Subtopic: Preservation of food by cooling and freezing
Question Statement:
Plank's equation constants $P$ and $R$ for a cylinder of diameter $a$ frozen from its outer surface are $P = 0.25$ and $R = 0.0625$. The ratio of the surface convection term parameter $P$ for a slab ($P_{slab} = 0.50$) to that of a cylinder ($P_{cyl} = 0.25$) is ________ (answer in integer).
Answer Key:
2
Step-by-Step Solution & Explanation
Plank's geometric coefficients:
• Infinite slab of thickness $a$: $P = 1/2 = 0.50, R = 1/8 = 0.125$
• Infinite cylinder of diameter $a$: $P = 1/4 = 0.25, R = 1/16 = 0.0625$
• Sphere of diameter $a$: $P = 1/6 \approx 0.167, R = 1/24 \approx 0.0417$
Ratio: $\frac{P_{slab}}{P_{cyl}} = \frac{0.50}{0.25} = 2.0$.