Afreezer compartment is covered with a 2-mm-thick layer of frost at the time it malfunctions. if the compartment is in ambient air at 20 °c and a coefficient of h 2 w/(m2 k) characterizes heat transfer by natural convection from the exposed surface of the layer, estimate the time required to completely melt the frost. the frost may be assumed to have a mass density of 700 kg/m3 and a latent heat of 334 kj/kg.

The time required to melt the frost is 3.25 hours.

Explanation:

The time required to melt the frost dependes on the latent heat of the frost and the amount of heat it is transfered by convection to the air .

The heat transferred per unit area can be expressed as:

being hc the convective heat transfer coefficient (2 Wm^-2K^-1) and ΔT the difference of temperature (20-0=20 °C or K).

If we take 1 m^2 of ice, with 2 mm of thickness, we have this volume

The mass of the frost can be estimated as

Then,  the amount of heat needed to melt this surface (1 m²) of frost is

The time needed to melt the frost can be calculated as