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# MCQs on Pohlhausen Equation

A small thermo-couple is positioned in a thermal boundary layer near a flat plate past which water flows at 30 degree Celsius and 0.15 m/s. The plate is heated to a surface temperature of 50 degree Celsius and at the location of the probe, the thickness is 15 mm. The probe is well-represented by

t – t S/t INFINITY – t S = 1.5 (y/δ) – 0.5 (y/δ) 3

Determine the heat transfer coefficient

a) 33.3 W/m2 K

b) 43.3 W/m2 K

c) 53.3 W/m2 K

d) 63.3 W/m2 K

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Answer: d

Explanation: h = Q/A (t INFINITY – t S) = 63.3 W/m2 K.

Air at 25 degree Celsius approaches a 0.9 m long and 0.6 m wide flat plate with a velocity 4.5 m/s. Let the plate is heated to a surface temperature of 135 degree Celsius. Find local heat transfer coefficient from the leading edge at a distance of 0.5 m

a) 5.83 W/m2 K

b) 6. 83 W/m2 K

c) 7. 83 W/m2 K

d) 8. 83 W/m2 K

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Answer: a

Explanation: h = Nu k/x = 5. 83 W/m2 K.

Consider the above problem, find the total rate of heat transfer from the plate to the air

a) 316.78 W

b) 416.78 W

c) 516.78 W

d) 616.78 W

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Answer: c

Explanation: Q = h A d t = 516.78 W.

A small thermo-couple is positioned in a thermal boundary layer near a flat plate past which water flows at 30 degree Celsius and 0.15 m/s. The plate is heated to a surface temperature of 50 degree Celsius and at the location of the probe, the thickness of thermal boundary layer is 15 mm. If the temperature profile as measured by the probe is well-represented by

t – t S/t INFINITY – t S = 1.5 (y/δ t) – 0.5 (y/δ t) 3

Determine the heat flux from plate to water

a) 266 W/m2

b) 1266 W/m2

c) 2266 W/m2

d) 3266 W/m2

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Answer: b

Explanation: Q/A = – k (t INFINITY – t S) d/d y [t – t S/t INFINITY – t S] Y = 0. So, heat flux = 1266 W/m2.

Atmospheric air at 30 degree Celsius temperature and free stream velocity of 2.5 m/s flows along the length of a flat plate maintained at a uniform surface temperature of 90 degree Celsius. Let length = 100 cm, width = 50 cm and thickness = 2.5 cm. Thermal conductivity of the plate material is 25 W/m K, find heat lost by the plate

a) 155.88 W

b) 165.88 W

c) 175.88 W

d) 185.88 W

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Answer: d

Explanation: Q = h A d t where, Nu = h l/k. So, Q = 185.88 W.

Consider the above problem, find the temperature of bottom surface of the plate for steady state condition

a) 90.372 degree Celsius

b) 80.372 degree Celsius

c) 70.372 degree Celsius

d) 60.372 degree Celsius

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Answer: a

Explanation: Q = – k A (t S – t B)/δ.

Ambient air at 20 degree Celsius flows past a flat plate with a sharp leading edge at 3 m/s. The plate is heated uniformly throughout its entire length and is maintained at a surface temperature of 40 degree Celsius. Calculate the distance from the leading edge at which the flow in the boundary layer changes from laminar to turbulent conditions. Assume that transition occurs at a critical Reynolds number of 500000

a) 4.67 m

b) 3.67 m

c) 2.67 m

d) 1.67 m

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Answer: c

Explanation: Re = x U INFINITY/v.

Ambient air at 20 degree Celsius flows past a flat plate with a sharp leading edge at 3 m/s. The plate is heated uniformly throughout its entire length and is maintained at a surface temperature of 40 degree Celsius. Calculate the thickness of the hydrodynamic boundary layer. Assume that transition occurs at a critical Reynolds number of 500000

a) 16.5 mm

b) 17.5 mm

c) 18.5 mm

d) 19.5 mm

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Answer: b

Explanation: Thickness = 4.64/ (Re) ½.

Ambient air at 20 degree Celsius flows past a flat plate with a sharp leading edge at 3 m/s. The plate is heated uniformly throughout its entire length and is maintained at a surface temperature of 40 degree Celsius. Calculate the thickness of the thermal boundary layer. Assume that transition occurs at a critical Reynolds number of 500000

a) 19.23 mm

b) 18.23 mm

c) 17.23 mm

d) 16.23 mm

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Answer: a

Explanation: Thickness = 0.976 (Thickness of hydrodynamic boundary layer)/ (Pr) 1/3.

Ambient air at 20 degree Celsius flows past a flat plate with a sharp leading edge at 3 m/s. The plate is heated uniformly throughout its entire length and is maintained at a surface temperature of 40 degree Celsius. Calculate the local convective heat transfer coefficient. Assume that transition occurs at a critical Reynolds number of 500000

a) 4.519 k J/m2 hr degree

b) 5.519 k J/m2 hr degree

c) 6.519 k J/m2 hr degree

d) 7.519 k J/m2 hr degree

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Answer: d

Explanation: h = Nu k/x.