Wall heat flux BC in multiphase

CFDtoy

In single phase flow, specifying Q can be used to computed T based on fourier law. When i specify Q for a multiphase problem, should i use the same Q for both phases (say 2 phases available)?? Even if i try to use modified conductivity as K=alpha*Ki (i=liquid or gas), the resulting temperature prediction becomes too high..

is there any model to specify Q for multiphase simulations??

Thanks,

CFDtoy