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# A 3.0-cm-thick plate has heat generated uniformly at the rate of $5 \times 10^5 \mathrm{~W} / \mathrm{m}^3$. One side of the plate is maintained at $200^{\circ} \mathrm{C}$ and the other side at $45^{\circ} \mathrm{C}$. Calculate the temperature at the center of the plate for $k=16 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$.

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Data given:

• Thickness of a plate: $x=3\text{ cm}$;
• Heat generated per unit volume: $\dot{q}=5\cdot 10^5~\frac{\text{ W}}{\text{ m}^3}$;
• Temperature of one side of plate: $T_1=200~\text{ \degree C}$;
• Temperature of the other side of plate: $T_2=45\text{ \degree C}$;
• Thermal conductivity: $k=16~\frac{\text{ W}}{\text{ m}\text{ \degree C}}$.

Required:

• Temperature at the center needs to be calculated.

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