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GATE2019-1-47

Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to $10000 \: Wm^{-3}$, while the left and right slabs have no internal heat generation. All slabs have thickness equal to $1 \: m$ and thermal conductivity of each slab is equal to $5 \: Wm^{-1}K^{-1}$. The two extreme faces are exposed to fluid with heat transfer coefficient $100 \: WM^{-2}K^{-1}$ and bulk temperature $30^{\circ} C$ as shown. The heat transfer in the slabs is assumed to be one dimensional and steady, and all properties are constant. In the left extreme face temperature $T_1$ is measured to be $100^{\circ} C$, the right extreme face temperature $T_2$ is ______$^{\circ} C$.

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