Cooling of hot metal forging

[engineer23]

If a hot metal forging is cooled by dropping it into a pool of water, how many boundary/initial conditions do I need to solve for the temperature? I don't want to make any assumptions about temperature gradients within the forging itself (Biot number may be large, which precludes use of lumped capacitance method). If I start with the heat diffusion equation and eliminate generation, I need 2 boundary conditions for each of the three coordinate directions and 1 initial condition for the time dependent term, which is 7 conditions altogether?

 

[Mech_Engineer]

Are you taking into account the fact that typically a hot metal forging will be much hotter than the boiling point of water, so initial cooling will not be achieved through conduction or convection but rather by vaprization of water touching its surface? Once the forging cools to below the boiling point of water, then the part will be subject to natural convective currents in the fluid around it.