Heat Source Term Research Articles

High power laser heating of nuclear ceramics for the generation of controlled spatiotemporal gradients

The use of high-power lasers to reach the high temperatures typical for off-normal conditions in nuclear reactor fuel or to determine its properties at high temperature is a relevant and proven technique in the nuclear research community. Conducting studies at high temperature with full control in space and time of the thermal gradients is, however, a challenge. In this paper, we present a combination of methodologies, experiments, and models to drive nuclear fuel samples in thermal conditions relevant to the study of nuclear fuel materials. Based on the use of high-power (kW) lasers with beam shaping and temporal laser control, our experimental approach allows one to heat depleted UO2 samples and obtain precise control of the temporal gradients, in the ms range, and spatial gradients, in the 100 μm range. The coupling with numerical simulations allows one to determine the temperature distribution in the depth of the sample and to develop a thermo-mechanical interpretation of the results. We will present the methodology allowing one to properly compare experimental and simulation results by taking into account the optical response of the instrumentation, the laser–UO2 interaction, and the resulting heat source term. We will show that we can express the heat source term resulting from the laser loading either by an analytical description or statistically based on Monte-Carlo simulation. A fairly good agreement between the recorded temperature and the simulation results is shown. The presented methodology can be extended to other materials with a proper choice of laser wavelength and instrumentation based on the optical properties of the investigated material.

Variable viscosity effects on unsteady MHD reactive third-grade fluid with asymmetric convective cooling within porous Couette device

The principal motive of this study is to present a detailed account of the impact of both flow and energy profile of a time-dependent, incompressible, reactive third-grade fluid having low electrical conductivity besides variable viscosity through a porous channel accompanied by asymmetric cooling at the walls. The highly coupled equation of motion and energy manifested as non-linear partial differential equations are represented as algebraic equations using an implicit finite difference scheme and solved numerically by implementing the damped-Newton method. The solution obtained is eventually simulated using MATLAB and the resulting graphs representing the influence of non-dimensional parameters on the flow field and temperature field are discussed thoroughly. It is noted that an increase in γ values enhances non-Newtonian fluid properties which result in the thickening of the fluid and consequently fall in fluid velocity. An increase in reaction parameter and variable viscosity values remarkably enhances viscous heating source terms and contributes to the overall rise in fluid temperature. It is also observed that due to the nature of coupling of the source terms, for the majority of the non-dimensional parameters, there is a simultaneous increase or decrease in the momentum and energy profile of the fluid.

An analytical study of coupled convective heat and mass transfer with volumetric heating describing sublimation of a porous body under most sensitive temperature inputs: Application of freeze-drying

Sublimation heat-mass transfer has great applications in the pharmaceutical and food industries, such as the preservation of biological products, accelerated freeze-drying (AFD), energy storage systems, microwave freeze-drying, and enabling long-time active covid like vaccines. The current technological demand encourages investigators to provide new knowledge for freeze-drying so that it reduces the high economic cost, prevents materials from being denatured, and remains stable for a long time. In connection with this, it is of key interest to analyze the impact of convective heat and mass transfer, the rate of water vaporization, and the volumetric heating source under the most realistic temperature inputs. Despite the available works on sublimation, there is still a lack of mathematical modeling that accounts for these informations together and is presently being considered. This paper presents a heat and mass transfer problem describing sublimation in a half-porous space. The mathematical model accounts for convective heat/mass transfer and a volumetric heat source within dried and frozen regions. In addition, convection driven by the mass transfer of ice crystals within the dried region is also considered. Three different types of temperature input are placed at the surface x=0 to obtain the rapid sublimation process without harming the material properties. The exact solution to the problem is obtained successfully by using similarity transformation. The impact of various problem parameters on sublimation is comprehensively studied. In this study, it is found that with a volumetric heating source term G0, material sublimates faster than without one. Furthermore, convective heat transfer in terms of Pe1 and Pe2, enhances the temperature within the porous medium, and as a result, material sublimates faster than usual. As the value of the convective term β goes up, a reduction in the temperature field is observed. The temperature of the medium rises as the value of the Kirpichev-like number Ki increases. Similar observation is found in the case of Biot like number Bi. The concentration profile decreases as the value of the Luikov number Lu increases. It is also found that Newton-type temperature input offers a faster sublimation rate in comparison to constant and flux-type temperature input. The analytical results obtained in this study show excellent agreement with previous available results. These results provide a comprehensive theoretical and mathematical understanding of sublimation heat/mass transfer and are expected to be useful in energy storage systems, food technology, and accelerated freeze drying.

