Question Bank • QB_DFE_EXP_003 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Transient heat transfer in simple geometry

Question Statement:

A spherical fruit of radius $r = 0.03\text{ m}$ has thermal conductivity $k = 0.50\text{ W/(m}\cdot\text{K)}$. It is cooled in chilled air with convective heat transfer coefficient $h = 10.0\text{ W/(m}^2\cdot\text{K)}$. Taking characteristic length $L_c = r / 3$, the Biot number ($Bi = \frac{h L_c}{k}$) is ________ (round off to 1 decimal place).

Answer Key:

0.2

Step-by-Step Solution & Explanation

1. Characteristic length for a sphere: $L_c = \frac{V}{A} = \frac{\frac{4}{3} \pi r^3}{4 \pi r^2} = \frac{r}{3} = \frac{0.03\text{ m}}{3} = 0.010\text{ m}$ 2. Biot number $Bi$: $Bi = \frac{h L_c}{k} = \frac{10.0 \times 0.010}{0.50} = \frac{0.10}{0.50} = 0.20$
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