# Question: find analytical expression for the temperature distribution in the...

###### Question details

Find analytical expression for the temperature distribution 𝑇(𝑥) in the plane wall which has uniform surface temperatures 𝑇1(𝑥 = 0) and 𝑇2(𝑥 = 𝐿) and 𝑇1 > 𝑇2. Thermal conductivity varies linearly with temperature, i.e. 𝑘 = 𝑘0(1 + 𝑏𝑇). Consider three different cases, (i) 𝑏 > 0, (ii) 𝑏 = 0, and (iii) 𝑏 < 0. For each case, which one is the closest 𝑇(𝑥) profile in Figure below?