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For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relation
Nu = 0.664 (Re) 0.5 (Pr) 0.33
Which of the following is then a false statement?
The average heat transfer coefficient increases as
Nu = 0.664 (Re) 0.5 (Pr) 0.33
Which of the following is then a false statement?
The average heat transfer coefficient increases as
- a)1/5 power of plate length
- b)2/3 power of thermal conductivity
- c)1/3 power of specific heat
- d)4/5 power of a free stream velocity
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
For turbulent flow over a flat plate, the average value of Nusselt num...
The average heat transfer coefficient reduces with length as 1/5th power of the length.
Most Upvoted Answer
For turbulent flow over a flat plate, the average value of Nusselt num...
False Statement: The average heat transfer coefficient increases as 1/5 power of plate length.
Explanation:
The Nusselt number (Nu) is defined as the ratio of convective to conductive heat transfer across a boundary layer. It is used to predict the heat transfer coefficient in convective heat transfer. For turbulent flow over a flat plate, the average value of Nusselt number is given by the relation:
Nu = 0.664 (Re)0.5(Pr)0.33
Where,
Re = Reynolds number
Pr = Prandtl number
Reynolds number (Re) is a dimensionless number that describes the ratio of inertial forces to viscous forces and is given by:
Re = ρ u L / μ
Where,
ρ = density of fluid
u = velocity of fluid
L = characteristic length (plate length in this case)
μ = dynamic viscosity of fluid
Prandtl number (Pr) is a dimensionless number that describes the ratio of momentum diffusivity to thermal diffusivity and is given by:
Pr = μ Cp / k
Where,
Cp = specific heat capacity of fluid
k = thermal conductivity of fluid
Now, let's analyze the given options one by one:
a) 1/5 power of plate length: This statement is false. As we can see from the above equations, the Nusselt number depends on the Reynolds and Prandtl numbers. The plate length (L) only appears in the Reynolds number. Hence, the average heat transfer coefficient does not depend on the plate length to the power of 1/5.
b) 2/3 power of thermal conductivity: This statement is true. As we can see from the Prandtl number equation, the Nusselt number depends on the thermal conductivity (k) to the power of 1/3.
c) 1/3 power of specific heat: This statement is true. As we can see from the Prandtl number equation, the Nusselt number depends on the specific heat capacity (Cp) to the power of 1/3.
d) 4/5 power of a free stream velocity: This statement is false. The free stream velocity (u) appears in the Reynolds number equation. Therefore, the average heat transfer coefficient depends on the free stream velocity to the power of 1/2, not 4/5.
In conclusion, the false statement is option 'A', which states that the average heat transfer coefficient increases as 1/5 power of plate length.
Explanation:
The Nusselt number (Nu) is defined as the ratio of convective to conductive heat transfer across a boundary layer. It is used to predict the heat transfer coefficient in convective heat transfer. For turbulent flow over a flat plate, the average value of Nusselt number is given by the relation:
Nu = 0.664 (Re)0.5(Pr)0.33
Where,
Re = Reynolds number
Pr = Prandtl number
Reynolds number (Re) is a dimensionless number that describes the ratio of inertial forces to viscous forces and is given by:
Re = ρ u L / μ
Where,
ρ = density of fluid
u = velocity of fluid
L = characteristic length (plate length in this case)
μ = dynamic viscosity of fluid
Prandtl number (Pr) is a dimensionless number that describes the ratio of momentum diffusivity to thermal diffusivity and is given by:
Pr = μ Cp / k
Where,
Cp = specific heat capacity of fluid
k = thermal conductivity of fluid
Now, let's analyze the given options one by one:
a) 1/5 power of plate length: This statement is false. As we can see from the above equations, the Nusselt number depends on the Reynolds and Prandtl numbers. The plate length (L) only appears in the Reynolds number. Hence, the average heat transfer coefficient does not depend on the plate length to the power of 1/5.
b) 2/3 power of thermal conductivity: This statement is true. As we can see from the Prandtl number equation, the Nusselt number depends on the thermal conductivity (k) to the power of 1/3.
c) 1/3 power of specific heat: This statement is true. As we can see from the Prandtl number equation, the Nusselt number depends on the specific heat capacity (Cp) to the power of 1/3.
d) 4/5 power of a free stream velocity: This statement is false. The free stream velocity (u) appears in the Reynolds number equation. Therefore, the average heat transfer coefficient depends on the free stream velocity to the power of 1/2, not 4/5.
In conclusion, the false statement is option 'A', which states that the average heat transfer coefficient increases as 1/5 power of plate length.
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For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relationNu = 0.664 (Re)0.5(Pr)0.33Which of the following is then a false statement?The average heat transfer coefficient increases asa)1/5 power of plate lengthb)2/3 power of thermal conductivityc)1/3 power of specific heatd)4/5 power of a free stream velocityCorrect answer is option 'A'. Can you explain this answer?
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For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relationNu = 0.664 (Re)0.5(Pr)0.33Which of the following is then a false statement?The average heat transfer coefficient increases asa)1/5 power of plate lengthb)2/3 power of thermal conductivityc)1/3 power of specific heatd)4/5 power of a free stream velocityCorrect answer is option 'A'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relationNu = 0.664 (Re)0.5(Pr)0.33Which of the following is then a false statement?The average heat transfer coefficient increases asa)1/5 power of plate lengthb)2/3 power of thermal conductivityc)1/3 power of specific heatd)4/5 power of a free stream velocityCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relationNu = 0.664 (Re)0.5(Pr)0.33Which of the following is then a false statement?The average heat transfer coefficient increases asa)1/5 power of plate lengthb)2/3 power of thermal conductivityc)1/3 power of specific heatd)4/5 power of a free stream velocityCorrect answer is option 'A'. Can you explain this answer?.
For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relationNu = 0.664 (Re)0.5(Pr)0.33Which of the following is then a false statement?The average heat transfer coefficient increases asa)1/5 power of plate lengthb)2/3 power of thermal conductivityc)1/3 power of specific heatd)4/5 power of a free stream velocityCorrect answer is option 'A'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relationNu = 0.664 (Re)0.5(Pr)0.33Which of the following is then a false statement?The average heat transfer coefficient increases asa)1/5 power of plate lengthb)2/3 power of thermal conductivityc)1/3 power of specific heatd)4/5 power of a free stream velocityCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For turbulent flow over a flat plate, the average value of Nusselt number is prescribed by the relationNu = 0.664 (Re)0.5(Pr)0.33Which of the following is then a false statement?The average heat transfer coefficient increases asa)1/5 power of plate lengthb)2/3 power of thermal conductivityc)1/3 power of specific heatd)4/5 power of a free stream velocityCorrect answer is option 'A'. Can you explain this answer?.
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