Project ForgeFour steady state temperature profiles for 1-D heat transfer in a solid slab are plotted (I: peak at left edge, decreasing rightward, concave down; II: minimum at left edge, increasing rightward, concave up; III: increasing from left, peaking near the right edge, concave down; IV: high at left edge with steep initial drop, flattening to a minimum at the right edge, concave up). Match: P: uniform heat generation, left surface insulated; Q: uniform heat generation, right surface insulated; R: uniform heat consumption, left surface insulated; S: uniform heat consumption, right surface insulated.
- P-I, Q-III, R-II, S-IV
- BP-II, Q-III, R-I, S-IV
- CP-I, Q-IV, R-II, S-III
- DP-II, Q-IV, R-I, S-III
Explanation
An insulated boundary has zero flux (zero slope) there. Heat GENERATION requires a concave-down profile with its maximum (zero-slope point) AT the insulated face: left-insulated generation peaks at the left edge (P-I); right-insulated generation peaks near the right edge (Q-III). Heat CONSUMPTION requires a concave-up profile with its minimum at the insulated face: left-insulated consumption has its minimum at the left edge (R-II); right-insulated consumption has its minimum at the right edge, approached with a flattening (zero-slope) curve there (S-IV).
Source: GATE CH 2010 (2010)
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