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Water at 0C0^{\circ} \mathrm{C} releases 333.7 kJ/kg333.7 \mathrm{~kJ} / \mathrm{kg} of heat as it freezes to ice (ρ=920 kg/m3)\left(\rho=920 \mathrm{~kg} / \mathrm{m}^{3}\right) at 0C0^{\circ} \mathrm{C}. An aircraft flying under icing conditions maintains a heat transfer coefficient of 150 W/m2150 \mathrm{~W} / \mathrm{m}^{2}. C{ }^{\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 mm/min1 \mathrm{~mm} / \mathrm{min} or less?


Answered 1 year ago
Answered 1 year ago
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We list our givens:

h=150 W m2oC Heat transfer coefficient.ρ=920 kg m3 Density of ice at 0oC.x=1 mm min Rate of ice formation.L=333.7 kJ kg Latent heat of water at 0oC.T=0oC Temperature of ice.\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 1mmmin\frac{1\text{mm}}{\text{min}}.

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