SECTION A (50%)
●
: Section A and Section B.
1. The final treatment of a novel polymer material requires holding the material
above a temperature of 100°C for 5 minutes. This is achieved by suspending
the polymer rod in a moving airstream that has a free air temperature of
150°C. The rod is held vertically, with the air stream moving horizontally.
There are two sections
The air velocity is 10m/s. The polymer rod has a diameter of 5cm and a length
of 2m. Physical properties are shown in the table below.
Material
Air
Air
Property
Density
Specific heat capacity
Polymer
Thermal conductivity
Polymer Specific heat capacity
Polymer Density
a) Sketch a suitable arrangement including a heating element.
Value
1.16 kg/m³
1006 J/kgK
11.0 W/mK
1200 J/kgK
1500 kg/m³
[3 marks]
b) Using a value of the heat transfer coefficient of 80 W/m°K, and taking care
to justify the approach you adopt, calculate the total time required to heat-
treat the sample.
i.
ii.
[6 marks]
c) Further study of the novel polymer suggests that the polymer should
remain below a temperature of 135°C to minimise reduction in the
structural strength of the polymer. Demonstrate whether this criterion is
met or not.
[6 marks]
d) One of the engineering team working with you on this project proposes a
reduction in the heated free air temperature to 110°C to save energy.
Assess this proposal in terms of:
Page 2 of 15
The total cycle time for treatment of one rod
The relative energy cost when compared to the original condition of
using heated air at 150°C.
Note that the air is heated from an ambient temperature of 20°C and
assume all properties of the gas (except the free air temperature) remain
constant.
Consequently, provide an informed response to the engineer's suggestion.
[10 marks]
Ref: ME20214G74-2
Turn the page over Module Code: MECH267001
2. Biogas is produced through anaerobic digestion of waste food. It has a
composition of 80% methane and 20% carbon dioxide (by volume). The
biogas is burned stoichiometrically in air (of composition 21% oxygen and
79% nitrogen by volume) with the flame used to heat a tube containing flowing
water. The biogas has an initial temperature of 25°C and the combustion
gases exit from the burner at 102°C.
a) Write a stoichiometric equation for the combustion of methane in air, and
then adapt it for burning the biogas in air, assuming products are carbon
dioxide, water, nitrogen only.
[5 marks]
b) Calculate the mass flowrate of air for the complete combustion of 1 kg/s of
biogas. Molecular weights of appropriate elements and compounds can be
found on page 9.
[5 marks]
c) From considering the combustion of the biogas, show that an energy
transfer takes place of 35.5 kJ per kg of biogas that is burned.
[5 marks]
d) After heating, in the burner, the hot water passes through a shell and tube
heat exchanger and is used to heat an oil flow. The water from the shell
and tube heat exchanger passes directly back to the burner at 20°C.
The flowrate of biogas into the combustor is 50 kg/s.
Water enters the burner with a flow rate of 7kg/s at a temperature of 20˚C.
Oil enters the shell and tube heat exchanger at a flow rate of 37.5 kg/s at a
temperature of -5°C.
i.
ii.
Sketch the arrangement
Calculate the surface area of the heat exchanger, given an overall
heat transfer coefficient of 750 W/m² K
Take heat capacities as water 4.2 kJ/kgK oil 1.6 kJ/kgK
Page 3 of 15
[10 marks]
Ref: ME20214G74-2
Turn the page over Module Code: MECH267001
SECTION B (50%)
Water with a density of 1000 kg/m³ and dynamic viscosity of 1.0 x 10-³ Pa.s flows
under gravity from a reservoir through a galvanized iron pipe with an equivalent
roughness of 0.15mm at a flow rate of 600 litres per minute into the local
atmosphere. The flow path comprises a sharp edged entrance from the reservoir
into the pipe (loss factor (K₁) of 0.5, based on average outlet velocity), a 4m
horizontal length of the galvanized pipe of 80mm internal diameter, a fully open
gate valve (KL = 0.15, based on average inlet velocity) and a 6m horizontal length
of the galvanised pipe of 40mm internal diameter. There is no fitting or restriction
at the outlet of the pipe into the local atmosphere and so no additional minor head
loss. The liquid surface of the reservoir is exposed to the local atmosphere.
a)
3.
Sketch the system and calculate the mean velocity and the Reynolds
number of the flow in the two different pipe sections and state whether the
flow is laminar or turbulent in each.
[6 marks]
Determine the height of water in the reservoir required above the sharp
edged entrance into the pipe to achieve the required flow rate. Note, the
major and minor head losses can be summed in this flow path, like resistors
in series, and the general equation for energy conservation in pipes
compares the pressures at the inlet and outlet of the system only.
[10 marks]
c)
The gate valve is replaced by a fully open globe valve (K₁ = 10, based on
average inlet velocity). Determine the change in the height of water in the
reservoir required above the sharp edged entrance into the pipe to achieve
the required flow rate.
b)
d) Provide an explanation for the result obtained in part c).
Page 4 of 15
[4 marks]
[5 marks]
Ref: ME20214G74-2
Turn the page over Module Code: MECH267001
4. A new design of telecommunications tower is modelled as a 5m diameter
perfectly smooth sphere on top of a vertical perfectly smooth cylinder, 30m high
and 2m diameter. It has to withstand an aerodynamic force imposed by a 100
km/h wind. For air take the density to be 1.20 kg/m³ and the kinematic viscosity
to be 1.5 x 10-5 m²/s.
a)
b)
c)
d)
Estimate at 100km/h the aerodynamic drag force acting on the sphere.
[7 marks]
Estimate at 100km/h the aerodynamic drag force acting on the cylinder.
[7 marks]
Estimate the bending moment at the base of the tower.
[5 marks]
Discuss why these results should only be regarded as an estimate of the
influence of drag on the real tower.
