Thermal analysis of laser-irradiated tissue phantoms using dual phase lag model coupled with transient radiative transfer equation

The present work is concerned with the development and application of dual phase lag (DPL) based heat conduction model for investigating the thermal response of laser-irradiated biological tissue phantoms. The developed heat transfer model has been coupled with the transient form of radiative transfer equation (RTE) that describes the phenomena of light propagation inside the tissue phantom. The RTE has been solved using the discrete ordinate method (DOM) to determine the 2-D distribution of light intensity within the tissue phantom, while finite volume method (FVM) based discretization scheme has been employed for solving the heat transfer model. The developed numerical model has first been verified against the results available in the literature. The results obtained in the form of temperature distribution through DPL model have been compared with conventional Fourier heat conduction model as well as with hyperbolic model. The effects of two phase lags terms in the form of relaxation times i.e. τT and τq associated with DPL model on the resultant thermal profiles have been investigated. Thereafter, the temperature distribution inside the biological tissue phantom embedded with optical inhomogeneities of varying contrast levels have been determined using the DPL-based model. Here the optical inhomogeneities represent the malignant (absorbing inhomogeneity) and benign (scattering inhomogeneity) cells present in an otherwise homogeneous medium. Results of the study reveal that the hyperbolic heat conduction model consistently predicts high temperature values and also the associated thermal profiles exhibit the largest amplitude of oscillations throughout the body of the tissue phantom. The DPL-based model results into relatively lesser oscillations due to the coupled effects of τT and τq. The conventional Fourier model, on the other hand, results into the lowest temperature values without any oscillations in the temperature profiles. The effect of the presence of varying nature of optical inhomogeneities is also brought out quite clearly using the developed DPL-based heat conduction model.