GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Three slabs are joined together as shown in the figure. There is no thermal contact resistance at interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to $10000{\mathit{W}\mathit{m}}^{-3}$, while the left and right slabs have no internal heat generation. All slabs have thickness equal to $1\mathit{m}$ and thermal conductivity of each slab is equal to 5 ${\mathit{W}\mathit{m}}^{-1}{\mathit{K}}^{-1}$. The two extreme faces are exposed to fluid with heat transfer coefficient $100{\mathit{W}\mathit{m}}^{-2}{\mathit{K}}^{-1}$ and bulk temperature ${30}^{\circ }\mathit{C}$ as shown. The heat transfer in the slabs is assumed to be one dimensional and steady, and all properties are constant. If the left extreme face temperature ${\mathit{T}}_1$ is measured to be ${100}^{\circ }\mathit{C}$, the right extreme face temperature ${\mathit{T}}_2$ is __________________${}^{\circ }\mathit{C}.$