Three identical rods have been joined at a junction to make it a $Y$ shape structure. If two free ends are maintained at $90\,^oC$ and the third end is at $30\,^oC$ , then what is the junction temperature $\theta $ ?......... $^oC$
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Themal resistance $=\frac{\mathrm{L}}{\mathrm{KA}}=$ same for all $=\mathrm{R}(\mathrm{let})$ using kirchoff's law for heat current
$\mathrm{i}_{1}+\mathrm{i}_{2}+\mathrm{i}_{3}=0$
$\Rightarrow \frac{30-\theta}{R}+\frac{90-\theta}{R}+\frac{90-\theta}{R}=0$
$30-\theta+180-2 \theta=0 \Rightarrow 210=3 \theta \Rightarrow \theta=70^{\circ} \mathrm{C}$
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