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A coolant fluid at 30°C flows over a heated flat plate maintained at aconstant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated asT = 30 + 70exp (–y) where y (in m) is the distance normal to the plate andT is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m2K) at that location will be:
- a)0.2
- b)1
- c)5
- d)10
Correct answer is option 'B'. Can you explain this answer?
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A coolant fluid at 30°C flows over a heated flat plate maintained...
Ans. (b)
Given T = 30 + 70 e-y
or
Given T = 30 + 70 e-y
or
We know that
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A coolant fluid at 30°C flows over a heated flat plate maintained...
Given data:
- Coolant fluid temperature, Tcoolant = 30°C
- Plate temperature, Tplate = 100°C
- Boundary layer temperature distribution equation, T = 30 + 70exp(y)
- Thermal conductivity of the fluid, k = 1.0 W/mK
Objective:
To determine the local convective heat transfer coefficient at a given location on the plate.
Solution:
The heat transfer coefficient can be determined using Newton's Law of Cooling, which states that the rate of heat transfer between a solid surface and a fluid is directly proportional to the temperature difference between the two and the heat transfer coefficient.
The heat transfer rate can be expressed as:
q = hA(Tplate - Tcoolant)
Where:
q = heat transfer rate
h = convective heat transfer coefficient
A = surface area
Tplate = plate temperature
Tcoolant = coolant temperature
To determine the convective heat transfer coefficient, we need to evaluate the surface temperature gradient (∂T/∂y) at the given location.
Given that the boundary layer temperature distribution is given by:
T = 30 + 70exp(y)
Differentiating the above equation with respect to y, we get:
∂T/∂y = 70exp(y)
Calculation:
At the given location, let's assume the surface temperature gradient (∂T/∂y) is equal to ∂T/∂y = 70exp(0) = 70.
Using the formula for the convective heat transfer coefficient, we can rearrange the equation as follows:
h = q / (A(Tplate - Tcoolant))
Since the area is not given, we can assume a unit area, i.e., A = 1 m².
Substituting the given values, we get:
h = q / (1 * (100 - 30))
h = q / 70
Since the thermal conductivity of the fluid is given as 1.0 W/mK, the heat transfer rate (q) can be calculated using Fourier's Law of Heat Conduction:
q = kA(∂T/∂y)
Substituting the given values, we get:
q = 1.0 * 1 * 70
Now substituting the value of q in the heat transfer coefficient equation, we get:
h = (1.0 * 1 * 70) / 70
h = 1.0 W/m²K
Therefore, the local convective heat transfer coefficient at the given location is 1.0 W/m²K. Hence, the correct answer is option 'B'.
- Coolant fluid temperature, Tcoolant = 30°C
- Plate temperature, Tplate = 100°C
- Boundary layer temperature distribution equation, T = 30 + 70exp(y)
- Thermal conductivity of the fluid, k = 1.0 W/mK
Objective:
To determine the local convective heat transfer coefficient at a given location on the plate.
Solution:
The heat transfer coefficient can be determined using Newton's Law of Cooling, which states that the rate of heat transfer between a solid surface and a fluid is directly proportional to the temperature difference between the two and the heat transfer coefficient.
The heat transfer rate can be expressed as:
q = hA(Tplate - Tcoolant)
Where:
q = heat transfer rate
h = convective heat transfer coefficient
A = surface area
Tplate = plate temperature
Tcoolant = coolant temperature
To determine the convective heat transfer coefficient, we need to evaluate the surface temperature gradient (∂T/∂y) at the given location.
Given that the boundary layer temperature distribution is given by:
T = 30 + 70exp(y)
Differentiating the above equation with respect to y, we get:
∂T/∂y = 70exp(y)
Calculation:
At the given location, let's assume the surface temperature gradient (∂T/∂y) is equal to ∂T/∂y = 70exp(0) = 70.
Using the formula for the convective heat transfer coefficient, we can rearrange the equation as follows:
h = q / (A(Tplate - Tcoolant))
Since the area is not given, we can assume a unit area, i.e., A = 1 m².
Substituting the given values, we get:
h = q / (1 * (100 - 30))
h = q / 70
Since the thermal conductivity of the fluid is given as 1.0 W/mK, the heat transfer rate (q) can be calculated using Fourier's Law of Heat Conduction:
q = kA(∂T/∂y)
Substituting the given values, we get:
q = 1.0 * 1 * 70
Now substituting the value of q in the heat transfer coefficient equation, we get:
h = (1.0 * 1 * 70) / 70
h = 1.0 W/m²K
Therefore, the local convective heat transfer coefficient at the given location is 1.0 W/m²K. Hence, the correct answer is option 'B'.
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A coolant fluid at 30°C flows over a heated flat plate maintained at aconstant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated asT = 30 + 70exp (–y) where y (in m) is the distance normal to the plate andT is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m2K) at that location will be:a)0.2b)1c)5d)10Correct answer is option 'B'. Can you explain this answer?
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A coolant fluid at 30°C flows over a heated flat plate maintained at aconstant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated asT = 30 + 70exp (–y) where y (in m) is the distance normal to the plate andT is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m2K) at that location will be:a)0.2b)1c)5d)10Correct 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 coolant fluid at 30°C flows over a heated flat plate maintained at aconstant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated asT = 30 + 70exp (–y) where y (in m) is the distance normal to the plate andT is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m2K) at that location will be:a)0.2b)1c)5d)10Correct 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 coolant fluid at 30°C flows over a heated flat plate maintained at aconstant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated asT = 30 + 70exp (–y) where y (in m) is the distance normal to the plate andT is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m2K) at that location will be:a)0.2b)1c)5d)10Correct answer is option 'B'. Can you explain this answer?.
A coolant fluid at 30°C flows over a heated flat plate maintained at aconstant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated asT = 30 + 70exp (–y) where y (in m) is the distance normal to the plate andT is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m2K) at that location will be:a)0.2b)1c)5d)10Correct 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 coolant fluid at 30°C flows over a heated flat plate maintained at aconstant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated asT = 30 + 70exp (–y) where y (in m) is the distance normal to the plate andT is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m2K) at that location will be:a)0.2b)1c)5d)10Correct 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 coolant fluid at 30°C flows over a heated flat plate maintained at aconstant temperature of 100°C. The boundary layer temperature distribution at a given location on the plate may be approximated asT = 30 + 70exp (–y) where y (in m) is the distance normal to the plate andT is in °C. If thermal conductivity of the fluid is 1.0 W/mK, the local convective heat transfer coefficient (in W/m2K) at that location will be:a)0.2b)1c)5d)10Correct answer is option 'B'. Can you explain this answer?.
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