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A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Asuming kinematic viscosity, v = 30 x 10-6 m2/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is ____
(Important - Enter only the numerical value in the answer)
Correct answer is '6'. Can you explain this answer?
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Calculation of Thermal Boundary Layer Thickness
Given:
Prandtl number, Pr = 1
Temperature of fluid, T∞ = 500 K
Temperature of plate, Tw = 300 K
Length of plate, L = 1.5 m
Velocity of fluid, V = 10 m/s
Kinematic viscosity, ν = 30 x 10-6 m2/s
Distance from leading edge, x = 0.5 m
Reynolds number (Re) can be calculated as:
Re = (ρVx)/μ
where ρ is the density of the fluid, and μ is the dynamic viscosity.
Using the ideal gas law, ρ can be calculated as:
ρ = P/(R*T∞)
where P is the pressure of the fluid, and R is the gas constant.
Assuming the pressure and gas constant to be constant, ρ can be simplified as:
ρ = constant/T∞
Using the value of ρ, Re can be further simplified as:
Re = constant*Vx/ν
Using the calculated value of Re, the thermal boundary layer thickness (δ) can be calculated using the relation:
δ/x = 0.664/√Re*Pr1/2
Substituting the given values, we get:
Re = 2.5 x 105
δ/x = 0.664/√(2.5 x 105) = 0.006 m
Converting δ to mm, we get:
δ = 6 mm
Therefore, the thermal boundary layer thickness at 0.5 m from the leading edge is 6 mm.
Given:
Prandtl number, Pr = 1
Temperature of fluid, T∞ = 500 K
Temperature of plate, Tw = 300 K
Length of plate, L = 1.5 m
Velocity of fluid, V = 10 m/s
Kinematic viscosity, ν = 30 x 10-6 m2/s
Distance from leading edge, x = 0.5 m
Reynolds number (Re) can be calculated as:
Re = (ρVx)/μ
where ρ is the density of the fluid, and μ is the dynamic viscosity.
Using the ideal gas law, ρ can be calculated as:
ρ = P/(R*T∞)
where P is the pressure of the fluid, and R is the gas constant.
Assuming the pressure and gas constant to be constant, ρ can be simplified as:
ρ = constant/T∞
Using the value of ρ, Re can be further simplified as:
Re = constant*Vx/ν
Using the calculated value of Re, the thermal boundary layer thickness (δ) can be calculated using the relation:
δ/x = 0.664/√Re*Pr1/2
Substituting the given values, we get:
Re = 2.5 x 105
δ/x = 0.664/√(2.5 x 105) = 0.006 m
Converting δ to mm, we get:
δ = 6 mm
Therefore, the thermal boundary layer thickness at 0.5 m from the leading edge is 6 mm.
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A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Asuming kinematic viscosity, v = 30 x 10-6 m2/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is ____(Important - Enter only the numerical value in the answer)Correct answer is '6'. Can you explain this answer?
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A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Asuming kinematic viscosity, v = 30 x 10-6 m2/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is ____(Important - Enter only the numerical value in the answer)Correct answer is '6'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Asuming kinematic viscosity, v = 30 x 10-6 m2/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is ____(Important - Enter only the numerical value in the answer)Correct answer is '6'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fluid (Prandtl number, Pr = 1) at 500 K flows over a flat plate of 1.5 m length, maintained at 300 K. The velocity of the fluid is 10 m/s. Asuming kinematic viscosity, v = 30 x 10-6 m2/s, the thermal boundary layer thickness (in mm) at 0.5 m from the leading edge is ____(Important - Enter only the numerical value in the answer)Correct answer is '6'. Can you explain this answer?.
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