  In the referred paper("H. Karani, C. Huber, Physical Review E, 91(2)(2015)
023304"), a total heat flux continuity condition for conjugate heat transfer
problems with moving interfaces was proposed. The authors asserted both
conductive and advective heat fluxes are conserved simultaneously in their
formulation. This condition had been cited by many subsequent studies. However,
it is found that the total heat flux continuity condition violates Galilean
invariance. The original diffusion heat flux continuity condition is reasonable
for both stationary and moving interfaces.
