Within the framework of the potent lumped model, unsteady heat conduction takes place in a solid body whose space–mean temperature varies with time. Conceptually, the lumped model subscribes to the notion that the external convective resistance at the body surface dominates the internal conductive resistance inside the body. For forced convection heat exchange between a solid body and a neighboring fluid, the criterion entails to the lumped Biot number Bil=(h¯/ks)(V/A)<0.1, in which the mean convective coefficient h¯ depends on the impressed fluid velocity. However, for natural convection heat exchange between a solid body and a fluid, the mean convective coefficient h¯ depends on the solid-to-fluid temperature difference. As a consequence, the lumped Biot number must be modified to read Bil=(h¯max/ks)(V/A)<0.1, wherein h¯max occurs at the initial temperature Ti for cooling or at a future temperature Tfut for heating. In this paper, the equivalence of the lumped Biot number criterion is deduced from the standpoint of the solid thermal conductivity through the solid-to-fluid thermal conductivity ratio.
The multiplicity of steady-state solutions arising from microwave heating. I. Infinite Biot number and small penetration depth