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 $100^{\circ}C$ and $40^{\circ}C$ respectively. Given the thermal conductivity of rod x is three times of that of rod y , the temperature at junction points $B$ and $E$ are (close to) :
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Solution
Let $\left\lbrack R = \frac{\mathcal{l}}{3KA} \right\rbrack$
$$T_{A} = 100 \bullet \frac{11R/2}{\longrightarrow}{\text{ }T}_{F} = 40$$
$$\begin{array}{r} \left\lbrack H = \frac{100 - 40}{\frac{11R}{2}} \right\rbrack\ldots\#(1) \end{array}$$
$$\begin{array}{r} H = \frac{100 - T_{B}}{R}\ldots\ldots\#(2) \end{array}$$
$$\begin{array}{r} H = \frac{T_{E} - 40}{3R}\ldots.\#(3) \end{array}$$
using (1) and (2)
$${120 = 1100 - 11{\text{ }T}_{A} }{T_{B} = 89^{\circ}C }$$using (1) and (3)
$$T_{E} = 73^{\circ}C$$
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