3. Given a composite material made of (A) pure aluminum, Al (B) beryllium, Be and (C) pure copper, Cu, and knowing four temperatures surrounding a central node at the intersection of these three materials (e.g., T1, T2, T3and T4surrounding Tm,n). A. For steady state 2-dimensional heat transfer with constant k values for each material (kAl, kBeand kCu) and that the grid surrounding these nodes is not square with Δx ≠Δy, write an equation to find Tm,nas a function of the four known temperatures, three known thermal conductivities, and grid spacings, Δxand Δy. Start by writing heat transfer rate equations from each direction, then use Σq = 0. You may stop there instead of solving for Tm,n. B. Given T1= 580 K, T2= 556 K, T3= 612 K, and T4= 620 K, and using Appendix Table A.1, find Tm,n. (you may look up k values at 600 K as a reasonable approximation; Note: the values under “properties at various temperatures” lists k on the top line, and cpon the line below for 200, 400, 600, 800, etc. Kelvin.) Here, you may assume that Δx = Δy and Δz = 1 m.
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