초록
In this paper, a new performance equation of bath tubs has been derived, which is very characteristically illuminating and in good agreement with experiments : $$T=T_{\infty}+(T_0-T_{\infty})e-\frac{k(A'_f+A_0)}{Mc_{P{\Delta}x}t$$, where $T_{\infty}$ is the temperature of the bathroom, $T_0$ that of the bathwater at t=0, k the overall heat conductivity of the tub- wall, $A'_f$ the equivalent surface area to the wall, $A_0$ the submerged area of the tub-wall, M mass of the bath-water, $C_p$ the specific heat of the bathwater and ${\Delta}x$ the thickness of the tub-wall. Here the equivalent-free surface area is written as $$A'_f=mA_f,\;m=const.(1-{\phi})^{0.88}$$ : where m is a numerical factor which is determined by a simple experiment and some calculation, {\phi}$ the relative humidity and $A_f$ the real free-surface area. From this study, it has been clarified that cooling of bath-water is mainly due to mass-transfer through evaporation from the free surface and conductive heat loss through the tub-wall is minor, which rather gaily mock at common sense. The effect of keeping bathwater warn by increase of the tub-wall thickness is also analyzed by a new idea of the thickness gain factor.