Measurement of the Effective Thermal Diffusivity of the Cylindrical Vegetables

Abstract

The thermal diffusivity coefficient, κ, of cylindrical vegetables, burdock, carrot, cucumber and radish, were calculated from rate of temperature change of the center and surface of them when they were suddenly immersed in ice-water bath. The temperature was measured and recorded with a recorder employing preamplifiers and copper-constantan thermocouples, and κ was obtained by substitution in the following equation:
κ=1/α₁² (t₂-t₁)lege(vo)t=t₁/(vo)t=t₂
where t₁ is initial time after immersion of vegetables when the semi-logalithmic curve of the center temperature versus time becomes linear, t₂ is any subsequent time linear portion of curve, (vo) t=t₁ is center temperature at t₁, (vo)_t=t2 is center temperature at t₂, κ is thermal diffusivity and α₁ is the smallest root of
(va)_t=t1/(vo)_t=t2=Jo (aα₁)
where V_a=surface trmperature at t₂, a=mean radius,
Jo (aα₁)=Bessel's function of O order. From the results, the locations of the mass-average temperature of the vegetables were obtained by the following equation:
r/a=aα₁/rα₁
where r is the location of the mass-average temperature found as the root of
2J₁(aα₁)/aα₁=Jo(rα₁)
where J₁(aα₁)=Bessel's function of the first order.