Two very long (in the direction normal to the page) bars having the prescribed initial temperature distributions are to be soldered together. At time t = 0, the m = 3 face of the copper (pure) bar contacts the n = 4 face of the steel (AISI 1010) bar. The solder and flux act as an interfacial layer of negligible thickness and effective contact resistance R"t,c = 2 x 10-5 m2 ∙ K/W.

(a) Derive the explicit, finite-difference equation in terms of Fo and Bic = ∆x/kR"t,c, for T4,2 and determine the corresponding stability criterion.

(b) Using Fo = 0.01, determine T4.2 one time step after contact is made. What is ∆t? Is the stability criterion satisfied?

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Initial Temperatures (K) nim 1 2 3 4 5 6 700 700 700 1000 900 800 700 700 700 1000 900 800 700 700 3 700 800 1000 900 Interface with soider and flux Copper, Steel, AISI 1010 pure 2,3 5.3 3, 3, 4. 1,3 2, 2 3, 2 4, 2 5. 2 1, 2 6. 2 2, 1 3, 1 6. Ax = Ay = 20 mm