Nonlocal heat conduction approach in a bi-layer tissue during magnetic fluid hyperthermia with dual phase lag model

In this work, a nonlocal dual-phase-lag (NL DPL) model is introduced to accommodate the effects of thermomass and size-dependent thermophysical properties at nanoscale heat transport. Heat transfer at nanoscale is essentially nonlocal and quite different from that at the micro- or macro scale. To illustrate the nonlocal effect, a bi-layered structure is considered during magnetic fluid hyperthermia (MFH) treatment which is used successfully in prostate, liver, and breast tumors and the effect of size-dependent characteristic lengths is discussed in tumor and normal region of tissue. The problem is solved by using the finite difference scheme in space coordinate and Legendre wavelet Galerkin approach in time coordinate with the Dirichlet, Neumann and Robin boundary conditions. The effect of boundary conditions, characteristic lengths, phase lag parameters and nanomaterial parameters is discussed in tumor and healthy tissue domain and the results are presented graphically. This study is expected to be helpful for modeling of bioheat transfer equation at nano-scale, and may be beneficial to design nano-sized and multi-layered devices for heat transfer.