3. An experimental arrangement for measuring the thermal conductivity of solid materials involves the use of two long rods that are equivalent in every respect, expect that one is fabricated from a standard material, aluminum, of known thermal conductivity, $k_A = 200 \text{ W/m-K}$, while the other is fabricated from the material whose thermal conductivity is desired, $k_B$. Both rods are attached at one end to a heat source of fixed temperature $T_b = 100^\circ C$, are exposed to a fluid of temperature $25^\circ C$, and are instrumented with thermocouples to measure the temperature at a fixed distance $x_1$ from the heat source. If the measurements reveal $T_A = 75^\circ C$ and $T_B = 60^\circ C$ at $x_1$, what is the thermal conductivity $k_B$ of the test material? (Ans: $k_B = 56.6 \text{ W/m-K}$)
