Heat transfer through fractal-like porous media: A tessellated continuum approach

A tessellated continuum approach to thermal analysis: discontinuity networks

“…The drawback with the Galerkin approach, however, is that discontinuous behaviour arising from the closing of the pores during the mapping (which is pervasive on tessellations) cannot readily be accommodated. This paper extends the work in references [1,2] by incorporating a network of lines/surfaces on a tessellation at which discontinuous behaviour occurs. The discontinuities can be viewed as enforcing internal boundary conditions where (say) heat fluxes on different parts of a pore's surface are mapped to a single line.…”

“…The ability to match physics on pre-fractals and tessellation was established in reference [2]. The basic idea is to describe the physics of interest in each domain on control volumes, which identify continuous spaces through which matter can flow.…”

“…In the recently developed method of tessellated continuum mechanics, physics defined on fractal porous media is mapped to a corresponding continuum [1,2]. The classical Galerkin finite element method (GFEM) can then be combined with tessellated continuum mechanics to describe thermal physics in cellular structures.…”

“…Similarly, the networkD 3 inT 3 again includesD 1 and the three expansion maps {P 1 , P 2 , P 3 } applied to the networkD 2 inT 2 …”

“…In order to represent better the types of complex geometries found in cellular material, the authors have investigated the use of fractals [2,18], which arise in many other areas of science [19] and play a part in describing a variety of behaviours in nonlinear systems [20]. Fractals can be constructed in a number of ways, but a particularly attractive procedure is by application of a small number of affine contraction maps [2,20,21]. Although complex geometries can readily be represented using fractals, their subsequent use in practical analysis is beset with difficulties.…”