Module Code: MECH267001

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

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