Question Bank • QB_DFE_013 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Steady state heat transfer in conduction, convection and radiation

Question Statement:

Milk flows turbulently through a stainless steel tube of inner diameter $D = 0.025\text{ m}$ in a tubular pasteurizer. The Reynolds number is $Re = 10000$, Prandtl number is $Pr = 4.0$, and thermal conductivity of milk is $k = 0.58\text{ W/(m}\cdot\text{K)}$. Using the Dittus-Boelter heating correlation $Nu = 0.023 Re^{0.8} Pr^{0.4}$, the convective heat transfer coefficient $h$ inside the tube in $\text{W/(m}^2\cdot\text{K)}$ is ________ (round off to 1 decimal place).

Answer Key:

1472.4

Step-by-Step Solution & Explanation

1. Nusselt number calculation: $Nu = 0.023 Re^{0.8} Pr^{0.4}$ $(10000)^{0.8} = 1584.893$ $(4.0)^{0.4} = 1.74110$ $Nu = 0.023 \times 1584.893 \times 1.74110 = 63.465$ 2. Convective film coefficient $h$: $h = \frac{Nu \cdot k}{D} = \frac{63.465 \times 0.58}{0.025} = \frac{36.8097}{0.025} = 1472.388\text{ W/(m}^2\cdot\text{K)} \approx 1472.4\text{ W/(m}^2\cdot\text{K)}$
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