Ch 5 - Practice problem - Transport properties- SOLUTION.pdf

Ch 5 - Practice problem - Transport properties-...

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ENGG 201 (Dr. Sumon) Ch 5 Transport Processes 1 | P a g e Chapter 5 – Problems on Transport processes Problem # 1 Consider steady state heat transfer between two large parallel plates at constant temperatures of 𝑇𝑇 1 = 200 𝐾𝐾 and 𝑇𝑇 2 = 400 𝐾𝐾 that are 1 cm apart. Determine the rate of heat transfer between the plates per unit area if the space between the plates is filled with nitrogen gas. Consider the collision diameter of nitrogen is 364 pm. Also determine how temperature changes with distance. (N = 14). SOLUTION Given, Collision diameter, 𝜎𝜎 = 364 𝑝𝑝𝑝𝑝 = 364 × 10 −12 𝑝𝑝 Molar mass of nitrogen (N 2 ), 𝑀𝑀 = 28 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 × 1 𝑘𝑘𝑘𝑘𝑘𝑘𝑘𝑘 1000 𝑘𝑘𝑘𝑘𝑘𝑘 = 0.028 𝑘𝑘𝑘𝑘 𝑘𝑘𝑘𝑘𝑘𝑘 The average temperature, 𝑇𝑇 𝑎𝑎𝑎𝑎𝑘𝑘 = 𝑇𝑇 1 +𝑇𝑇 2 2 = 200+400 2 = 300 𝐾𝐾 Heat capacity at constant volume, 𝐶𝐶 𝑉𝑉 = 1.5 𝑅𝑅 = 1.5 × 8.314 𝐽𝐽 𝑘𝑘𝑘𝑘𝑘𝑘 . 𝐾𝐾 Avogadro’s number, 𝑁𝑁 𝐴𝐴 = 6.023 × 10 23 / 𝑝𝑝𝑚𝑚𝑚𝑚 Find, heat transfer rate. First, determine conductivity at the average temperature 𝜅𝜅 = 𝐶𝐶 𝑉𝑉 𝑁𝑁 𝐴𝐴 𝜋𝜋𝜎𝜎 2 𝑅𝑅𝑇𝑇 𝜋𝜋𝑀𝑀 = 1.5 × 8.314 𝐽𝐽 𝑝𝑝𝑚𝑚𝑚𝑚 . 𝐾𝐾 6.023 × 10 23 1 𝑝𝑝𝑚𝑚𝑚𝑚 × 𝜋𝜋 × (364 × 10 −12 ) 2 𝑝𝑝 2 8.314 𝐽𝐽 𝑝𝑝𝑚𝑚𝑚𝑚 . 𝐾𝐾 × 300 𝐾𝐾 𝜋𝜋 × 0.028 𝑘𝑘𝑘𝑘 𝑝𝑝𝑚𝑚𝑚𝑚 = 0.008376 𝐽𝐽 𝑝𝑝 . 𝐾𝐾 . 𝑠𝑠 = 8.376 × 10 −3 𝑊𝑊 𝑝𝑝 . 𝐾𝐾 [Units: 𝐽𝐽 𝑘𝑘𝑘𝑘 = 𝑁𝑁 . 𝑘𝑘 𝑘𝑘𝑘𝑘 = 𝑘𝑘𝑘𝑘 . 𝑚𝑚 𝑠𝑠 2 . 𝑘𝑘 𝑘𝑘𝑘𝑘 = 𝑘𝑘 𝑠𝑠 , 𝑐𝑐𝑚𝑚𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟 𝑎𝑎𝑟𝑟𝑟𝑟∗𝑟𝑟𝑟𝑟𝑘𝑘𝑡𝑡𝑟𝑟𝑟𝑟𝑎𝑎𝑟𝑟𝑟𝑟𝑡𝑡𝑟𝑟 𝑘𝑘𝑟𝑟𝑎𝑎𝑔𝑔𝑔𝑔𝑟𝑟𝑔𝑔𝑟𝑟 , 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑠𝑠 = 𝐽𝐽 𝑠𝑠 𝑘𝑘 2 . 𝐾𝐾 𝑚𝑚 = 𝑊𝑊 𝑘𝑘 . 𝐾𝐾 ] Heat transfer rate Z-axis L=1 cm = 0.01 m Plate 1 Plate 2 Transport of heat
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