Question Bank • QB_DFE_EXP_077 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:

A blackbody food dehydration surface ($1.0\text{ m}^2$) is heated to $400\text{ K}$. Assuming an ideal black surface emissivity of $\epsilon = 1.0$ and Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/(m}^2\cdot\text{K}^4)$, calculate the total radiant emissive power in $\text{W}$.

Answer Key:

1451.52

Step-by-Step Solution & Explanation

Stefan-Boltzmann law: $E_b = \sigma T^4 = (5.67 \times 10^{-8}) \times (400)^4 = (5.67 \times 10^{-8}) \times 2.56 \times 10^{10} = 1451.52\text{ W/m}^2$ For area $A = 1.0\text{ m}^2$: $Q = 1451.52\text{ W}$
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