A cylinder of radius R and length l is made up of substance whose thermal conductivity K varies with the distance x from the axis as `K=K_1x+K_2`. Determine the the effective thermal conductivity between the flat faces of the cylinder.

Explanation

To determine the effective thermal conductivity \( K_{\text{effective}} \) of a cylinder with varying thermal conductivity, we can follow these steps:

### Step 1: Understand the Problem
We have a cylinder of radius \( R \) and length \( l \). The thermal conductivity \( K \) varies with the distance \( x \) from the axis of the cylinder, given by the equation:
\[ K = K_1 x + K_2 \]

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