A tessellated continuum method for the analysis of fractal-like cellular heat exchangers

This paper presents ongoing research work directed towards the thermal analysis of cellular heat exchangers. A novel approach is explored which involves the representation of cellular heat exchanger designs with pre-fractals. Utilised here are hole-fill maps whose function is to map elements in a pre-fractal to tiles in a tessellated continuum. The purpose of this approach is to enable thermal analysis to be performed on tessellated continua as opposed to analysis on relatively complex fractal structures. The work reported in this paper is focused on two-dimensional fractal designs and in particular the classical Sierpinski gasket is chosen to test out the theories. Temperature distributions on both pre-fractals and tessellated continua are presented for different heat loading and cooling. The work demonstrates the feasibility of the approach where cooling channels in a pre-fractal manifest as line heat sinks in the corresponding tessellated continuum.