Project ForgeHeat is generated uniformly within a solid slab separating fluid 1 from fluid 2. The heat transfer coefficients between the solid slab and the fluids are h1 and h2 (h2>h1). The steady state temperature profile (T vs. x) for one-dimensional heat transfer, among 4 plotted options (two smooth parabolic curves with the peak shifted toward h1 or h2 respectively, and two piecewise-linear triangular profiles peaking exactly at the h1 or h2 boundary), is CORRECTLY shown by
- a smooth parabola peaking closer to the h1 (lower-h) boundary, with a quick rise from h1 followed by a longer, gradual decline to h2
- Ba smooth parabola peaking closer to the h2 (higher-h) boundary, with a long gradual rise from h1 followed by a quick decline to h2
- Ca piecewise-linear profile with a sharp peak exactly at the h1 boundary
- Da piecewise-linear profile with a sharp peak exactly at the h2 boundary
Explanation
Uniform generation within the slab requires a genuinely parabolic (not piecewise-linear) temperature profile, ruling out the two triangular options immediately. Solving the BVP kT''=−q with convective boundary conditions at both faces (representative values h1=1, h2=10, k=q=L=1, equal ambient temperatures) gives a peak location xm=0.286 — closer to the LOW-h (h1) boundary — reached via a short, steep rise from the h1 side followed by a long, gradual decline all the way to the h2 boundary. This confirms the peak shifts toward the boundary with the WEAKER cooling (lower h), matching the profile with a quick rise from h1 and gradual fall to h2.
Source: GATE CH 2011 (2011)
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