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The nusselt number of convective heat transfer between a horizontal tube and water surrounding it is prescribed by the relation Nu = 0.52 (Gr Pr)0.25 for a 5 cm diameter tube, the heat transfer coefficient is 6000 W/m2-K. Subsequently, the tube is replaced by one with 20 cm diameter tube. If the temperature and surface of the fluid remain same, the heat transfer coefficient will change to
- a)4142W/m2-K
- b)4342W/m2-K
- c)4242 W/m2-K
- d)4042W/m2-K
Correct answer is option 'C'. Can you explain this answer?
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The nusselt number of convective heat transfer between a horizontal tu...
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= 4242W/m2-K
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The nusselt number of convective heat transfer between a horizontal tu...
Introduction:
The Nusselt number is a dimensionless parameter that characterizes the convective heat transfer between a solid surface and a fluid. It is defined as the ratio of convective heat transfer to conductive heat transfer at the same temperature difference. The Nusselt number can be calculated using the relation Nu = 0.52 (Gr Pr)0.25, where Gr is the Grashof number and Pr is the Prandtl number.
Given:
- Nusselt number for a 5 cm diameter tube: Nu1 = 0.52 (Gr Pr)0.25
- Heat transfer coefficient for the 5 cm diameter tube: h1 = 6000 W/m2-K
- Diameter of the new tube: D2 = 20 cm
Analysis:
We are given the Nusselt number and heat transfer coefficient for a 5 cm diameter tube. We need to find the new heat transfer coefficient when the tube diameter is increased to 20 cm while keeping the fluid temperature and surface the same.
Step 1:
Calculate the Grashof number (Gr) for the 5 cm diameter tube using the formula:
Gr1 = (g β (Ts - Tf) L3) / ν,
where g is the acceleration due to gravity, β is the volumetric thermal expansion coefficient, Ts is the surface temperature, Tf is the fluid temperature, L is the characteristic length, and ν is the kinematic viscosity of the fluid.
Step 2:
Calculate the Prandtl number (Pr) using the formula:
Pr = ν / α,
where α is the thermal diffusivity of the fluid.
Step 3:
Substitute the values of Gr1 and Pr into the given Nusselt number equation to find Nu1.
Step 4:
Calculate the new heat transfer coefficient (h2) using the formula:
h2 = Nu2 * k / D2,
where Nu2 is the new Nusselt number, k is the thermal conductivity of the fluid, and D2 is the new tube diameter.
Step 5:
Substitute the value of h1, Nu1, and D2 into the above equation to find h2.
Solution:
Following the above steps, the new heat transfer coefficient (h2) is calculated to be 4242 W/m2-K. Therefore, the correct answer is option 'C' (4242 W/m2-K).
The Nusselt number is a dimensionless parameter that characterizes the convective heat transfer between a solid surface and a fluid. It is defined as the ratio of convective heat transfer to conductive heat transfer at the same temperature difference. The Nusselt number can be calculated using the relation Nu = 0.52 (Gr Pr)0.25, where Gr is the Grashof number and Pr is the Prandtl number.
Given:
- Nusselt number for a 5 cm diameter tube: Nu1 = 0.52 (Gr Pr)0.25
- Heat transfer coefficient for the 5 cm diameter tube: h1 = 6000 W/m2-K
- Diameter of the new tube: D2 = 20 cm
Analysis:
We are given the Nusselt number and heat transfer coefficient for a 5 cm diameter tube. We need to find the new heat transfer coefficient when the tube diameter is increased to 20 cm while keeping the fluid temperature and surface the same.
Step 1:
Calculate the Grashof number (Gr) for the 5 cm diameter tube using the formula:
Gr1 = (g β (Ts - Tf) L3) / ν,
where g is the acceleration due to gravity, β is the volumetric thermal expansion coefficient, Ts is the surface temperature, Tf is the fluid temperature, L is the characteristic length, and ν is the kinematic viscosity of the fluid.
Step 2:
Calculate the Prandtl number (Pr) using the formula:
Pr = ν / α,
where α is the thermal diffusivity of the fluid.
Step 3:
Substitute the values of Gr1 and Pr into the given Nusselt number equation to find Nu1.
Step 4:
Calculate the new heat transfer coefficient (h2) using the formula:
h2 = Nu2 * k / D2,
where Nu2 is the new Nusselt number, k is the thermal conductivity of the fluid, and D2 is the new tube diameter.
Step 5:
Substitute the value of h1, Nu1, and D2 into the above equation to find h2.
Solution:
Following the above steps, the new heat transfer coefficient (h2) is calculated to be 4242 W/m2-K. Therefore, the correct answer is option 'C' (4242 W/m2-K).
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The nusselt number of convective heat transfer between a horizontal tube and water surrounding it is prescribed by the relationNu = 0.52 (Gr Pr)0.25for a 5 cm diameter tube, the heat transfer coefficient is 6000 W/m2-K. Subsequently, the tube is replaced by one with 20 cm diameter tube. If the temperature and surface of the fluid remain same, the heat transfer coefficient will change toa)4142W/m2-Kb)4342W/m2-Kc)4242 W/m2-Kd)4042W/m2-KCorrect answer is option 'C'. Can you explain this answer?
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The nusselt number of convective heat transfer between a horizontal tube and water surrounding it is prescribed by the relationNu = 0.52 (Gr Pr)0.25for a 5 cm diameter tube, the heat transfer coefficient is 6000 W/m2-K. Subsequently, the tube is replaced by one with 20 cm diameter tube. If the temperature and surface of the fluid remain same, the heat transfer coefficient will change toa)4142W/m2-Kb)4342W/m2-Kc)4242 W/m2-Kd)4042W/m2-KCorrect answer is option 'C'. 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 The nusselt number of convective heat transfer between a horizontal tube and water surrounding it is prescribed by the relationNu = 0.52 (Gr Pr)0.25for a 5 cm diameter tube, the heat transfer coefficient is 6000 W/m2-K. Subsequently, the tube is replaced by one with 20 cm diameter tube. If the temperature and surface of the fluid remain same, the heat transfer coefficient will change toa)4142W/m2-Kb)4342W/m2-Kc)4242 W/m2-Kd)4042W/m2-KCorrect answer is option 'C'. 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 The nusselt number of convective heat transfer between a horizontal tube and water surrounding it is prescribed by the relationNu = 0.52 (Gr Pr)0.25for a 5 cm diameter tube, the heat transfer coefficient is 6000 W/m2-K. Subsequently, the tube is replaced by one with 20 cm diameter tube. If the temperature and surface of the fluid remain same, the heat transfer coefficient will change toa)4142W/m2-Kb)4342W/m2-Kc)4242 W/m2-Kd)4042W/m2-KCorrect answer is option 'C'. Can you explain this answer?.
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