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.