BENG3 THERMAL & FLUIDS ENGINEERING (THER305)
TUTORIAL EXAMPLES in 1-D TRANSIENT CONDUCTION
[Click here for spreadsheet solutions
to all questions]
1. The surface of a thick plate originally at 50°C is suddenly raised to a temperature of 80°C. If the material properties of the plate are such that a=2x10-6 m²/s, find the time required for a plane 3cm from the surface to reach 65°C. Use a plane spacing of 10 mm, and time interval of 25 seconds. Compare the answers using both explicit and implicit methods. [471 sec; 508 sec]
2.
One end of a steel poker 60 cm long is placed 10 cm
into a flame. The flame temperature is 1000ºC, and the poker’s temperature is
20ºC. Estimate how long it takes for the other end of the poker to reach a
temperature where it cannot be safely touched.
For steel assume l
= 45 W/mK, r
= 7850 kg/m³ and cp = 460
J/kgK, and the maximum temperature which can be safely touched is 46ºC. Assume
no heat losses to the surrounding air. Use the explicit method with a Fourier
number of 0.25. [~20 sec]
3. A large mild steel plate is 250mm thick and is originally at 45°C. One surface is exposed to hot air at 200°C with h=210 W/m²K. Determine the temperature at the surface and at a depth of 20mm, 3 minutes after exposure to the hot air. Assume a=2x10-5 m²/s, l=45W/mK. Use the implicit method with a plane spacing of 10mm. [84°C, 74°C]
4.
Nylon tube used in the motor industry needs to be at a
temperature of between 110°C and 120°C in order to be formed so that when it cools to ambient
temperature it remains in the formed shape. A new method of forming proposes to
pass the nylon tube through a hot air curtain at 150°C before forming it. Using
the implicit method, 0.1 mm steps in thickness and
1 sec steps in time, and assuming no heat transfer from the inside surface of
the tube:
(a) Determine the minimum length of the hot air curtain if the nylon tube
passes through it at a speed of 2.5 cm/s, and
(b) Determine the heat transfer rate to the nylon tube. [ 52.5 cm, 113 W]
Thermal conductivity of nylon: 0.25 W/mK
Density of nylon: 1150 kg/m³
Specific Heat Capacity of nylon: 1.65 kJ/kgK
Surface heat transfer coefficient between the hot air and the tube outer
surface: 120 W/m²K
Tube wall thickness: 0.90 mm; Tube
outside diameter: 10mm
5.
A church with granite walls 750 mm thick is being
investigated for the purposes of designing a warm air circulation heating
system. During a typical 12 hour Sunday heating cycle in winter (4°C outside
air temperature) the inside air temperature rises rapidly to, and remains at,
22°C. The inside and outside surface heat transfer coefficients are 15 W/m²K and 30 W/m²K respectively. Using the implicit method
with a 50mm plane spacing and time step of 20 minutes:-
(a) Estimate the heat stored per cubic meter of wall (above 4°C) over
the 12 hour period; Click here for results [7470 kJ]
(b) Estimate the heat transferred through the wall over the 12 hour
period and compare this with that which would occur assuming steady state conditions;
[63.5 kJ c.f. 2108 kJ]
(c) Estimate how long it would take to reach steady conditions. [approximately 4 days]
For granite assume l = 2.79 W/mK, r = 2630 kg/m³ and cp = 775 J/kgK