer is computed from Eqs. (1) and (2), respectively. The values obtained from Eq. (2) have slightly a different tendency from those obtained from Eq. (1) as shown in Fig. (3).
This difference arises from the effect of radiative heat-transfer. The measured lag of the thermometer is also affected by radiative heat transfer. So as we express the Nusselt number with the lag as
Nu=2r/k(1/αMC/S-H), ……(3)
where α is the time constant of the thermometer; M, C, and S are mass, specific heat, and surface of the thermometer bulb, respetively.
Substitutiug Eq. (3) into Eq. (2), it becomes equal to Eq. (1) in the expression. From the measurements the values of constants for the spherical thermometer are: K=0.40, n=0.5.
Empirical formulae of the Kata-thermometer are examined with equation, and the result agrees well with the values shown in Table 1, which suggests applicability of Eq. (1).