Question Bank • QB_DFE_014 NAT • 1 Mark

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

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

Question Statement:

Two large parallel blackbody surfaces at absolute temperatures $T_1 = 400\text{ K}$ and $T_2 = 300\text{ K}$ exchange heat purely by thermal radiation. Taking the Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/(m}^2\cdot\text{K}^4)$, the net radiation heat flux between the two surfaces in $\text{W/m}^2$ is ________ (round off to 1 decimal place).

Answer Key:

992.3

Step-by-Step Solution & Explanation

For two blackbody surfaces, emissivities $\epsilon_1 = \epsilon_2 = 1.0$: $q = \sigma (T_1^4 - T_2^4)$ $T_1^4 = (400)^4 = 2.56 \times 10^{10}\text{ K}^4$ $T_2^4 = (300)^4 = 0.81 \times 10^{10}\text{ K}^4$ $T_1^4 - T_2^4 = 1.75 \times 10^{10}\text{ K}^4$ $q = 5.67 \times 10^{-8} \times 1.75 \times 10^{10} = 5.67 \times 175 = 992.25\text{ W/m}^2 \approx 992.3\text{ W/m}^2$
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