Page 5 of 15
[6 marks]
Ref: ME20214G74-2
Turn the page over Module Code: MECH267001
Biot number, Bi =
Nusselt number, Nux
Prandtl number, Pr =
Composite cylinders
α
where v is kinematic viscosity
Stefan-Boltzmann constant,
o= 56.7 x 10 kWm
-12
n-² K-4
Newton's Law of Cooling
Composite plain walls
One dimensional heat transfer
Fourier's Law
Tt - To
To - Too
hv
KA
=
= exp
V
Rex
hx
k
Rex
ReL
Page 6 of 15
FORMULA SHEET
Heat Transfer
A
- [ht]
= exp
Forced Convection over a flat plate
≤500 000
Nux
> 500 000
Nux =
500 000
NUL
Thermal diffusivity, a =
Transient heat transfer: Lumped heat capacity system (Bi < 0.1)
Stanton number,
=
=
Grashof number, G₁
where t = is the time constant of the system.
cpV
hA
Q = ġA = −kA
Heat diffusion equation in cartesian coordinates
k
ə
1/2 (²017) = ( ² ( ² ) + 2, (^²7)
(二)={ (x
+
²₁ (^ ²) + ²/₂ (^²} + a₂
(KZT)
k
k
ġg
ду
ду,
дz
дz.
St =
where v is kinematic viscosity
No. of transfer units, NTU
dT
dx
• (-/-)
Q = -hA(T∞ - Tw)
(Tb - Ta)
{Σ (A) + Σ (4)}
=
0.332 Pr0.333
Re0.5
0.0296 Pr0.333 Re0.8
0.037 Pr0.333 Re8
k
pcp
h
pcpu
gβ∆Td3
v²
(Tb - Ta)
(In(ro/ri)`
{Σ (²n (7/²)) + Σ (1/²/A)}
2πlk
=
=
UA
Cmin
Nu
Re Pr
Turn the page over
The steady-state temperature distribution in a one-dimensional wall of thermal conductivity 50 W/m-K and thickness 50 mm is observed to be T(°C) = a + bx²,a = 200°C, b = -3,500°C/m2, and x is in meters.where Determine the heat fluxes at x = 50 mm in W/m-
4. 8.20 Engine oil flows through a 25-mm-diameter tube at a rate of 0.5 kg/s. The oil enters the tube at a temperature of 25°C, while the tube surface temperature is maintained at100°C. Determine the oil outlet temperature for a 5-m and for a 100-m long tube. For each case, compare the log mean temperature difference to the arithmetic mean temperature difference.
7.55 Consider a sphere with a diameter of 20 mm and a surface temperature of 60°C that is immersed in a fluid at a temperature of 30°C and a velocity of 2.5 m/s. Calculate the heat rate when the fluid is (a) water and (b) air at atmospheric pressure. Explain why the results for the two fluids are so different.
A drying oven consists of a long semicircular duct of diameter D = 1 m (Surface1). Materials to be dried cover the base of the oven (Surface 2). The wall(Surface 1) of the oven (81=0.8) is maintained at T1 = 1200 K, while the materials to be dried are considered a black body (82=1.0) is maintained at a temperature T2 = 325 K during the process. a. Calculate the view factor F12; b. Calculate the net radiation heat transfer rate from the oven wall to the material to be dried. Given: o = !5.67x108 W/m2-K and for a two-surface enclosure it is known
3. A co generation power plant operating in a thermodynamic cycle at steadystate. The plant provides electricity to a community at a rate of 80 MW.The energy discharges from the power plant by heat transfer is denoted on the figure by Q out: Of this, 70 MW is provided to the community for water heating and the remainder is discarded to the environment without use.The electricity is valued at $0.08 / kW-hr. If the cycle thermal efficiency is40%, determine: a) The rate energy is added by heat transfer Q in MW.in b) The rate energy is discarded to the environment, in MW c) The value of the electricity generated in $ per year.
2. 7.42 Hot water at 50°C is routed from one building in which it is generated to an adjoining building in which it is used for space heating. Transfer between the buildings occurs in a steel pipe (k = 60 W/m-K) of 100-mm outside diameter and 8-mm wall thickness. During the winter, representative environmental conditions involve air at T =-5°C and V = 3 m/sin cross flow over the pipe. a. If the cost of producing the hot water is $0.10/kWh, what is the representative daily cost of heat loss from an uninsulated pipe to the air per meter of pipe length? The convection resistance associated with water flow in the pipe may be neglected. b. Determine the savings associated with application of a 10-mm-thick coating of urethane insulation (k = 0.026 W/m-K) to the outer surface of the pipe.
Consider an airplane cruising at altitude of 10 km where standard atmospheric conditions are -50°C and 26.5 kPa at a speed of 800 km/h. Each wing of the airplane can be modeled as a 25-m x 3-m flat plate, and the friction coefficient of the wings is o.0016. Using the momentum-heat transfer analogy, determine the heat transfer coefficient for the wings at cruising conditions.
1 m^3 of saturated liquid water at 473 K is expanded isothermally in a closed system until its quality is 80 percent. Determine the total work produced by this expansion, in kJ.
A5-m x 5-m flat plate maintained at a constant temperature of 80°C is subjected to parallel flow of air at 1 atm, 20°C, and 10 m/s. The total drag force acting on the upper surface of the plate is measured to be 2.4 N. Using the momentum-heat transfer analogy, determine the average convection heat transfer coefficient and the rate of heat transfer between the upper surface of the plate and the air. Evaluate the air properties at 50°C and 1 atm.
In a counter-flow heat exchanger, 2 kg/s of hot water flows through the tubes and8 kg/s of cold water flows on the shell side. Which flow will experience the largesttemperature change? O Cold water O Hot water The change will be the same for both