## Related questions with answers

Water at $0^{\circ} \mathrm{C}$ releases $333.7 \mathrm{~kJ} / \mathrm{kg}$ of heat as it freezes to ice $\left(\rho=920 \mathrm{~kg} / \mathrm{m}^{3}\right)$ at $0^{\circ} \mathrm{C}$. An aircraft flying under icing conditions maintains a heat transfer coefficient of $150 \mathrm{~W} / \mathrm{m}^{2}$. ${ }^{\circ} \mathrm{C}$ between the air and wing surfaces. What temperature must the wings be maintained at to prevent ice from forming on them during icing conditions at a rate of $1 \mathrm{~mm} / \mathrm{min}$ or less?

Solution

VerifiedWe list our givens:

$\begin{aligned}\\ h & = 150 \frac{\text{ W}}{\text{ m}^2 \cdot ^o\text{C}} \rightarrow \text{ Heat transfer coefficient.}\\ \rho & = 920 \frac{\text{ kg}}{\text{ m}^3} \rightarrow \text{ Density of ice at } 0^o\text{C}.\\ x & = \frac{1\text{ mm}}{\text{ min}} \rightarrow \text{ Rate of ice formation.}\\ L & = 333.7 \frac{\text{ kJ}}{\text{ kg}} \rightarrow \text{ Latent heat of water at }0^o\text{C}.\\ T_{\infty} & = 0^o\text{C} \rightarrow \text{ Temperature of ice.}\\ \end{aligned}$

**Goal is to determine the temperature of wing to prevent ice formation more than** $\frac{1\text{mm}}{\text{min}}$.

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