A flat plane of thickness x has one surface maintained at T 1 and the other at T 2 (T 1 T 2 .

A flat plane of thickness Δx has one surface maintained at T ₁ and the other at T ₂ (T ₁ ≠ T ₂ . If the thermal conductivity varies with temperature according to:

K = a + bT + cT ³

where a, b, and c are constants, derive an expression for the one-dimensional heat flux q/A=q" in terms of Ax, T, T, a, b, and c. (10 marks) k-a+bT+cT T(0)=T, T(Ax)=T2 Ax