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ADDITIONAL PROBLEMS
1.
A plane wall 15 – cm thick has a thermal conductivity
given by the relation
k = 2.0 + 0.0005 T, W/m – K
where T is in Kelvin. If one surface of this wall is maintained
at 150 oC and the other at 50 oC, determine the rate of
heat transfer per square meter. Sketch the temperature
distribution through the wall. – F#1 (M2)
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2.
The composite wall of an oven consists of three
materials, two of which are of known thermal
conductivity, kA = 20 W/m – K and kC = 50 W/m – K, and
known thickness, LA = 0.30 m and LC = 0.15 m. The third
material, B, which is sandwiched between materials A
and C, is of known thickness, LB = 0.15 m, but unknown
thermal conductivity kB. Under steady – state operating
conditions, measurements reveal an outer surface
temperature of 600 oC, and an oven air temperature of
800 oC. The inside convection coefficient h is known to
be 25 W/m2 – K. The overall heat transfer rate per area is
550 W/m2. What is the value of kB? – E#1 (M2)
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3.
A 3 – m high and 5 – m wide wall consists of 16 – cm by 22 –
cm cross section horizontal bricks (k = 0.72 W/m – K)
separated by 3 – cm thick plaster layers (k = 0.22 W/m – K).
There are also 2 – cm thick plaster layers on each side of the
brick and a 3 – cm thick rigid foam (k = 0.026 W/m – K) on
the inner side of the wall. The indoor and outdoor
temperatures are 20 oC and -10 oC, respectively and the
convection heat transfer coefficients on the inner and outer
sides are h1 = 10 W/m2 – K and h2 = 25 W/m2 – K, respectively.
Assuming one – dimensional heat transfer and disregarding
radiation, determine the rate of heat transfer through the
wall. – E#2 (M2) (Q = 261.9 W)
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4.
A 0.964-m thick composite protective wall is formed of a 1-in
copper plate, a 1/8-in layer of asbestos, and a 2-in layer of
fiberglass placed one a top the other. The thermal
conductivities of the materials in units of Btu/h.ft. oF are as
follows: kCu = 0.240, kasb = 0.048 and kfib=0.022. The overall
temperature difference across the wall is 500oF. The wall is
covered with a 134-mm thick insulating material (k = 0.12
Btu/hr-ft-oF) on the inner surface and a 2.5-in thick concrete
(k = 0.8 Btu/hr-ft-oF) on the outer layer. Calculate the thermal
resistance of each layer of the wall and the heat transfer
rate per unit area through the composite. Illustrate also its
thermal resistance network analysis. (q = 13.1591 BTU/hr-ft2)
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5.
Two large aluminum plates (k = 240 W/m.K),
each 1 cm thick, with 10 µm surface roughness
the contact resistance Ri = 2.75 x 10-4 m2.K/W.
The temperatures at the outside surfaces are
395°C and 405°C. Calculate (a) the heat flux (b)
the temperature drop due to the contact
resistance.
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ASSIGNMENT
1.
A layer of 2-in thick firebrick (Kb = 1.0 Btu/hr.ft.°F) is placed
between two ¼-in thick steel plates (ki = 30 Btu/h.ft.°F). The
faces of the brick adjacent to the plates are rough, having
solid to solid contact over only 30 percent of the total area,
with the average height of asperities being 1/32-in. If the
surface temperatures of the steel plates are 200 and 800°F,
respectively; determine the overall rate of heat flow per unit
area. Kair = 0.02 Btu/h.ft.°F.
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ASSIGNMENT
2.
A copper slab (k=372 W/mOC) is 3mm thick. It is
protected from corrosion on each side by 2m
thick layer of stainless steel (k=17W/mOC). The
temperature is 400OC on one side of this
composite wall and 100OC on the other. Find
the distribution in the copper slab and the heat
conducted through the wall.
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ASSIGNMENT
3.
A large furnace has a composite wall of height 50 cm. It is consists of a
10-cm firebrick (k = 1.04 W/m K), a 25-cm Masonry brick (k = 0.69 W/m K)
and a 5-cm concrete (k = 1.37 W/m K). The masonry brick is sandwiched
by 8-cm high firebrick layer. The wall is furthered layered with a 15-cm
high concrete. The interior surface of the furnace wall is exposed to hot
gases at 1000oC while the exterior surface is exposed to atmospheric air
at 25oC. If the convective heat transfer coefficient at the interior and
exterior surfaces are 60 W/m2K and 20 W/m2K, respectively. Illustrate the
thermal resistance network for this problem. Calculate the heat transfer
per unit area of the furnace wall, from hot gases to the atmospheric air.
Estimate also the temperature of the interior and exterior surfaces and
the temperature at each interface.