13. Frost Damage in a Spherical Orange

In this chapter, we will investigate how frost damage penetrates a spherical and ripe orange. We assume that there is a sudden change in outside temperature at night with convection heat transfer at the surface of the orange. Also, there is a cloudy sky so there is minimal radiation heat loss to the night sky. The temperature change in the spherical orange occurs only in the radial direction. So, orange’s temperature is only functions of radius, R, and time, θ, as given in Equation 13-1 in spherical coordinates. Inside the orange, there are no temperature gradients in polar and azimuthal directions.