Page 47 - Introduction to Computational Fluid Dynamics

P1: IWV/ICD
May 25, 2005
0 521 85326 5
10:49
CB908/Date
0521853265c02
26
5 5 1D HEAT CONDUCTION
mm mm
PRESS PRESS

250 C 250 C

ADHESIVE
X

12 3 4 5 6 7

∆X = 2 mm
Figure 2.5. Bonding of plastic sheets – Problem 1.

Mathematically more rigorous arguments concerning this stability condition
4
will be discussed in the next chapter. Here we consider a problem to develop
essential understanding.

Problem 1 [80]
Two plastic sheets, each 5 mm thick, are to be bonded together with a thin layer
of adhesive that fuses at 140 C. For this purpose, they are pressed between two
◦
surfaces at 250 C (see Figure 2.5). Determine the time for which the two sheets
◦
should be pressed together, if the initial temperature of the sheets (and the ad-
hesive) is 30 C. For plastic sheets, k = 0.25 W/m-K, C = 2,000 J/kg-K, and
◦
3
ρ = 1,300 kg/m .

Solution
In this problem, we measure x from the edge of one of the sheets as shown. We
divide the domain of 10 mm such that x = 2 mm. This will yield seven grid
nodes, as shown in Figure 2.5. Note that the distance between nodes 1 and 2 and
that between 6 and 7 will be 1 mm. In this problem, area A is constant and may
2
be assigned value of 1 m (say). Also, since there is no internal heat generation,

4 The USER file for this problem is given in Appendix B.