Measurements show that steady-state conduction through a plane wall without heat generation produced a convex temperature distribution

Question:

Measurements show that steady-state conduction through a plane wall without heat generation produced a convex temperature distribution such that the mid- point temperature was 6.To higher than expected for a linear temperature distribution.

Tu2 ΔΤ, TU2 AT Tx) T2 7-

Assuming that the thermal conductivity has a linear dependence on temperature, k = ko (1 + aT), where a is a constant, develop a relationship to evaluate a in terms of ∆T₀' T₁, and T₂.

Distribution
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