GATE ME 2024 Set 1 — Question 49
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Heat Transfer → Heat Exchangers → Effectiveness-NTU Method
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Question
A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of 1 shell and 20,000 tubes. Water flows through each of the tubes at a rate of 1 kg/s with an inlet temperature of 30 °C. The steam in the condenser shell condenses at the rate of 430 kg/s at a temperature of 50 °C. If the heat of vaporization is 2.326 MJ/kg and specific heat of water is 4 kJ/(kg.K), the effectiveness of the heat exchanger is ________ (rounded off to 3 decimal places).
Correct answer
0.62 to 0.63
Solution
Given:
Number of tubes,
Mass flow rate of water per tube,
Total mass flow rate of water,
Specific heat of water,
Heat capacity rate of water, Mass flow rate of steam,
Heat of vaporization,
Total heat transfer rate, In a condenser, the hot fluid (steam) undergoes phase change at constant temperature (), so its heat capacity rate . Thus, .The maximum possible heat transfer rate is:
The effectiveness is defined as:
Rounding off to 3 decimal places, we get .
Number of tubes,
Mass flow rate of water per tube,
Total mass flow rate of water,
Specific heat of water,
Heat capacity rate of water, Mass flow rate of steam,
Heat of vaporization,
Total heat transfer rate, In a condenser, the hot fluid (steam) undergoes phase change at constant temperature (), so its heat capacity rate . Thus, .The maximum possible heat transfer rate is:
The effectiveness is defined as:
Rounding off to 3 decimal places, we get .
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