Subtopic: Biot number calculation for spherical fruit
Question Statement:
A spherical fruit of radius $R = 30\text{ mm}$ has a thermal conductivity $k = 0.5\text{ W/(m}\,\text{K)}$. It is blast-chilled in air where the convective surface heat transfer coefficient is $h = 20.0\text{ W/(m}^2\,\text{K)}$. Taking characteristic dimension $L_c = R/3$, the Biot number ($Bi$) for the fruit is ________ (round off to two decimal places).
Answer Key:
0.40
Step-by-Step Solution & Explanation
Characteristic length of a solid sphere:
$L_c = \frac{V}{A} = \frac{\frac{4}{3} \pi R^3}{4 \pi R^2} = \frac{R}{3} = \frac{0.030}{3} = 0.0100\text{ m}$
The Biot number is:
$Bi = \frac{h L_c}{k} = \frac{20.0 \times 0.0100}{0.5} = 0.400$
Rounding to two decimal places: $0.40$.