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Estimate the heat transfer from a 40 W incandescent bulb at 125 degree Celsius to 25 degree Celsius in quiescent air. Approximate the bulb as a 50 mm diameter sphere. The approximate correlation for the convection coefficient is
Nu = 0.60 (Gr Pr) 0.25
Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the sphere
Nu = 0.60 (Gr Pr) 0.25
Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the sphere
- a)4.71 W
- b)5.71 W
- c)6.71 W
- d)7.71 W
Correct answer is option 'D'. Can you explain this answer?
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Estimate the heat transfer from a 40 W incandescent bulb at 125 degree...
Explanation: Q = h A d t = 7.71 W.
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Estimate the heat transfer from a 40 W incandescent bulb at 125 degree...
Estimation of Heat Transfer from Incandescent Bulb
Given parameters:
- Power of bulb (P) = 40 W
- Temperature of bulb (T1) = 125°C
- Temperature of air (T2) = 25°C
- Diameter of bulb (D) = 50 mm
Step 1: Calculation of Grashof Number (Gr)
Gr = (gβΔT D^3)/(ν^2)
where,
g = acceleration due to gravity = 9.81 m/s^2
β = coefficient of thermal expansion of air = 1/T1
ΔT = temperature difference = T1 - T2
ν = kinematic viscosity of air at mean film temperature
D = diameter of bulb
Assuming the mean film temperature to be (T1 + T2)/2 = 75°C, we can calculate the kinematic viscosity of air using the Sutherland's equation:
ν = (1.458e-6 T^1.5)/(T + 110.4)
where T is the absolute temperature in Kelvin
ν = (1.458e-6 * 348.15^1.5)/(348.15 + 110.4) = 1.321e-5 m^2/s
Substituting the values in the Grashof number equation:
Gr = (9.81 * 1/T1 * (125 - 25) * (0.05)^3)/(1.321e-5)^2
Gr = 1.84e+11
Step 2: Calculation of Prandtl Number (Pr)
Pr = ν/α
where α is the thermal diffusivity of air at mean film temperature
Using the Sutherland's equation for α:
α = (1.83e-5 * T^1.5)/(T + 120)
where T is the absolute temperature in Kelvin
α = (1.83e-5 * 348.15^1.5)/(348.15 + 120) = 2.23e-5 m^2/s
Substituting the values in the Prandtl number equation:
Pr = 1.321e-5/2.23e-5
Pr = 0.593
Step 3: Calculation of Nusselt Number (Nu)
Nu = 0.60 * (Gr Pr)^0.25
Substituting the values:
Nu = 0.60 * (1.84e+11 * 0.593)^0.25
Nu = 71.46
Step 4: Calculation of Heat Transfer Coefficient (h)
h = Nu * k/D
where k is the thermal conductivity of air at mean film temperature
Using the Sutherland's equation for k:
k = (2.44e-2 * T^1.5)/(T + 273)
where T is the absolute temperature in Kelvin
k = (2.44e-2 * 348.15^1.5)/(348.15 + 273) = 2.07e-2 W/(m K)
Substituting the values in the heat transfer coefficient equation:
h = 71.46 * 2.07e-2/0.05
h = 29.50 W/(m^2 K)
Step 5: Calculation of Heat
Given parameters:
- Power of bulb (P) = 40 W
- Temperature of bulb (T1) = 125°C
- Temperature of air (T2) = 25°C
- Diameter of bulb (D) = 50 mm
Step 1: Calculation of Grashof Number (Gr)
Gr = (gβΔT D^3)/(ν^2)
where,
g = acceleration due to gravity = 9.81 m/s^2
β = coefficient of thermal expansion of air = 1/T1
ΔT = temperature difference = T1 - T2
ν = kinematic viscosity of air at mean film temperature
D = diameter of bulb
Assuming the mean film temperature to be (T1 + T2)/2 = 75°C, we can calculate the kinematic viscosity of air using the Sutherland's equation:
ν = (1.458e-6 T^1.5)/(T + 110.4)
where T is the absolute temperature in Kelvin
ν = (1.458e-6 * 348.15^1.5)/(348.15 + 110.4) = 1.321e-5 m^2/s
Substituting the values in the Grashof number equation:
Gr = (9.81 * 1/T1 * (125 - 25) * (0.05)^3)/(1.321e-5)^2
Gr = 1.84e+11
Step 2: Calculation of Prandtl Number (Pr)
Pr = ν/α
where α is the thermal diffusivity of air at mean film temperature
Using the Sutherland's equation for α:
α = (1.83e-5 * T^1.5)/(T + 120)
where T is the absolute temperature in Kelvin
