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The effect of following conditions on the average value of heat transfer coefficient in flow through a tube:
(i) two-fold increase in flow velocity by varying mass flow rate;
(ii) two-fold increase in the diameter of tube, the flow velocity is maintained constant by a change in the rate of liquid flow It may be presumed that there is no change in the temperatures of the liquid and the tube wall, and that the flow through the tube is turbulent in character.
Given Nu = 0.023 Re0.8 Pr0.4
(i) two-fold increase in flow velocity by varying mass flow rate;
(ii) two-fold increase in the diameter of tube, the flow velocity is maintained constant by a change in the rate of liquid flow It may be presumed that there is no change in the temperatures of the liquid and the tube wall, and that the flow through the tube is turbulent in character.
Given Nu = 0.023 Re0.8 Pr0.4
- a)74% increase & 13% increase
- b)74% increase & 13% decrease
- c)74% decrease & 13% increase
- d)74% decrease & 13% decrease
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The effect of following conditions on the average value of heat transf...
In case of turbulent flow through a tube, the average value of heat transfer coefficient is prescribed by the relation
Further as there is no change in the temperatures, the fluid properties remain constant.
(i) When the tube diameter and the fluid properties remain constant
That is, a two-fold increase in the flow velocity results into 74.1% increase in heat transfer.
(ii) when the flow velocity and the fluid properties remain unchanged
That is, with two-fold increase in tube diameter, the heat transfer decreases by 13%.
Further as there is no change in the temperatures, the fluid properties remain constant.
(i) When the tube diameter and the fluid properties remain constant
That is, a two-fold increase in the flow velocity results into 74.1% increase in heat transfer.
(ii) when the flow velocity and the fluid properties remain unchanged
That is, with two-fold increase in tube diameter, the heat transfer decreases by 13%.
Most Upvoted Answer
The effect of following conditions on the average value of heat transf...
In case of turbulent flow through a tube, the average value of heat transfer coefficient is prescribed by the relation
Further as there is no change in the temperatures, the fluid properties remain constant.
(i) When the tube diameter and the fluid properties remain constant
That is, a two-fold increase in the flow velocity results into 74.1% increase in heat transfer.
(ii) when the flow velocity and the fluid properties remain unchanged
That is, with two-fold increase in tube diameter, the heat transfer decreases by 13%.
Further as there is no change in the temperatures, the fluid properties remain constant.
(i) When the tube diameter and the fluid properties remain constant
That is, a two-fold increase in the flow velocity results into 74.1% increase in heat transfer.
(ii) when the flow velocity and the fluid properties remain unchanged
That is, with two-fold increase in tube diameter, the heat transfer decreases by 13%.
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Community Answer
The effect of following conditions on the average value of heat transf...
To determine the effect of the given conditions on the average value of the heat transfer coefficient, we need to analyze the Nusselt number equation.
The Nusselt number (Nu) is given by the equation:
Nu = 0.023 * Re^0.8 * Pr^0.4
Where:
Nu = Nusselt number
Re = Reynolds number
Pr = Prandtl number
Let's analyze each condition separately:
(i) Two-fold increase in flow velocity by varying mass flow rate:
In this case, the flow velocity is increased by two-fold while maintaining the same diameter of the tube.
Reynolds number (Re) is given by the equation:
Re = (ρ * V * D) / μ
Where:
ρ = density of the fluid
V = velocity of the fluid
D = diameter of the tube
μ = dynamic viscosity of the fluid
Since the flow velocity is increased by two-fold, the Reynolds number will also increase by two-fold, assuming all other parameters remain constant.
Therefore, the Nusselt number equation becomes:
Nu = 0.023 * (2*Re)^0.8 * Pr^0.4
Simplifying the equation:
Nu = 0.023 * 2^0.8 * Re^0.8 * Pr^0.4
Nu = 0.023 * 1.6818 * Re^0.8 * Pr^0.4
Nu = 0.039 * Re^0.8 * Pr^0.4
The new Nusselt number is 0.039 times the original Nusselt number.
