Question Bank • QB_DFE_EXP_065 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Transient heat transfer in simple geometry

Question Statement:

A spherical pea of diameter $10\text{ mm}$ ($r = 5\text{ mm}$) has thermal conductivity $k = 0.5\text{ W/(m}\cdot\text{K)}$. It is cooled in chilled water having convective heat transfer coefficient $h = 60\text{ W/(m}^2\cdot\text{K)}$. Calculate the Biot number ($Bi = h L_c / k$, where characteristic length $L_c = r/3$).

Answer Key:

0.2

Step-by-Step Solution & Explanation

Characteristic length for a solid sphere of radius $r = 0.005\text{ m}$: $L_c = \frac{V}{A} = \frac{\frac{4}{3}\pi r^3}{4\pi r^2} = \frac{r}{3} = \frac{0.005}{3}\text{ m}$ Biot number: $Bi = \frac{h L_c}{k} = \frac{60 \times (0.005 / 3)}{0.5} = \frac{60 \times 0.001667}{0.5} = \frac{0.10}{0.5} = 0.20$
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