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Question

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 $k=16 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}$.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 12**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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