Question Bank • QB_DFE_EXP_016 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 small food drying tray of surface area $0.50\text{ m}^2$ with emissivity $\epsilon = 0.90$ is heated by an overhead radiant ceramic heater maintained at $800\text{ K}$. The food tray surface is at $350\text{ K}$. Taking radiation shape factor $F_{12} = 1.0$ and Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/(m}^2\cdot\text{K}^4)$, the net rate of radiant heat transfer in watts is ________ (round off to nearest integer).

Answer Key:

1006

Step-by-Step Solution & Explanation

Radiant heat transfer formula: $q = \epsilon \sigma A F_{12} (T_1^4 - T_2^4)$ Given: • $\epsilon = 0.90$ • $\sigma = 5.67 \times 10^{-8}\text{ W/(m}^2\cdot\text{K}^4)$ • $A = 0.50\text{ m}^2$ • $T_1 = 800\text{ K} \implies T_1^4 = (800)^4 = 4.096 \times 10^{11}\text{ K}^4$ • $T_2 = 350\text{ K} \implies T_2^4 = (350)^4 = 1.5006 \times 10^{10}\text{ K}^4$ $T_1^4 - T_2^4 = 4.096 \times 10^{11} - 0.15006 \times 10^{11} = 3.94594 \times 10^{11}\text{ K}^4$ $q = 0.90 \times 0.50 \times (5.67 \times 10^{-8}) \times (3.94594 \times 10^{11}) = 0.45 \times 5.67 \times 3945.94 \approx 1006.8\text{ W} \approx 1007\text{ W}$
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