Problem: Consider the unsteady-state heat transfer in solid slabs with two different boundary conditions, respectively: (1) Semi-infinite boundary (see lecture note and Examples 12.1-1 in 2ndedition, or 11.1-1 in the 1stedition). At time t = 0, the surface at y = 0 is suddenly raised to temperature T1and maintained at that temperature for t > 0. (2) Finite boundary (see lecture note and Examples 12.1-2 in 2ndedition, or 11.1-2 in the 1stedition). At time t = 0, the surfaces at y = ±b is suddenly raised to temperature T1and maintained at that temperature for t > 0. Compare the solutions corresponding to the boundary conditions for SHORT times. What error is made by using the solution for the semi-infinite slab instead of that for the finite slab, when αt/b2= 0.01 and for a position 0.9 of the way from the midplane to the slab surface? Use the graphically presented solution for the finite boundary (Fig. 12.1-1, or 11.1-1 in the 1stedition) for making the comparison. Answer: Consider short times at which the heat flow does not reach the mid-plane of the solid
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