Consider two long, slender rods of the same diameter but different materials. One end of each rod is attached to a base surface maintained at 100°C, while the surfaces of the rods are exposed to ambient air at 20°C. By traversing the length of each rod with a thermocouple, it was observed that the temperatures of the rods were equal at the positions x_A = 0.15 m and x_B= 0.075 m, where x is measured from the base surface.
If the thermal conductivity of rod A is known to be k_A = 70 W/mK, determine the value of k_B for rod B.
ASSUMPTIONS:
(1) Steady-state conditions, (2) Rods are infinitely long fins of uniform cross-sectional area, (3) Uniform heat transfer coefficient, (4) Constant properties.