α = (1.83e-5 * 348.15^1.5)/(348.15 + 120) = 2.23e-5 m^2/s
Substituting the values in the Prandtl number equation:
Pr = 1.321e-5/2.23e-5
Pr = 0.593
Step 3: Calculation of Nusselt Number (Nu)
Nu = 0.60 * (Gr Pr)^0.25
Substituting the values:
Nu = 0.60 * (1.84e+11 * 0.593)^0.25
Nu = 71.46
Step 4: Calculation of Heat Transfer Coefficient (h)
h = Nu * k/D
where k is the thermal conductivity of air at mean film temperature
Using the Sutherland's equation for k:
k = (2.44e-2 * T^1.5)/(T + 273)
where T is the absolute temperature in Kelvin
k = (2.44e-2 * 348.15^1.5)/(348.15 + 273) = 2.07e-2 W/(m K)
Substituting the values in the heat transfer coefficient equation:
h = 71.46 * 2.07e-2/0.05
h = 29.50 W/(m^2 K)
Step 5: Calculation of Heat
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Estimate the heat transfer from a 40 W incandescent bulb at 125 degree Celsius to 25 degree Celsius in quiescent air. Approximate the bulb as a 50 mm diameter sphere. The approximate correlation for the convection coefficient isNu = 0.60 (Gr Pr)0.25Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the spherea)4.71 Wb)5.71 Wc)6.71 Wd)7.71 WCorrect answer is option 'D'. Can you explain this answer?
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Estimate the heat transfer from a 40 W incandescent bulb at 125 degree Celsius to 25 degree Celsius in quiescent air. Approximate the bulb as a 50 mm diameter sphere. The approximate correlation for the convection coefficient isNu = 0.60 (Gr Pr)0.25Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the spherea)4.71 Wb)5.71 Wc)6.71 Wd)7.71 WCorrect answer is option 'D'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about Estimate the heat transfer from a 40 W incandescent bulb at 125 degree Celsius to 25 degree Celsius in quiescent air. Approximate the bulb as a 50 mm diameter sphere. The approximate correlation for the convection coefficient isNu = 0.60 (Gr Pr)0.25Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the spherea)4.71 Wb)5.71 Wc)6.71 Wd)7.71 WCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Estimate the heat transfer from a 40 W incandescent bulb at 125 degree Celsius to 25 degree Celsius in quiescent air. Approximate the bulb as a 50 mm diameter sphere. The approximate correlation for the convection coefficient isNu = 0.60 (Gr Pr)0.25Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the spherea)4.71 Wb)5.71 Wc)6.71 Wd)7.71 WCorrect answer is option 'D'. Can you explain this answer?.
Estimate the heat transfer from a 40 W incandescent bulb at 125 degree Celsius to 25 degree Celsius in quiescent air. Approximate the bulb as a 50 mm diameter sphere. The approximate correlation for the convection coefficient isNu = 0.60 (Gr Pr)0.25Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the spherea)4.71 Wb)5.71 Wc)6.71 Wd)7.71 WCorrect answer is option 'D'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about Estimate the heat transfer from a 40 W incandescent bulb at 125 degree Celsius to 25 degree Celsius in quiescent air. Approximate the bulb as a 50 mm diameter sphere. The approximate correlation for the convection coefficient isNu = 0.60 (Gr Pr)0.25Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the spherea)4.71 Wb)5.71 Wc)6.71 Wd)7.71 WCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Estimate the heat transfer from a 40 W incandescent bulb at 125 degree Celsius to 25 degree Celsius in quiescent air. Approximate the bulb as a 50 mm diameter sphere. The approximate correlation for the convection coefficient isNu = 0.60 (Gr Pr)0.25Where the different parameters are evaluated at the mean film temperature, and characteristics length is the diameter of the spherea)4.71 Wb)5.71 Wc)6.71 Wd)7.71 WCorrect answer is option 'D'. Can you explain this answer?.
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