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Air at 20०C flows over a flat plate maintained at 75०C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50०C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.
Correct answer is between '24.15,24.20'. Can you explain this answer?
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Air at 20C flows over a flat plate maintained at 75C . Measurements sh...
Assuming linear variation of temperature
= 24.18 W/m2-°C
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Air at 20C flows over a flat plate maintained at 75C . Measurements sh...
Given data:
- Temperature of air, T∞ = 20°C
- Temperature of flat plate, Ts = 75°C
- Temperature at distance of 0.5 mm from plate surface, T = 50°C
- Thermal conductivity of air, k = 0.0266 W/m-K
To determine: Local heat transfer coefficient, h (in W/m²-K)
Assumptions:
- Steady-state and one-dimensional heat transfer
- Negligible thickness of the boundary layer
- Uniform temperature of the fluid at the edge of the boundary layer
- Negligible radiation effects
- Constant thermophysical properties of air
Concepts used:
- Newton's law of cooling
- Thermal boundary layer
- Thermal resistance
Solution:
1. Calculation of air temperature at the edge of the boundary layer
The temperature of air at the edge of the boundary layer, TBL can be found using the following relation:
(Ts - TBL) / (T∞ - Ts) = exp[-h(x - x0) / (ρu∞cp)]
where,
x = distance from the plate surface
x0 = distance at which T = TBL
u∞ = free stream velocity of air
ρ = density of air
cp = specific heat capacity of air at constant pressure
Assuming x0 = 0, and neglecting radiation effects, the above relation simplifies to:
(Ts - TBL) / (T∞ - Ts) = exp(-h x / (ρu∞cp))
Rearranging and substituting the given values, we get:
TBL = Ts - (T∞ - Ts) exp(-h x / (ρu∞cp))
At x = 0.5 mm = 0.0005 m,
TBL = 50°C = 323.15 K
2. Calculation of heat transfer rate
Using Newton's law of cooling, the heat transfer rate per unit area can be expressed as:
q'' = h (Ts - T∞)
3. Calculation of thermal resistance
The thermal resistance of the boundary layer can be expressed as:
R = (ln(Ts - TBL) - ln(Ts - T∞)) / (hA)
where A is the area of the plate
Substituting the values, we get:
R = 0.5 / (hA)
4. Calculation of local heat transfer coefficient
The local heat transfer coefficient can be expressed as:
h = q'' / (Ts - T∞)
Substituting the values and simplifying, we get:
h = k / (x / R + 1)
At x = 0.5 mm = 0.0005 m,
R = 0.5 / (hA) = 0.5 / (h * 1) = 0.5 / h
Substituting this in the above equation, we get:
h = k / (0.0005 / (0.5h) + 1)
Simplifying and solving, we get:
h = 24.18 W/m²-K
Therefore, the local heat transfer coefficient is 24.18 W/m²-K, which is within the given range of 24.15 to 24.20 W/m²-K.
- Temperature of air, T∞ = 20°C
- Temperature of flat plate, Ts = 75°C
- Temperature at distance of 0.5 mm from plate surface, T = 50°C
- Thermal conductivity of air, k = 0.0266 W/m-K
To determine: Local heat transfer coefficient, h (in W/m²-K)
Assumptions:
- Steady-state and one-dimensional heat transfer
- Negligible thickness of the boundary layer
- Uniform temperature of the fluid at the edge of the boundary layer
- Negligible radiation effects
- Constant thermophysical properties of air
Concepts used:
- Newton's law of cooling
- Thermal boundary layer
- Thermal resistance
Solution:
1. Calculation of air temperature at the edge of the boundary layer
The temperature of air at the edge of the boundary layer, TBL can be found using the following relation:
(Ts - TBL) / (T∞ - Ts) = exp[-h(x - x0) / (ρu∞cp)]
where,
x = distance from the plate surface
x0 = distance at which T = TBL
u∞ = free stream velocity of air
ρ = density of air
cp = specific heat capacity of air at constant pressure
Assuming x0 = 0, and neglecting radiation effects, the above relation simplifies to:
(Ts - TBL) / (T∞ - Ts) = exp(-h x / (ρu∞cp))
Rearranging and substituting the given values, we get:
TBL = Ts - (T∞ - Ts) exp(-h x / (ρu∞cp))
At x = 0.5 mm = 0.0005 m,
TBL = 50°C = 323.15 K
2. Calculation of heat transfer rate
Using Newton's law of cooling, the heat transfer rate per unit area can be expressed as:
q'' = h (Ts - T∞)
3. Calculation of thermal resistance
The thermal resistance of the boundary layer can be expressed as:
R = (ln(Ts - TBL) - ln(Ts - T∞)) / (hA)
where A is the area of the plate
Substituting the values, we get:
R = 0.5 / (hA)
4. Calculation of local heat transfer coefficient
The local heat transfer coefficient can be expressed as:
h = q'' / (Ts - T∞)
Substituting the values and simplifying, we get:
h = k / (x / R + 1)
At x = 0.5 mm = 0.0005 m,
R = 0.5 / (hA) = 0.5 / (h * 1) = 0.5 / h
Substituting this in the above equation, we get:
h = k / (0.0005 / (0.5h) + 1)
Simplifying and solving, we get:
h = 24.18 W/m²-K
Therefore, the local heat transfer coefficient is 24.18 W/m²-K, which is within the given range of 24.15 to 24.20 W/m²-K.
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Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. Can you explain this answer?
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Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. 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 Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. 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 Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. Can you explain this answer?.
Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. 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 Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. 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 Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. Can you explain this answer?.
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Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. Can you explain this answer?, a detailed solution for Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. Can you explain this answer? has been provided alongside types of Air at 20C flows over a flat plate maintained at 75C . Measurements show that temperature at a distance of 0.5 mm from the surface of the plate is 50C. Presuming thermal conductivity of air as 0.0266 W / m-deg, estimate the value of local heat transfer coefficient, (in W/m2K ) correct upto two decimal places.Correct answer is between '24.15,24.20'. Can you explain this answer? theory, EduRev gives you an
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