Four identical rods Ab, CD,CF and DE are joined as shown in figure . the length , cross -sectional area and thermal conductivity of each rod are. i, A and K respectively. the ends A, E and F are maintained at temperatures $T_{1}, T_{2} a n d T_{3}$ respectively.assuming no loss of heat to the atmosphere , find the temperature at B.

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Solution

Let the temp. at B be T
$\frac{Q_{A}}{t} = \frac{Q_{B}}{t} + \frac{Q_{C}}{t}$
$⟹ \frac{T - 1 - T}{I} = \frac{T - T_{3}}{3 I / 2} + \frac{T - T_{2}}{3 I / 2}$
$- 7 T = 3 T_{1} - 2 (T_{2} + T_{3})$
$⟹ \frac{K A (T_{1} - T)}{I} = \frac{K A (T - T_{3})}{I + (I / 2)} + \frac{K A (T - T_{2})}{I + (I / 2)}$
$⟹ 3 T_{1} - 3 T = 4 T - 2 (T_{2} + T_{3})$
$⟹ T = \frac{3 T_{1} + 2 (T_{2} + T_{3})}{7}$

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Q. Four identical rods AB, CD, CF and DE are joined as shown in figure (28-E8). The length, cross-sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperature T₁, T₂ and T₃ respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.

Four identical rods AB, CD, CF and DE are joined as shown in figure. The length, cross -sectional area and thermal conductivity of each rod are l, A and K respectively. The ends A, E and F are maintained at temperatures $T_{1}, T_{2}$ and $T_{3}$ respectively. Assuming no loss of heat to the atmosphere, find the temperature at B.