Question Bank • QB_DFE_EXP_019 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Transient heat transfer in simple geometry

Question Statement:

A thermocouple bead of radius $r = 1.0\text{ mm}$ (density $\rho = 8000\text{ kg/m}^3$, $C_p = 400\text{ J/(kg}\cdot\text{K)}$) has convective heat transfer coefficient $h = 200\text{ W/(m}^2\cdot\text{K)}$. The characteristic dimension $L_c = r/3$. The thermal time constant $\tau = \frac{\rho V C_p}{h A} = \frac{\rho L_c C_p}{h}$ of the thermocouple in seconds is ________ (round off to 2 decimal places).

Answer Key:

5.33

Step-by-Step Solution & Explanation

1. Characteristic length $L_c$: $L_c = \frac{0.001\text{ m}}{3} = 3.333 \times 10^{-4}\text{ m}$ 2. Thermal time constant $\tau$: $\tau = \frac{\rho L_c C_p}{h} = \frac{8000 \times (0.001 / 3) \times 400}{200} = \frac{8000 \times 0.001 \times 400}{600} = \frac{3200}{600} \approx 5.333\text{ s} \approx 5.33\text{ s}$
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