While solving the following problems, you should find missing material properties from
textbooks or other sources. In the problems, values of the nCand is your candidate number,
for example, a candidate number is 188888, (nCand/100) =1888.88.
You must use Word to prepare your report including diagrams and working. You will lose
marks without the working being shown in the report.
2
Problem 1 [15 Marks]
An electrically heated thin foil of length L = (nCand/10000)mm and width W = 8mm is used
as a wind speed meter. The foil is heated by an electric heater �̇ (Watts) and dissipates this
heat into the wind at both sides of the foil. To calibrate the speed meter, wind is blown parallel
to the longest side of the foil with a temperature T∞ = 10°C and velocity U∞ = 30m/s. The
surface temperature of the foil is measured, it can be assumed to be constant at Ts = 44 °C.
The local Nusselt number for turbulent flow 10% > �� > 5 × 10+
��. = 0.0296��6
7��.
8
9
when 60>Pr > 0.6
The local Nusselt number for laminar flow �� < 5 × 10+
��. = 0.332��6
7��.

6

when Pr > 0.6
i) Estimate the heat transfer rate by radiation.
ii) Estimate the dissipating power �̇
.
Problem 2 [15 Marks]
A composite plane wall is manufactured from two layers of different materials: A and B, as
shown in Fig 1. The layer of material A has thickness LA = 40mm and the conductivity
coefficient kA = 75W/mK, and wall material B has thickness LB = 20mm and kB= 150W/mK.
The uniform heat is generated in material B with the rate of energy generation: �̇
?_A =
1.5 × 10BW/m3
. The inner surface of the material A is well insulated, while the outer surface
of material B is cooled by a water stream with temperature T¥ = 20°C and convective heat
transfer coefficient h = (nCand/100)W/m2K.
i) Determine the temperature of the material A and the temperature (T2) of the cooled
surface.
ii) Sketch the temperature distribution over the wall thickness under steady-state
conditions.
Fig. 1 Composite wall
A B
40mm 20mm
Insulated
T0 T1 T2 Water T¥ =20°C
x
LA LB
3
Problem 3 [15 Marks]
Cylindrical fins are to be designed and used on an electronics heat sink. The fins are attached
to a square surface 15 ´ 15mm of the heat sink and its surface temperature is 65°C. The fins
are required to dissipate 0.6 W of heat by convection to the surrounding air which is at 25°C.
Each fin is made from aluminium (k = 180W/mK), the tip of each fin may be assumed to be
adiabatic and a convection heat transfer coefficient over the surfaces is h = 20W/m2
K.
i) Design the diameter and length of the fin, and estimate the number of fins required.
ii) Sketch the layout of the fins on the heat sink surface.
Problem 4 [15 Marks]
A cylindrical furnace shown in Fig. 2 has 0.7m diameter, and 0.35m height, it is open at one
end to large surroundings at 310 K. All surfaces of the furnace (the sides and the bottom) are
well insulated and may be assumed as black body. The cylindrical surface is at temperature of
1000K and the bottom is (nCand/100)K.
i) Determine the heat loss from the furnace to the surroundings, ignoring the heat transfer
by convection.
ii) If the side surface is a grey body, show how to determine the heat loss from the furnace
to the surroundings.
Fig. 2 Cylindrical furnace
Problem 5 [10 Marks]
A special freezer is designed to operate with an internal air temperature of (nCand/1000)K,
when the external air temperature is 300K and the internal and external convection heat transfer
coefficients are 10W/m2
K and 12W/m2K, respectively. The walls of the freezer are of
composite construction, comprising an inner layer of plastic (k = 1W/mK, and thickness of
4mm), and an outer layer of stainless steel (thickness of 1mm). Sandwiched between these two
layers is a layer of insulation material with k = 0.05W/mK.
i) Find the minimum thickness of insulation that is required to reduce the convective heat
loss to 10W/m2.
ii) Suggest two practical methods of reducing the thickness of the wall while reducing the
convective heat loss to 10W/m2
, demonstrate them by calculations.
Side T1=1000 K
Bottom T2=(nCand/100) K
D = 0.7 m
h = 0.35 m
Top T3=310 K
4
Problem 6 [10 Marks]
A very long copper wire has a diameter of (nCand/10000)mm, is exposed to a wind at a
temperature of 30°C. After 10s, the average temperature of the wire increased from 10 to 25°C.
i) Estimate the convective heat transfer coefficient.
ii) Assuming the estimated convective heat transfer coefficient is constant, determine the
temperature of the copper wire after further 10s.
iii) Assess and discuss the rate of the temperature variation over time for the copper wire.
Problem 7 [10 Marks]
A carbon steel pipe of inside and outside radii 0.05m and 0.08m respectively, is heated in a
such way that its inner and outer surfaces have uniform temperatures (nCand/1000)°C and
10°C.
i) Determine the temperature at the points where the radius is 0.06m.
ii) Determine the heat transfer rate of the pipe of unit length.
iii) Discuss how to determine the critical radius of insulation in order to reduce the heat
loss from the pipe by wrapping it using insulation materials.
Presentation of the report [10 Marks]

Sample Solution

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