Heat Transfer Miscellaneous
Direction: An un-insulated air conditioning duct of rectangular cross section 1 m × 0.5 m, carrying air at 20°C with a velocity of 10 m/s, is exposed to an ambient of 30°C. Neglect the effect of duct construction material. For air in the range of 20 – 30°C, data is as follows: thermal conductivity = 0.025 W/mK; viscosity = 18 μPa.s; Prandtl number = 0.73; density =1.2 kg/m3. For laminar flow Nusselt number is 3.4 for constant wall temperature conditions and, for turbulent flow, Nu = 0.023 Re0.8Pr0.33
- The heat transfer per meter length of the duct, in watts, is
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As Re > 4000, the flow is turbulent
Nu = 0.023 Re0.8Pr0.33
hL/k = 0.023 × (4.44 × 105)0.8 × (0.73)0.33
h × 0.0667/0.25 = 683.173
h = 25.60 W/m2K
Surface area of duct
A = 2 × al + 2 × bl
where, l = length of duct
∴ A = 3l
Heat transfer rate, Q = h A(T0 – T)
Q = 25.60 × 3l × (30 – 20)
Q/l = 769WCorrect Option: D
As Re > 4000, the flow is turbulent
Nu = 0.023 Re0.8Pr0.33
hL/k = 0.023 × (4.44 × 105)0.8 × (0.73)0.33
h × 0.0667/0.25 = 683.173
h = 25.60 W/m2K
Surface area of duct
A = 2 × al + 2 × bl
where, l = length of duct
∴ A = 3l
Heat transfer rate, Q = h A(T0 – T)
Q = 25.60 × 3l × (30 – 20)
Q/l = 769W
- The Reynolds number for the flow is
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Lc = 4A = 4 × 1 × 0.5 = 0.666 D 2 × 1.5
Reynolds number,Re = ρLcV = 1.2 × 0.66 × 10 = 4.4 × 105 . μ 18 × 10-6 Correct Option: C
Lc = 4A = 4 × 1 × 0.5 = 0.666 D 2 × 1.5
Reynolds number,Re = ρLcV = 1.2 × 0.66 × 10 = 4.4 × 105 . μ 18 × 10-6
- Consider a laminar boundary layer over a heated flat plate. The free stream velocity is U∞. At some distance x from the leading edge the velocity boundary layer thickness is δv and the thermal boundary layer thickness is δT. If the Prandtl number is greater than 1, then
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Prandtl number = Molecular diffusivity of momentum Molecular diffusivity of heat
From question, since prandtl number > 1
∴ Velocity boundry thickness (δv) > thermal boundary thickness (δt)Correct Option: A
Prandtl number = Molecular diffusivity of momentum Molecular diffusivity of heat
From question, since prandtl number > 1
∴ Velocity boundry thickness (δv) > thermal boundary thickness (δt)
- For the three-dimensional object shown in the figure below, five faces are insulated. The sixth face (PQRS), which is not insulated, interacts thermally with the ambient, with a convective heat transfer coefficient of 10W/m2K. The ambient temperature is 30°C. Heat is uniformly generated inside the object at the rate of 100 W/m3. Assuming the face PQRS to be at uniform temperature, its steady state temperature is
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Given data;
ho = W/m2K
ho = 30 °C
qG = 100 W/m3
Volume, V = 2×1×2=4 m3
Heat generated, Q = qG × V = 100 × 4 = 400 W
Convection heat transfer from face PQRS,
Q = ho A (Ts – To)
400 = 10 × 2 × 2 (Ts – 30)
Ts = 40°CCorrect Option: D
Given data;
ho = W/m2K
ho = 30 °C
qG = 100 W/m3
Volume, V = 2×1×2=4 m3
Heat generated, Q = qG × V = 100 × 4 = 400 W
Convection heat transfer from face PQRS,
Q = ho A (Ts – To)
400 = 10 × 2 × 2 (Ts – 30)
Ts = 40°C
- Heat transfer coefficients for free convection in gases, forced convection in gases and vapours, and for boiling water lie, respectively, in the range of
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5-15; 20-200 and 3000-50000 W/m2K
Correct Option: A
5-15; 20-200 and 3000-50000 W/m2K