Consider the flow of gas with density 1 kg/m3, viscosity 1.5 x 10-5 kg/ms, specific heat Cp = 846 J/kgK and thermal conductivity k = 0.01665 W/mK in a pipe of diameter D = 0.01 m and length L =1 m and assume that the viscosity does not change with temperature. The Nusselt number for flow in a pipe with (L/D) ratio greater than 10 and Reynolds number greater than 20000 is given by Nu = 0.026Re0.8Pr1/3. While the Nusselt number for a laminar flow for Reynolds number lessthan 2100 and (RePrD/L)andlt; 10 is Nu= 1.86 (RePrD/L)1/3. If the gas flows through the pipe with an average velocity of 0.1 m/s, then the heat transfer coefficient (in W/m2K) is _______.Correct answer is '2.47'. Can you explain this answer?

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Consider the flow of gas with density 1 kg/m³, viscosity 1.5 x 10^-5 kg/ms, specific heat C_p = 846 J/kgK and thermal conductivity k = 0.01665 W/mK in a pipe of diameter D = 0.01 m and length L =1 m and assume that the viscosity does not change with temperature. The Nusselt number for flow in a pipe with (L/D) ratio greater than 10 and Reynolds number greater than 20000 is given by Nu = 0.026Re^0.8Pr^1/3. While the Nusselt number for a laminar flow for Reynolds number less

than 2100 and (RePrD/L)< 10 is Nu= 1.86 (RePrD/L)^1/3. If the gas flows through the pipe with an average velocity of 0.1 m/s, then the heat transfer coefficient (in W/m²K) is _______.

Correct answer is '2.47'. Can you explain this answer?

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Consider the flow of gas with density 1 kg/m3, viscosity 1.5 x 10-5 kg...

Less than 0.2 is given by Nu = 3.66.

1. Calculate the Reynolds number:

Re = (ρVD)/μ
V = Q/A = (0.1 m3/s) / (π(0.01 m)2/4) = 127.3 m/s
Re = (1 kg/m3)(127.3 m/s)(0.01 m) / (1.5 x 10-5 kg/ms) = 8.49 x 106

2. Calculate the Prandtl number:

Pr = Cpμ/k = (846 J/kgK)(1.5 x 10-5 kg/ms) / (0.01665 W/mK) = 76.3

3. Calculate the Nusselt number:

Nu = 0.026Re0.8Pr1/3 = 0.026(8.49 x 106)0.8(76.3)1/3 = 1428.8

Since the Reynolds number is greater than 20000 and the (L/D) ratio is greater than 10, the flow is turbulent and we use the turbulent Nusselt number equation.

4. Calculate the heat transfer coefficient:

h = (k/D)(Nu) = (0.01665 W/mK)/(0.01 m)(1428.8) = 9.41 W/m2K

5. Calculate the heat transfer rate:

Q = hAΔT = (9.41 W/m2K)(π(0.01 m)2)(1000 K) = 295.3 W

For this flow condition, the heat transfer rate is 295.3 W.

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Consider the flow of gas with density 1 kg/m3, viscosity 1.5 x 10-5 kg...

Given: C

_p = 846 J/kgK, μ = 1.5 x 10^-5

kg/ms

ρ = 1 kg/m

, k = 0.01665 W/mK

D = 0.01 m, L = 1 m, V = 0.1 m/s

= 66.67 < 2100

Re < 2100 and RePr(D/L) < 10 indicate that the flow is laminar.

For laminar flow, Nu = 1.86(RrPrD/L)

^1/3
= 1.86(0.5081)^1/3
= 2.47

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Consider the flow of gas with density 1 kg/m3, viscosity 1.5 x 10-5 kg/ms, specific heat Cp = 846 J/kgK and thermal conductivity k = 0.01665 W/mK in a pipe of diameter D = 0.01 m and length L =1 m and assume that the viscosity does not change with temperature. The Nusselt number for flow in a pipe with (L/D) ratio greater than 10 and Reynolds number greater than 20000 is given by Nu = 0.026Re0.8Pr1/3. While the Nusselt number for a laminar flow for Reynolds number lessthan 2100 and (RePrD/L)< 10 is Nu= 1.86 (RePrD/L)1/3. If the gas flows through the pipe with an average velocity of 0.1 m/s, then the heat transfer coefficient (in W/m2K) is _______.Correct answer is '2.47'. Can you explain this answer?

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