Investigation and modeling of heat transfer with phase-lag in biological tissues

Abstract

In this report, the equivalence between the phase-lagging and fractional (fractal) models of anomalous diffusion is investigated. Their respective solutions, each providing its own unique physical description of a heat transfer process, are equated to yield the fundamental correlative solution. The simplest form of the expression, however, is not closed-form. Nevertheless, being analytical, numerical methods remain pertinent. The dimensionless diffusivity is then plotted against time for the range of Hurst exponents, elucidating the nuances of the equivalent responses in characterising sub-, super-, as well as the three classical models of heat diffusion. Independent validation of the preceding study is through a numerical algebraic constraint of the zero function solution. A good initial approximation of the three coupled variables is germane to the extraction of any semblance of the exact numerical solution, and wherein accentuates the extreme sensitivity of the equivalent solution.