Control of Interface Migration in Nonequilibrium Crystallization of Li2SiO3 from Li2O-SiO2 Melt by Spatiotemporal Temperature and Concentration Fields

During liquid-solid transformation, bulk mass and thermal diffusion, along with the evolved interfacial latent heat, work in tandem to generate interfacial thermodynamic and kinetic forces, the interplay of which decides the solidification velocity and consequently the solidified phase attributes. Hence, access to interface dynamics information in dependence of bulk transfer processes is pivotal to tailor the desired quantity of solid phases of unique compositions. It finds particular application for engineering concentrated Lithium (Li) phases out of Li-ion battery slags, thus generating a high value-added product from a conventional waste process stream. However, considerable challenge exists to predict the impact of the diverse external cooling rates on the evolving internal transfer processes and thus tuning solidification routes for achieving phases of interest. Hence, in this work, a thermodynamically consistent nonequilibrium model, by considering spatiotemporal temperature and concentration fields, is developed and applied to study solidification of Li2SiO3 from a Li2O-SiO2 melt that constitutes an important subsystem of the Li containing battery-recycling slags. The approach treats the sharp solid/liquid interface as a moving heat source. In the presence of different heat extraction profiles, it evaluates the spatial temperature heterogeneity and its implicit correlation to internal material fluxes resulting from maximization of dissipation and consequently the interrelation to interface velocities. Model calculations revealed that irrespective of the external cooling rate, for an initial short time duration, the magnitude of which increased with decreasing cooling rates, the interface velocities show a reducing trajectory directly relatable to the reducing thermodynamic forces due to localized interfacial temperature rise from the generated latent heat of fusion from the initial solidification. This is followed by a thermodynamically controlled regime, whereby for each cooling rate, the interface velocities increase until a maxima, the magnitude of which decreases with decreasing cooling rates. Finally, the interface propagation speeds decrease as controlled by the kinetic regime.

A Non-Fourier Bioheat Transfer Model for Cryosurgery of Tumor Tissue with Minimum Collateral Damage

BACKGROUND AND OBJECTIVES

Incorporation of non-Fourier heat conduction while studying heat transfer phenomena in biological materials has emerged has an important approach as it predicts better and more realistic results than Fourier based models. In this article we have proposed a non-Fourier computational model and applied the same to simulate cryosurgery of lung tumor and attempted minimization of freezing damage of healthy lung tissue using pulsed laser irradiation.

METHODS

A non-Fourier bioheat transfer model for phase change in biological tissues is solved via a Fourier heat conduction based solution approach. A unified model is proposed combining all variants of bioheat models: Fourier's heat conduction based Pennes' bioheat model, hyperbolic heat conduction model and dual phase lag model. The proposed model takes into account the different thermophysical properties of frozen and unfrozen regions. In order to mimic the actual biotransport process, the blood perfusion and metabolic heat generation are switched off in the frozen region. Implicit source based enthalpy method is used to model phase change process. A new iterative enthalpy update equation is developed for capturing evolution of freezing front implicitly. Finite Volume based numerical discretization technique is used to discretize the governing PDE. The resulting discrete algebraic equation set is solved implicitly by Tri-diagonal Matrix Algorithm. The proposed model is verified with existing results from the literature.

RESULTS

For Fourier heat conduction, freezing time of 99.99% of tumor is 1247s, which increases to 1267s for τ_q= 5s (τ_T= 0s) and again reduces to 1255s for τ_q= 5s and τ_T= 3s. τ_q and τ_T are phase lag parameters for non-Fourier heat conduction. For τ_q= 5s and τ_T= 0.05s, the freezing damage of healthy tissue decreases by 23.76% when pulsed laser irradiation (I_o = 10⁶ W/m²) is used to warm the neighboring healthy tissue.

CONCLUSIONS

So non-Fourier bioheat transport models are better and more accurate in predicting temperature history, freezing time and freezing front propagation as compared to Fourier based models. Pulsed laser irradiation can prove to be a very efficient technique in minimizing collateral damage during cryosurgery.

An improved analytical model for heat flow in cancerous tumours to avoid thermal injuries during hyperthermia

The present study highlights an analytical hybrid scheme consisted of a shift of variables and finite integral transform for analysing a local thermal non-equilibrium (LTNE) bioheat model. This model can have utilised to be a betterment of prediction of the temperature field in the localised hyperthermia therapy (LHT) for the treatment of cancer patients. As the hyperthermia treatment is only the application in living tissues, an appropriate initial condition for the therapeutic thermal response is proposed instead of a constant temperature taken in the previous studies based on the 1-D heat flow. The present analysis suggests the therapeutic exposure time of 7776.8s (2.16 h) with constant heat flux and the exposure time of 10969.9s (3.06 h) with a sinusoidal heat flux within the usual temperature range of the hyperthermia (in a combination of thermal ablation and medium temperature hyperthermia) to be more effective in the treatment protocol. The presented results show that fatal injuries (tissue trauma, thermal burn, etc.) of internal organs might be possible to avoid by the current therapeutic condition. Therefore, this study may nullify the adverse effect of the existing model with the constant heating and consequently, the repercussion of the several therapeutic variables is to estimate with the development of a thermal profile for the suitability of a therapeutic condition. On the other hand, the present study well matches with the published analysis in case of both the theoretical and experimental (live tissues of the pig due to unavailability of real-time data on the human body) studies and it found the maximum deviation of the thermal response as 2.26% and 2.66%, respectively.

Numerical Modeling of Heat and Mass Transfer during Cryopreservation Using Interval Analysis

In the paper, the numerical analysis of heat and mass transfer proceeding in an axially symmetrical articular cartilage sample subjected to the cryopreservation process is presented. In particular, a two-dimensional (axially symmetrical) model with imprecisely defined parameters is considered. The base of the heat transfer model is given by the interval Fourier equation and supplemented by initial boundary conditions. The phenomenon of cryoprotectant transport (Me2SO) through the extracellular matrix is described by the interval mass transfer equation. The liquidus-tracking (LT) method is used to control the temperature, which avoids the formation of ice regardless of the cooling and warming rates. In the LT process, the temperature decreases/increases gradually during addition/removal of the cryoprotectant, and the articular cartilage remains on or above the liquidus line so that no ice forms, independent of the cooling/warming rate. The discussed problem is solved using the interval finite difference method with the rules of directed interval arithmetic. Examples of numerical computations are presented in the final part of the paper. The obtained results of the numerical simulation are compared with the experimental results, realized for deterministically defined parameters.

Inverse investigation of non-Fourier heat conduction in tissue

This paper attempts to describe the heat conduction in tissue using the dual-phase-lag mode. Evaluating the thermo-physical parameters is one of the ways to certify the thermal behavior. As a result, the paper simultaneously and inversely estimates the values of τ_q, τ_T and α for bologna based on the dual-phase-lag mode with the measurement data in the literature. The inconsistence in theory discovered in the literatures is eliminated. The calculated results of temperature variation with the estimated values of τ_q, τ_T and α at the measurement location are very close to the experimental data and address the rationality of the present results.