Steel-reinforced concrete pillars are used in the construction of large buildings. Structural failure can occur at high temperatures due to fire because of softening of the metal core. Consider a 200mm thick composite pillar consisting of central steel core of 40mm thick sandwiched between two 80mm thick concrete walls. Assume a thermal contact resistance of R"=0.2 at the concrete-steel interface. The pillar is at a uniform initial temperature of Ti=27C and is suddenly exposed to combustion products at T?=900C, h=40 on both exposed surfaces. The surroundings temperature is also 900C.
Steel properties: ks=55, ?=8000, Cs=450
Concrete properties: kc=1.4, ?=2300, Cc=900, ?=0.9 ?x=10mm, ?t=100s
- Derive the equations for the implicit FV method for the following cells:
1) Cell that faces convective and radiative ht transfer from the surroundings (cell 1)
2) Cell that has a face coincides with the concrete-steel interface ( cell 8, cell 9)
c. Plot the midpoint temperature of the steel pillar with R” =0 and R” =0.20 for 0 \leq t \leq 10,000 seconds.
d. Plot the temperature of the steel at the middle of the pillar for e=0 and e =0.9 for 0 \leq t \leq 10,000 seconds