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A spherical thermocouple junction of diameter 0.706 mm is to be used for the measurement of temperature of a gas stream. The convective heat transfer coefficient on bead surface is 400 W/m2K, Thermophysical properties of thermocouple material are k = 20 W/mK, c = 400 J/kgK and r = 8500 kg/m3. If the thermocouple initially at 30°C is placed in a hot stream of 300°C, the time taken by the bead to reach 298°C, is
[2004]
  • a)
    2.35 s
  • b)
    4.9 s
  • c)
    14.7 s
  • d)
    29.4 s
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A spherical thermocouple junction of diameter 0.706 mm is to be used f...
Given
h = 400 W/m2K, k = 20 W/mK c = 400 J/kg.K, ρ = 8500 kg/m3

Biot Number =  hL/k

Since Bi< 0.1, lumped system analysis can be used



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Most Upvoted Answer
A spherical thermocouple junction of diameter 0.706 mm is to be used f...
°C is exposed to the gas stream at 200 °C, we can calculate the rate of heat transfer from the gas to the thermocouple using the following formula:

q = h * A * ΔT

where:
q = rate of heat transfer (W)
h = convective heat transfer coefficient (W/m2K)
A = surface area of the thermocouple junction (m2)
ΔT = temperature difference between the gas and thermocouple (K)

First, let's calculate the surface area of the thermocouple junction:

r = diameter/2 = 0.706 mm / 2 = 0.353 mm = 0.353 * 10^-3 m

A = 4 * π * r^2 = 4 * 3.14159 * (0.353 * 10^-3)^2 = 1.56 * 10^-7 m2

Next, let's calculate the temperature difference:

ΔT = T_gas - T_thermocouple = 200 °C - 30 °C = 170 °C

Now we can calculate the rate of heat transfer:

q = 400 W/m2K * 1.56 * 10^-7 m2 * 170 K = 1.06 * 10^-3 W

Therefore, the rate of heat transfer from the gas to the thermocouple is approximately 1.06 milliwatts.
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A spherical thermocouple junction of diameter 0.706 mm is to be used for the measurement of temperature of a gas stream. The convective heat transfer coefficient on bead surface is 400 W/m2K, Thermophysical properties of thermocouple material are k = 20 W/mK, c = 400 J/kgK and r = 8500 kg/m3. If the thermocouple initially at 30°C is placed in a hot stream of 300°C, the time taken by the bead to reach 298°C, is[2004]a)2.35 sb)4.9 sc)14.7 sd)29.4 sCorrect answer is option 'B'. Can you explain this answer?
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A spherical thermocouple junction of diameter 0.706 mm is to be used for the measurement of temperature of a gas stream. The convective heat transfer coefficient on bead surface is 400 W/m2K, Thermophysical properties of thermocouple material are k = 20 W/mK, c = 400 J/kgK and r = 8500 kg/m3. If the thermocouple initially at 30°C is placed in a hot stream of 300°C, the time taken by the bead to reach 298°C, is[2004]a)2.35 sb)4.9 sc)14.7 sd)29.4 sCorrect answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A spherical thermocouple junction of diameter 0.706 mm is to be used for the measurement of temperature of a gas stream. The convective heat transfer coefficient on bead surface is 400 W/m2K, Thermophysical properties of thermocouple material are k = 20 W/mK, c = 400 J/kgK and r = 8500 kg/m3. If the thermocouple initially at 30°C is placed in a hot stream of 300°C, the time taken by the bead to reach 298°C, is[2004]a)2.35 sb)4.9 sc)14.7 sd)29.4 sCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical thermocouple junction of diameter 0.706 mm is to be used for the measurement of temperature of a gas stream. The convective heat transfer coefficient on bead surface is 400 W/m2K, Thermophysical properties of thermocouple material are k = 20 W/mK, c = 400 J/kgK and r = 8500 kg/m3. If the thermocouple initially at 30°C is placed in a hot stream of 300°C, the time taken by the bead to reach 298°C, is[2004]a)2.35 sb)4.9 sc)14.7 sd)29.4 sCorrect answer is option 'B'. Can you explain this answer?.
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