This is a transport process assignment given by Dr. Ray at UWO. Please find the attachment for details.

Assignment 2 (Due 13 October 2017) Problem 1: Steady state heat flow in a semi-circular bent metal rod having a spike: Athin metal rod (diameter, d 2 5 mm; thermal conductivity, k 2 100 W/m/DC) of length (L) of 50cm is bent into a semi-circular ring and its ends are fixed to a metal wall at TW = 200 0C. A 10 cmlong (Ls) spike of same metal (diameter, d = 5 mm, thermal conductivity, k = 100 W/m/OC), iswelded to the middle of the ring. The ring and the spike loses heat to the ambient at 20°C, theheat transfer coefficient being 10 W/mZIOC. Assume that the temperature at any cross-section ofthe ring and spike are uniform. Since the diameter of the ring is much larger than the rod, thering may be considered as a straight rod for heat flow as shown in the figure below. The spike The straightened TS (y) or 65 (5) Tr(x) or Br (a)l-rEFT—Ta _ 13—11, 2 _ 4m; 2 _— on i and i’ S TW—Ta’ dk B Define E, = x/Lr, 8 = y/Ls, 0, = w—Ta dk. Calculate the steady-state temperature profile, 6r(E_,) and 09(5). State clearly the boundaryconditions used. One can use boundary condition at y = Ls either conduction-convectionboundary condition (exact BC), or as an approximation, temperature gradient equal to 0. Determine the values of 845,) and 85(6) for both cases, and calculate the errorfor 85(@ 6: 1). Ray, AK 1 CBE 9160 Transport Processes

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