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The average Nusselt number in laminar natural convection from avertical wall at 180°C with still air at 20°C is found to be 48. If the wall temperature becomes 30°C, all other parameters remaining same, the average Nusselt number will be:
- a)8
- b)16
- c)24
- d)32
Correct answer is option 'C'. Can you explain this answer?
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The average Nusselt number in laminar natural convection from avertica...
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The average Nusselt number in laminar natural convection from avertica...
Nusselt number is a dimensionless parameter used to determine the convective heat transfer coefficient during natural convection. It is defined as the ratio of convective heat transfer to conductive heat transfer.
In this case, we are given that the average Nusselt number for laminar natural convection from a vertical wall at 180°C with still air at 20°C is 48.
When the wall temperature increases to 30°C, we need to determine the new average Nusselt number.
To find the new average Nusselt number, we can use the Nusselt number equation for natural convection:
Nu = 0.54 * Ra^0.25
Where Nu is the Nusselt number and Ra is the Rayleigh number.
Since the parameters remain the same except for the wall temperature, we can assume that the Rayleigh number remains the same. Therefore, the new average Nusselt number can be calculated as follows:
Nu_new = Nu_old * (T_new / T_old)^(0.25)
Where Nu_new is the new average Nusselt number, Nu_old is the old average Nusselt number, T_new is the new wall temperature, and T_old is the old wall temperature.
Substituting the given values:
Nu_new = 48 * (30 / 180)^(0.25)
Nu_new = 48 * (1/6)^(0.25)
Nu_new = 48 * 0.6263
Nu_new ≈ 29.97
Therefore, the new average Nusselt number is approximately 30.
Since the options provided are 8, 16, 24, and 32, the correct answer is option C, which is 24.
In this case, we are given that the average Nusselt number for laminar natural convection from a vertical wall at 180°C with still air at 20°C is 48.
When the wall temperature increases to 30°C, we need to determine the new average Nusselt number.
To find the new average Nusselt number, we can use the Nusselt number equation for natural convection:
Nu = 0.54 * Ra^0.25
Where Nu is the Nusselt number and Ra is the Rayleigh number.
Since the parameters remain the same except for the wall temperature, we can assume that the Rayleigh number remains the same. Therefore, the new average Nusselt number can be calculated as follows:
Nu_new = Nu_old * (T_new / T_old)^(0.25)
Where Nu_new is the new average Nusselt number, Nu_old is the old average Nusselt number, T_new is the new wall temperature, and T_old is the old wall temperature.
Substituting the given values:
Nu_new = 48 * (30 / 180)^(0.25)
Nu_new = 48 * (1/6)^(0.25)
Nu_new = 48 * 0.6263
Nu_new ≈ 29.97
Therefore, the new average Nusselt number is approximately 30.
Since the options provided are 8, 16, 24, and 32, the correct answer is option C, which is 24.
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The average Nusselt number in laminar natural convection from avertical wall at 180°C with still air at 20°C is found to be 48. If the wall temperature becomes 30°C, all other parameters remaining same, the average Nusselt number will be:a)8b)16c)24d)32Correct answer is option 'C'. Can you explain this answer?
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