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Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. The average Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within the temperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?
- a)0.5
- b)0.84
- c)1.19
- d)1.41
Correct answer is option 'C'. Can you explain this answer?
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Steam at 100oC is condensing on a vertical steel plate. The condensate...
We have average heat transfer coefficient for Laminar flow through vertical plate condensation as
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Steam at 100oC is condensing on a vertical steel plate. The condensate...
Given:
- Steam temperature (Ts) = 100°C
- Plate temperature (Tp1) = 100°C
- Plate temperature (Tp2) = 55°C
- Nusselt number at Tp1 (Nu1) = ?
- Nusselt number at Tp2 (Nu2) = ?
- The flow of condensate is laminar
- Physical properties of the fluid and steel remain constant within the temperature range of interest
To find: Ratio of Nu2/Nu1 using Nusselt equations for film-type condensation
Solution:
Nusselt equations for the film-type condensation are given as:
- Nu1 = 0.943 * (Gr * Pr)^0.25
- Nu2 = 0.943 * (Gr * Pr)^0.25
Where,
- Gr = Grashof number
- Pr = Prandtl number
For film-type condensation, Grashof number is given as:
- Gr = (gβΔT*L^3)/ν^2
Where,
- g = acceleration due to gravity = 9.81 m/s^2
- β = coefficient of thermal expansion = 1/Ts
- ΔT = temperature difference = Ts - Tp
- L = characteristic length = distance between the top and bottom of the plate
- ν = kinematic viscosity of fluid
Prandtl number is given as:
- Pr = ν/α
Where,
- α = thermal diffusivity of fluid
We can assume the fluid to be saturated steam, and its physical properties can be obtained from steam tables at 100°C.
- ν = 0.0268 * 10^-6 m^2/s
- α = 2.62 * 10^-5 m^2/s
At Tp1 = 100°C,
- ΔT1 = Ts - Tp1 = 0°C
- Gr1 = (gβΔT1*L^3)/ν^2 = 0
- Pr1 = ν/α = 1.02
Hence, Nu1 = 0.943 * (Gr1 * Pr1)^0.25 = 0.943 * (0 * 1.02)^0.25 = 0
At Tp2 = 55°C,
- ΔT2 = Ts - Tp2 = 45°C
- Gr2 = (gβΔT2*L^3)/ν^2 = 1.06 * 10^11
- Pr2 = ν/α = 1.02
Hence, Nu2 = 0.943 * (Gr2 * Pr2)^0.25 = 0.943 * (1.06 * 10^11 * 1.02)^0.25 = 39.4
Therefore, the ratio of Nu2/Nu1 = Nu2/0 = ∞
But in reality, we know that Nu1 cannot be zero. This is because film-type condensation does not occur when the plate temperature is equal to the saturation temperature of the fluid. Hence, we need to use a modified Nusselt equation that takes into account the fact that Nu1 cannot be zero.
One such modified equation is given as:
- Nu1 = 0.943 * (Gr1 * Pr1)^0.25 *
- Steam temperature (Ts) = 100°C
- Plate temperature (Tp1) = 100°C
- Plate temperature (Tp2) = 55°C
- Nusselt number at Tp1 (Nu1) = ?
- Nusselt number at Tp2 (Nu2) = ?
- The flow of condensate is laminar
- Physical properties of the fluid and steel remain constant within the temperature range of interest
To find: Ratio of Nu2/Nu1 using Nusselt equations for film-type condensation
Solution:
Nusselt equations for the film-type condensation are given as:
- Nu1 = 0.943 * (Gr * Pr)^0.25
- Nu2 = 0.943 * (Gr * Pr)^0.25
Where,
- Gr = Grashof number
- Pr = Prandtl number
For film-type condensation, Grashof number is given as:
- Gr = (gβΔT*L^3)/ν^2
Where,
- g = acceleration due to gravity = 9.81 m/s^2
- β = coefficient of thermal expansion = 1/Ts
- ΔT = temperature difference = Ts - Tp
- L = characteristic length = distance between the top and bottom of the plate
- ν = kinematic viscosity of fluid
Prandtl number is given as:
- Pr = ν/α
Where,
- α = thermal diffusivity of fluid
We can assume the fluid to be saturated steam, and its physical properties can be obtained from steam tables at 100°C.
- ν = 0.0268 * 10^-6 m^2/s
- α = 2.62 * 10^-5 m^2/s
At Tp1 = 100°C,
- ΔT1 = Ts - Tp1 = 0°C
- Gr1 = (gβΔT1*L^3)/ν^2 = 0
- Pr1 = ν/α = 1.02
Hence, Nu1 = 0.943 * (Gr1 * Pr1)^0.25 = 0.943 * (0 * 1.02)^0.25 = 0
At Tp2 = 55°C,
- ΔT2 = Ts - Tp2 = 45°C
- Gr2 = (gβΔT2*L^3)/ν^2 = 1.06 * 10^11
- Pr2 = ν/α = 1.02
Hence, Nu2 = 0.943 * (Gr2 * Pr2)^0.25 = 0.943 * (1.06 * 10^11 * 1.02)^0.25 = 39.4
Therefore, the ratio of Nu2/Nu1 = Nu2/0 = ∞
But in reality, we know that Nu1 cannot be zero. This is because film-type condensation does not occur when the plate temperature is equal to the saturation temperature of the fluid. Hence, we need to use a modified Nusselt equation that takes into account the fact that Nu1 cannot be zero.
One such modified equation is given as:
- Nu1 = 0.943 * (Gr1 * Pr1)^0.25 *
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Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. Can you explain this answer?
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Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. 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 Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. Can you explain this answer?.
Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. 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 Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. Can you explain this answer?.
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Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Steam at 100oC is condensing on a vertical steel plate. The condensate flow is laminar. Theaverage Nusselt numbers are Nu1 and Nu2, when the plate temperatures are 100 and 55o C.respectively. Assume the physical properties of the fluid and steel to remain constant within thetemperature range of interest. Using Nusselt equations for film-type condensation, what is the value of the ratio Nu2/Nu1 ?a)0.5b)0.84c)1.19d)1.41Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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