Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Tempe

Question

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100^{\circ} \mathrm{C}$ and $40^{\circ} \mathrm{C}$ respectively. Given the thermal conductivity of $\operatorname{rod} x$ is three times of that of $\operatorname{rod} y$, the temperature at junction points $B$ and $E$ are (close to):

Professor PC Thomas Classes · Answer

By applying the principle of steady-state heat conduction, the sum of heat currents at any junction is zero ($\sum \frac{dQ}{dt} = 0$). Writing the nodal equations for the junctions B and E using $H = \frac{KA\Delta T}{L}$ and substituting $K_x = 3K_y$, we can solve the coupled linear equations for the temperatures $T_B$ and $T_E$, which yields approximately $89^\circ	ext{C}$ and $73^\circ	ext{C}$ respectively.