Natural convection in heat transfer

I am solving natural convection problem for 5hrs in which first problem start with conduction and finish with natural convection effects for solid liquid interface location. During first 1 and 2hrs the conduction held and remaining 3 to 5hrs natural convection held. The natural convection shows very good effect ,but the conduction first 1 and 2hrs the conduction takes place very first (i.e. solid liquid interface location moves very fast). I used heat capacity methods. Also the time steps I kept as 0.1 then also the conduction becomes very fast for first 1 and 2hrs. Can anybody give the answer why it is happened. Or how I have to controlled the conduction for first 1 and 2hrs for solid liquid effect. Or Which parameters I have to controlled.

Thanks in advanced.
Vinay Patel