To calculate the percentage increase in the average value of the heat transfer coefficient, we can use the following formula:
Percentage increase = (New Nu - Old Nu) / Old Nu * 100
Percentage increase = (0.039 - 0.023) / 0.023 * 100
Percentage increase = 69.57%
Therefore, the average value of the heat transfer coefficient increases by 69.57% when there is a two-fold increase in flow velocity by varying mass flow rate.
(ii) Two-fold increase in the diameter of the tube, the flow velocity is maintained constant by a change in the rate of liquid flow:
In this case, the diameter of the tube is increased by two-fold while maintaining the same flow velocity.
Since the flow velocity is constant, the Reynolds number remains the same.
The Nusselt number equation remains the same:
Nu = 0.023 * Re^0.8 * Pr^0.4
Therefore, there is no change in the average value of the heat transfer coefficient when there is a two-fold increase in the diameter of the tube while maintaining a constant flow velocity.
In conclusion:
(a) The average value of the heat transfer coefficient increases by 69.57% when there is a two-fold increase in flow velocity by varying mass flow rate.
(b) There is no change in the average value of the heat transfer coefficient when there is a two-fold increase in the diameter of the tube while maintaining a constant flow velocity.
The Nusselt number (Nu) is given by the equation:
Nu = 0.023 * Re^0.8 * Pr^0.4
Where:
Nu = Nusselt number
Re = Reynolds number
Pr = Prandtl number
Let's analyze each condition separately:
(i) Two-fold increase in flow velocity by varying mass flow rate:
In this case, the flow velocity is increased by two-fold while maintaining the same diameter of the tube.
Reynolds number (Re) is given by the equation:
Re = (ρ * V * D) / μ
Where:
ρ = density of the fluid
V = velocity of the fluid
D = diameter of the tube
μ = dynamic viscosity of the fluid
Since the flow velocity is increased by two-fold, the Reynolds number will also increase by two-fold, assuming all other parameters remain constant.
Therefore, the Nusselt number equation becomes:
Nu = 0.023 * (2*Re)^0.8 * Pr^0.4
Simplifying the equation:
Nu = 0.023 * 2^0.8 * Re^0.8 * Pr^0.4
Nu = 0.023 * 1.6818 * Re^0.8 * Pr^0.4
Nu = 0.039 * Re^0.8 * Pr^0.4
The new Nusselt number is 0.039 times the original Nusselt number.
To calculate the percentage increase in the average value of the heat transfer coefficient, we can use the following formula:
Percentage increase = (New Nu - Old Nu) / Old Nu * 100
Percentage increase = (0.039 - 0.023) / 0.023 * 100
Percentage increase = 69.57%
Therefore, the average value of the heat transfer coefficient increases by 69.57% when there is a two-fold increase in flow velocity by varying mass flow rate.
(ii) Two-fold increase in the diameter of the tube, the flow velocity is maintained constant by a change in the rate of liquid flow:
In this case, the diameter of the tube is increased by two-fold while maintaining the same flow velocity.
Since the flow velocity is constant, the Reynolds number remains the same.
The Nusselt number equation remains the same:
Nu = 0.023 * Re^0.8 * Pr^0.4
Therefore, there is no change in the average value of the heat transfer coefficient when there is a two-fold increase in the diameter of the tube while maintaining a constant flow velocity.
In conclusion:
(a) The average value of the heat transfer coefficient increases by 69.57% when there is a two-fold increase in flow velocity by varying mass flow rate.
(b) There is no change in the average value of the heat transfer coefficient when there is a two-fold increase in the diameter of the tube while maintaining a constant flow velocity.
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The effect of following conditions on the average value of heat transfer coefficient in flow through a tube:(i) two-fold increase in flow velocity by varying mass flow rate;(ii) two-fold increase in the diameter of tube, the flow velocity is maintained constant by a change in the rate of liquid flow It may be presumed that there is no change in the temperatures of the liquid and the tube wall, and that the flow through the tube is turbulent in character.GivenNu = 0.023 Re0.8 Pr0.4a)74% increase & 13% increaseb)74% increase & 13% decreasec)74% decrease & 13% increased)74% decrease & 13% decreaseCorrect answer is option 'B'. Can you explain this answer?
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