Page 179 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

TRANSIENT HEAT CONDUCTION ANALYSIS
5
2
is exposed to (a) a heat flux of 3 × 10 W/m and (b) a sudden rise in surface temperature
◦
of 200 C. Calculate the temperature at a depth of 1 cm after a time of 10 seconds for both
cases. Verify the results with analytical results. 171
◦
Exercise 6.10.2 A fin of length 1 cm is initially at the ambient temperature of 30 C. If the
base temperature is suddenly raised to a temperature of 150 C and maintained at that value,
◦
determine the temperature distribution in the fin after 30 seconds if the thermal diffusivity
2
of the fin material is 1 × 10 −5 m /s. The heat transfer coefficient between the fin surface
2◦
and the ambient is 100 W/m C. The cross section of the fin is 6 mm by 5 mm.
Exercise 6.10.3 A short aluminium cylinder 2.5 cm in diameter and 5 cm long is initially
at a uniform temperature of 100 C. It is suddenly subjected to a convection environment
◦
◦
2◦
at 50 C and h = 400 W/m C. Calculate the temperature at a radial position of 1 cm from
outer surface and a distance of 0.5 cm from one end of the cylinder 10 seconds after exposure
to the environment.
Exercise 6.10.4 A plane wall of thickness 4 mm has internal heat generation of 25 MW/m 3
with thermal properties of k = 20 W/m C, ρ = 8000 kg/m 3 and specific heat c p =
◦
500 J/kg C. It is initially at a uniform temperature of 50 C and is suddenly subjected to
◦
◦
heat generation and a convective boundary condition as shown in Figure 6.17 Calculate
the temperature at a location of 2 mm after 10 seconds.
Exercise 6.10.5 A stainless steel plate size 2 cm × 1 cm is surrounded by an insulating
◦
block as shown in Figure 6.18 and is initially at a uniform temperature of 40 C with a
2
◦
convection environment at 40 C. The plate is suddenly exposed to a radiant flux of 15 kW/m .
Calculate the temperature at the centre of the top and bottom surfaces after 10 s. Take the
3
◦
properties of the stainless steel as k = 18 W/mK, ρ = 8000 kg/m , c p = 0.46 kJ/kg C, and
2
h = 30 W/m K.
2
2
h = 500 W/m °C h = 400 W/m °C
T a = 30°C T a = 100°C
Figure 6.17 Plane wall discretization

q rad
h, T a

1 cm

2 cm
Figure 6.18 Stainless steel plate