A spherical steel ball of 12mm diameter is initially at 1000k. It is slowly cooled in a surrounding of 300k. The heat transfer coefficient between the steel ball and the surrounding is 5w/m^2 k. The thermal conductivity of steel is 20w/m-k. The temperature difference between the centre and the surface of the steel ball is
Answers
Small because conduction resistance is far less than the convective resistance.
Concept:
Biot Number gives an indication of the ratio of internal (conduction) resistance to the surface (convection) resistance.
Bi=hLck=Rth,conductionRth,convection
Bi<<1⇒Rth,conductionRth,convection<<1⇒Rth,conduction<<Rth,convection
When the value of Bi is small, it indicates that the system has small conduction resistance i.e. relatively small temperature gradient or the existence of practically uniform temperature within the system.
The convective resistance then predominates and the transient phenomenon is controlled by the convective heat exchange.
Calculation:
Characteristic dimension, L=VA=43πr34πr2=r3=2mm
Bi=hLk=5×0.00220=0.0005
For the given condition the Biot number tends to zero, that means conduction resistance is far less than convection resistance.