Find Time to Melt Ice Ball in Water Bath: Heat Conduction

[funoras]

Homework Statement

An ice ball is melting in a water bath. Find the time needed for the ice ball to completely melt. Heat transfer is only due to heat conduction. The radius of the ball is R_0=1cm. The temperature of the water in the bath is t=10°. There is an infinite amount of water compared to the size of the ice ball.
Heat of fusion of water is \lambda=334 kJ/kg
Density of ice is \rho=900 kg/m^3
Thermal conductivity of water is K=0,6 W/(m*K)

Homework Equations

Q=4/3*\pi R_0^3\rho\lambda

The Attempt at a Solution

The equation above is the only thing i know.

 

[LawrenceC]

What class are you taking? The reason why I ask is because this can be considered a moving boundary boundary problem with phase change which is rather advanced.