Thermodynamics Ice Melting Question

[ConnorM]

Homework Statement

1. On a hot summer day, you planned a trip to a beach, but you inadvertently took a wrong turn and now you’re worried the ice in your cooler is going to melt. The cooler is 0.5 m × 0.5 m × 0.4 m, and is made with 5 cm thick Styrofoam (k = 0.033 W/m2K). Help your panicking friends by calculating the available time to find the beach before the ice melts away completely. Assume that internal convection coefficient is high enough that the inner surface of the Styrofoam matches that of the melting ice. Assume also that the temperature at the outer surface of the cooler is 10°C and the temperature of the surroundings is 35°C. Neglect any heat transfer from the bottom of the cooler (assume the cooler is resting on the foam filled seat of your car which acts as an insulator). The latent heat of fusion of the ice is 334 kJ/kg.
   

Homework Equations

Basic conduction/convection equations
Q=mL
L - heat of fusion

The Attempt at a Solution

I'm wondering how to determine the inner h value of the cooler and the outer h value in order to determine the heat transfer via convection. I'm confused as to what "Assume that internal convection coefficient is high enough that the inner surface of the Styrofoam matches that of the melting ice. " means.

Also, should a mass have been given in this problem?

 

[Zer0]

My opinion is that mass should be given and if this is in steady state condition i think we have assume that the rate of heat flowing through the styrafoam is completley taken by melting ice to do its change of state.

 

[haruspex]

should a mass have been given in this problem?

Assume it is filled with ice.

Assume that internal convection coefficient is high enough that the inner surface of the Styrofoam matches that of the melting ice.

You have not been told the initial temperature of the ice, so you will have to assume 0C. This statement just means that all the ice will melt before any of the meltwater rises above 0C.

 

[Zer0]

Assume it is filled with ice.

You have not been told the initial temperature of the ice, so you will have to assume 0C. This statement just means that all the ice will melt before any of the meltwater rises above 0C.

Is the mass of ice is required in order to calculate the time?

 

[Chestermiller]

Regarding the convection heat transfer coefficients, the statement about the interface between the styrofoam and the ice means that the inner h is infinite. You don't need to know the outer h because you are told that the temperature at the interface between the styrofoam and the air is 10 C.

Regarding Zer0's question, Haruspex has made it clear that you are supposed to assume that initially, you have a solid block of ice in the chest. Knowing the density of ice and the volume of the chest tells you the mass of ice.