Assignment 2
1. A 2-m × 3-m flat plate is suspended in a room and is subjected to airflow parallel to its surfaces
along its 3-m-long side. The free stream temperature and velocity of air are 20 °C and 7 m/s.
The total drag force acting on the plate is measured to be 0.86 N. Determine the average
convection heat transfer coefficient for the plate.
The properties of air at 20°C and 1 atm are:
𝜌 =1.204 kg/m3, Cp=1.007 kJ/kg K, Pr = 0.7309
2. The forming section of a plastics plant puts out a continuous sheet of plastic that is 4 ft wide
and 0.04 in. thick at a velocity of 30 ft/min. The temperature of the plastic sheet is 200 °F when
it is exposed to the surrounding air, and a 2-ft-long section of the plastic sheet is subjected to
airflow at 80 °F at a velocity of 10 ft/s on both sides along its surfaces normal to the direction
of motion of the sheet, as shown in Figure. Determine (a) the rate of heat transfer from the
plastic sheet to the air by forced convection and radiation and (b) the temperature of the plastic
sheet at the end of the cooling section. Take the density, specific heat, and emissivity of the
plastic sheet to be 𝜌 = 75 lbm/ft3, Cp = 0.4 Btu/lbm · °F, and 𝜖 = 0.9.
𝑘 = 0.1623𝐵𝑡𝑢/(ℎ. 𝑓𝑡. ℉); Pr= 0.7202; 𝜗 = 0.204 × 10−3 𝑓𝑡 2 /𝑠
3. Water enters a 2.5 cm-internal-diameter thin copper tube of a heat exchanger at 15 °C at a rate
of 0.3 kg/s, and is heated by steam condensing outside at 120 °C. If the average heat transfer
coefficient is 800 W/m2.K, determine the length of the tube required in order to heat the water
to 115 °C. Data: , Cp = 4187 J/kg.K
4. Consider the flow of oil at 20 °C in a 30-cm-diameter pipeline at an average velocity of 2 m/s.
A 200-m-long section of the horizontal pipeline passes through icy waters of a lake at 0 °C.
Measurements indicate that the surface temperature of the pipe is very nearly 0 °C.
Disregarding the thermal resistance of the pipe material, determine,
i.
The temperature of the oil when the pipe leaves the lake
ii.
The rate of heat transfer from the oil, and
iii.
The pumping power required to overcome the pressure losses and to maintain the flow
of the oil in the pipe
Data: 𝜌 = 888.1 kg/m3, Cp = 4187 J/kg.K ; 𝑘 = 0.145𝑊/(𝑚. 𝐾) Pr= 10863;
𝜗 = 9.429 × 10−4 𝑚2 /𝑠
5. A 6-m-long section of an 8-cm-diameter horizontal hot water pipe passes through a large room
whose temperature is 20 °C. If the outer surface temperature of the pipe is 70 °C, determine
the rate of heat loss from the pipe by natural convection.
Data: 𝑘 = 0.02699 𝑊/(𝑚. 𝐾); Pr = 0.7241; 𝜗 = 1.750 ×
10−5 𝑚2
𝑠
1
; 𝛽 = 318 𝐾 −1
6. Using dimensional analysis obtain a correlation for free convection. The physical parameters
involved are:
i.
A length parameter,
ii.
Density
iii.
Specific heat
iv.
Thermal conductivity
v.
Viscosity
vi.
Coefficient of cubical expansion
vii.
Temperature difference
viii.
gravitational acceleration
ix.
Convection heat transfer coefficient
7. Air at 1 atm pressure flows over a plate 0.5 long with a free stream velocity of 5 m/s. The film
temperature is 60°C. If the friction coefficient on the plate is found as 3.68 ×10–3 for one side,
determine the average convective heat transfer coefficient.
8. A vertical plate 0.80 m high and 1 m wide is maintained at 35°C in still air at 25°C. Determine
the value of the average convection coefficient.
Data: The property values are evaluated at (25 + 35)/2 = 30°C with usual units
ρ = 1.165; v = 16 × 10–6 ; Pr = 0.701; k = 0.02675; β = 1/303
9. Water in a tank is heated by a horizontal steam pipe of 0.25 m diameter, maintained at 60°C.
The water is at 20°C. Calculate the value of the convective heat transfer coefficient. The
property values are: ρ = 995; ν = 0.657 × 10–6 m2/s, Pr = 4.34, k = 0.628 W/m2 K; β = 0.41 ×
10–3/K
10. Water in a tank is heated by a horizontal steam pipe of 0.5 m dia, maintained at 60°C. The
water is at 20°C. Calculate the value of the convective heat transfer coefficient (in 𝑊 ⁄𝑚2 . 𝐾 )
using the following correlation:
0.518(𝐺𝑟 𝑃𝑟)0.25
𝑁𝑢 = 0.36 +
[1 + (0.559⁄𝑃𝑟)9⁄16 ]4⁄9
The property values are: 𝜗 = 0.657 × 10−6 𝑚2 ⁄𝑠; 𝑃𝑟 = 4.34; 𝑘 = 0.628 𝑊 ⁄𝑚. 𝐾
𝛽 = 0.41 × 10−3 𝐾 −1