Adiabatic-isothermal mixed boundary conditions in heat transfer

Abstract

Mixed boundary conditions of the adiabatic-isothermal type often arise in the mathematical modeling of heat transfer phenomena. Under certain circumstances, the mixed condition gives rise to singular behavior which cannot be adequately treated by numerical means alone. The numerical procedure must be supplemented by an asymptotic analysis for the local behavior near the singularity. In the special case of a mixed boundary condition on a straight boundary, the strength of the singularity is given in terms of a path-independent integral, the value of which can be determined from the numerical solution for the far-field behavior. Implications of overlooking the singular behavior due to the mixed boundary condition are discussed.