thermal BC's across the interanl surface between the heat sink and air in the channel

n Model Library : Heat transfer module : Tutorial models: heat sink .

It is considered the temperature filed is continuous across the internal surface between the heat sink and the air channel. first of all :

what about heat flux ? It is considered continuous too or not ? if it is not, What kind of thermal BC's across the internal surface between heat sink and air channel ? Please can you state your answer in equations?

thanks

Ahmed ... Udmercy