UPSCALING IN DYNAMICAL HEAT TRANSFER PROBLEMS IN BIOLOGICAL TISSUES
Claudia Timofte · Acta Physica Polonica B · 2008
The asymptotic behaviour of the solution of a nonlinear dynamical boundary-value problem describing the bio-heat transfer in microvascular tissues is analysed. Our domain is an e-periodic structure, consisting of two parts: a solid tissue part and small regions of blood of a certain temperature, e representing a small parameter related to the characteristic size of the blood regions. In such a domain, we shall consider a heat equation, with nonlinear sink and source terms and with a dynamical condition imposed on the boundaries of the blood zones. The limit equation, as e → 0, is a new heat equation, with extra-terms coming from the influence of the non-homogeneous dynamical boundary condition.