ENME3HM
Tutorial Problems: Free Convection
1)
A square plate 0.4m x 0.4m is maintained at a constant temperature of 400K. The plate is
positioned vertically in air of ambient temperature 300K.
a) Determine the boundary layer thickness as the heated air leaves the plate (x=0,4m)
b) Calculate ℎ̅ for free convection.
Given:
1
1
1
𝛿𝑥
−
= 0.393𝑃𝑟 −2 (0.952 + 𝑃𝑟)4 𝐺𝑟𝑥 4
𝑥
1
̅̅̅̅ = 0.518(𝐺𝑟𝐿 𝑃𝑟)4
𝑁𝑢
𝑃𝑟 = 0.7
𝜈 = 20.92 × 10−6 𝑚2 /𝑠
𝑘 = 30 × 10−3 𝑊/𝑚𝐾
(Answer: 1.5 mm and h=5.06 W/m2K)
2)
Consider a square plate 0.5m x 0.5m with one side insulated and the other maintained at
385K. The plate is in still air at 315K. For free convection calculate ℎ̅ for:
a) Horizontal plate face upwards
(Answer: 6.45 W/m2K)
b) Plate vertical
(Answer: 0.87 W/m2K)
c) Horizontal plate hot face downwards
(Answer: 2.84 W/m2K)
Use formulae of the form:
̅̅̅̅
𝑁𝑢 = 𝐶(𝐺𝑟𝐿 𝑃𝑟)𝑛
3)
A heating system consists of resistance wires, 0.5 mm in diameter, strung across an air duct. A
constant power supply is connected to the heating elements which dissipate heat at the rate
of 50 W/metre length. If the air velocity is 6 m/s and its incoming temperature is 15°C,
determine the wire temperature.
(Answer: Approx. 98°C)
If, due to control failure, the fan is shut off but the power supply to the wires remains on;
determine the approximate temperature the wires would reach if radiation is neglected.
(Note: although and accurate temperature is not required for this last part, the method of
obtaining a good answer must be made clear.)
(Answer: Approx. 442°C)
4)
Calculate the current that is drawn from a 220 Volt supply when an 8 mm tungsten rod is
maintained at 300°C in ambient air (26°C). The rod is held horizontally and is 0.6 m in length.
The following values of viscosity, conductivity and Prandtl number are obtained for the film
temperature.
𝑃𝑟 = 0.687
𝜈 = 30.73 × 10−6 𝑚2 /𝑠
𝑘 = 36.69 × 10−3 𝑊/𝑚𝐾
𝐺𝑟
Comment briefly on the physical significance of the following: 𝑅𝑒 2 and 𝐺𝑟𝑃𝑟.
(Answer: 0.314A)
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