Hey guys, I'm hoping someone can help me out, as i have an exam tomorrow and have no began panicing as i've found a question i can't seem to get to the end of... Here is the question itself; A large crucible contains a metal of thermal conductivity, κ = 12.5 Watts. m-1.K-1, electrical resistivity, ρ = 5 × 10-7 Ω.m, and melting point 70°C. A vertical electrical conductor ends in a hemisphere of radius 10 mm which is just embedded in the surface of the metal. If the crucible is maintained at 50 °C, what is the greatest current that can flow from the contact to the crucible without melting taking place? You may ignore heat losses through the conductor and the atmosphere and that all dimensions of the crucible are large compared to the radius of the conductor. My thinking was; As the current flows out it heats the metal by ohmic resistance. The heat generated flows out to infinity (the crucible is very large) by conduction along a temperature gradient. To solve the problem you i assume you need to set up the equations for heat generation and flow in a radial element (a thin hemispherical shell). Hence, I started by expressing my heat flow as followed (Q) (k = conductivity of material); dQ/dt = k A dT/dx I then evaluated both dQ/dt and dT/dr and the points r and r+dr The left hand side for dQ/dt gives you the heat flow dQ(dr)/dt - this i reconginised was the power.. which can be expressed as P = I^2 * R and R can be changed for (rho * L)/A This meant i could take out several constants.. including I and would now be evaluated at points r/A(r) I continued to try and evaluate points to get to a point where i can actually solve for I.. Struggling to say the least. And some advice and guidance would be so appreciated! Thanks guys... hope you can follow my thinking.