2. Heat transfer rates are given by the general equation:
3. For heat conduction:
4. For radiation:
5. Overall heat-transfer coefficients are given by:
(a) for heat conductances in series,
(b) for radiation convection and conduction,
6. For convection heat-transfer coefficients are given by equations of the general form:
(Nu) = K(Pr)k(Gr)m(L/D)n
for natural convection:
and for forced convection:
It is desired to limit the heat loss from a wall of polystyrene foam to
8 J s-1 when the temperature on one side is 20°C and on
the other -18°C. How thick should the polystyrene be?
Calculate the overall heat-transfer coefficient from air to a product
packaged in 3.2 mm of solid cardboard, and 0.1 mm of celluloid, if the
surface air heat transfer coefficient is 11 J
m-2 s-1 °C-1.
The walls of an oven are made from steel sheets with insulating board
between them of thermal conductivity 0.18 J m-1 s-1 °C-1.
If the maximum internal temperature in the oven is 300°C and the outside
surface of the oven wall must not rise above 50°C, estimate the minimum
necessary thickness of insulation assuming surface heat transfer coefficients
to the air on both sides of the wall are 15 J m-2 s-1
°C-1. Assume the room air temperature outside the oven
to be 25°C and that the insulating effect of the steel sheets can
Calculate the thermal conductivity of uncooked pastry if measurements
show that with a temperature difference of 17°C across a large slab
1.3 cm thick the heat flow is 0.5 J s-1 through an area of
10 cm2 of slab surface.
A thick soup is being boiled in a pan and because of inadequacy of stirring
a layer of soup builds up on the bottom of the pan to a thickness of 2
mm. The hot plate is at an average temperature of 500°C, the heat-transfer
coefficient from the plate to the pan is 600 J
m-2 s-1 °C-1,
and that from the soup layer to the surface of the bulk soup is 1400 J
m-2 s-1 °C-1.
The pan is of aluminium 2 mm thick. Find the temperature between the layer
of soup and the pan surface. Assume the thermal conductivity of the soup
layer approximates that of water.
Peas are being blanched by immersing them in hot water at 85°C until
the centre of the pea reaches 70°C. The average pea diameter is 0.0048
m and the thermal properties of the peas are: thermal conductivity 0.48
heat 3.51 x 103 J kg-1 °C-1 and density
990 kg m-3. The surface heat-transfer coefficient to the peas
has been estimated to be 400 J
m-2 s-1 °C-1.
(a) How long should it take the average pea to reach 70°C if its initial
temperature was 18°C just prior to immersion? (b) If the diameter
of the largest pea is 0.0063 m, what temperature will its centre have
reached when that of the average pea is 70°C?
Some people believe that because of' its lower thermal conductivity stainless
steel is appreciably thermally inferior to copper or mild steel as constructional
material for a steam-jacketed pan to heat food materials. The condensing
heat transfer coefficient for the steam and the surface boiling coefficient
on the two sides of the heating surface are respectively 10,000 J
m-2 s-1 °C-1
and 700 J
m-2 s-1 °C-1.
The thickness of all three metal walls is 1.6 mm. Compare the heating
rates from all three constructions (assuming steady state conditions).
A long cylinder of solid aluminium 7.5 cm in diameter initially at a uniform
temperature of 5°C, is hung in an air blast at 100°C. If it is
found that the temperature at the centre of the cylinder rises to 47.5°C
after a time of 850 seconds, estimate the surface heat transfer coefficient
from the cylinder to the air.
A can of pumpkin puree 8.73 cm diameter by 11.43 cm in height is being
heated in a steam retort in which the steam pressure is 100 kPa above
atmospheric pressure. The pumpkin has a thermal conductivity of 0.83 J
m-1 s-1 °C-1,
a specific heat of 3770 J kg-1 °C-1 and a density
of 1090 kg m-3. Plot out the temperature at the centre of the
can as a function of time until this temperature reaches 115°C if
the temperature in the can prior to retorting was 20°C.
A steam boiler can be represented by a vertical cylindrical vessel 1.1
m diameter and 1.3 m high, and it is maintained internally at a steam
pressure of 150 kPa. Estimate the energy savings that would result from
insulating the vessel with a 5 cm thick layer of mineral wool assuming
heat transfer from the surface is by natural convection. The air temperature
of the surroundings is 18°C and the thermal conductivity of the insulation
is 0.04 J
m-1 s-1 °C-1.
11. It is desired to chill 3 m3 of water per hour by means of horizontal coils in which ammonia is evaporated. The steel coils are 2.13 cm outside diameter and 1.71 cm inside diameter and the water is pumped across the outside of these at a velocity of 0.8 m s-1. Estimate the length of pipe coil needed if the mean temperature difference between the refrigerant and the water is 8°C, the mean temperature of the water is 4°C and the temperature of the water is decreased by 15°C in the chiller.
[ 53.1 m ]
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