## Related questions with answers

Plate glass at $600^{\circ} \mathrm{C}$ is cooled by passing air over its surface such that the convection heat transfer coefficient is $h=$ $50 \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}$. To prevent cracking, it is known that the temperature gradient must not exceed $15^{\circ} \mathrm{C} / \mathrm{mm}$ at any point in the glass during the cooling process. If the thermal conductivity of the glass is $1.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$ and its surface emissivity is $0.8$, what is the lowest temperature of the air that can initially be employed for the cooling? Suppose that the temperature of the air equals that of the surroundings.

Solution

VerifiedWe will start by writing down the given data from the text of the problem :

$\begin{align*} T_s &= 600\text{ C}\\\\ h &= 50 \frac{\text{ W}}{\text{ m}^2 \text{K}}\\\\ \frac{dT}{dx} &= 15 \frac{\text{ C}}{\text{ mm}}\\\\ k &= 1.4 \frac{\text{ W}}{\text{ m K}}\\\\ \epsilon &= 0.8 \end{align*}$

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