Application design and two-phase flow simulation of a circulating solar heat collection tube in the desalination system of western China

This paper designed a kind of circulating solar heat collection tubes (CSHT) for a cyclic desalination system. CSHT was consist of tubes with vacuum layer, I-shaped and U-shaped connectors. In order to analyze the influence of factors of solar intensity (I), inlet fluid temperature (Ti), inlet velocity (u) and tube diameter (D) on the thermal performance of CSHT, phase transformation process in tubes was simulated by FLUENT, and User-Defined Functions of mass and heat source terms were introduced. Results showed outlet temperature and vapor mass fraction were both positively correlated with I and Ti, but negatively correlated with u and D. Then sensitivity analysis was introduced and conducted for ranking the factors, and their average sensitivity values were in descending order of I, D, u, Ti. Under orthogonal test, three optimal schemes (D = 25 mm) of simulation were picked out, and their average heat collection efficiency and exergy efficiency were 81.31% and 77.50%, respectively. Finally, similarity criterion was applied to transmit information of quantitative data from experimental model to corresponding prototype. Through similarity criteria analysis, three optimal schemes were obtained under the condition of tube diameter is 37 mm (diameter is 25 mm in numerical simulation). Optimal operation velocities can be 0.097 m/s, 0.127 m/s and 0.164 m/s respectively in the pilot of CSHT, under the solar intensity values of 800 W/m2, 1000 W/m2 and 1200 W/m2.

Numerical simulation of the nanofluid flow consists of gyrotactic microorganism and subject to activation energy across an inclined stretching cylinder

The current study examines the numerical simulation of the nanoliquid boundary layer flow comprising gyrotactic microbes with mass and energy transmission across a stretching inclined cylinder. The consequences of chemical reaction, heat generation/absorption, buoyancy force and Arrhenius activation energy is also considered on the nanofluid flow. The flow mechanism has been modeled in the form of system of nonlinear partial differential equations (PDEs). That system of PDEs is further transform into the dimensionless set of ordinary differential equations (ODEs) through the similarity substitutions. The obtained set of differential equations are numerically computed through the parametric continuation method (PCM). The effects of the distinct physical constraints on the energy, velocity, mass and the motile microbe profiles are discoursed and evaluated through Tables and Figures. It has been noticed that the velocity curve drops with the influence of inclination angle and Richardson number, while enhances against the variation of curvature factor. Furthermore, the energy field boosts with the upshot of inclination angle and heat source term, while declines with the influence of Prandtl number and Richardson number.

Global well‐posedness of the 3D primitive equations with only horizontal eddy diffusivity and delays in both convective and heat source terms

In ocean and atmospheric dynamics, the strong horizontal turbulent mixing tends to produce horizontal eddy viscosity, so the horizontal scale is much larger than the vertical scale. At the same time, as a fluid, the motion of the atmosphere or the ocean has a delayed property to some extent. In this paper, we consider 3D viscous primitive equations with only horizontal eddy diffusivity and delays in both convective and heat source terms. With some suitable assumptions on delay term, we prove the existence and uniqueness of strong solution with initial data and obtain the existence and uniqueness of the stationary solution. Moreover, we prove that the strong solution converges exponentially to the stationary solution under some suitable assumptions.

Improved multi-relaxation time thermal pseudo-potential lattice Boltzmann method with multi-block grid and complete unit conversion for liquid–vapor phase transition

In recent years, the thermal pseudo-potential lattice Boltzmann method (LBM) has been widely adopted in numerical simulations of liquid–vapor phase transition systems. However, the unit conversion for thermal pseudo-potential LBM remains incomplete and elusive, and the numerical simulation efficiency is limited by the uniformly single-block grid. In this paper, the dimensionless evolution equations of thermal pseudo-potential LBM with multi-relaxation time operators are derived for the convenience of adopting real physical parameters and improvement of computational efficiency. The energy equation is re-derived and improved for enhanced accuracy and convenience of numerical calculation. Additionally, a more accurate Martin–Hou equation of state for cryogen is adopted and a modified term for surface tension coefficient is improved to confirm that the surface tension coefficient is grid independent. Moreover, a three-layer boundary structure for the coarse grid is proposed to introduce the multi-block grid into the thermal pseudo-potential LBM for taking into account the intermolecular force and internal heat source term. The aforementioned works improve the thermal pseudo-potential LBM and enable efficient and accurate simulation of the liquid–vapor phase transition within the three-dimensional structure with real physical parameters of a specific working fluid. Finally, numerical simulations are adopted to validate the efficiency and accuracy of the proposed improvements for simulating liquid–vapor phase transition.

Analysis on roles of thermal radiation to evaporation and combustion of fuel droplets

Thermal radiation is a significant mode of energy transmission besides conduction and convection in most combustion systems. Accurate treatment of thermal radiation is a crucial element for predicting the flame structure and pollutant formation. However, thermal radiation to fuel droplet evaporation is often neglected in the numerical simulations of two-phase spray combustion systems. In this paper, computational analysis on the thermal radiation to evaporation and combustion of fuel droplets in two-phase spray combustion is conducted. The influence of flame radiation on droplet evaporation and combustion is studied by adding radiation source term to the energy equation describing droplet evaporation process. Radiation transfer equation is solved, in which the radiation of CO2, H2O and soot is imposed to consider radiation effect of the flame. The partially premixed combustion model is employed, in which radiation heat transfer between droplet and ambient gases is taken into account. A reduced chemical reaction mechanism for n-heptane consisting of 76 species and 349 reactions is used. Four different numerical setups have been used and compared, and the simulation results coincide with the experiment data in terms of spray statistics and flame shapes. The peak flame temperature increases by 28 K when the radiative heat source term in the evaporation process is considered. The droplet evaporation is significantly enhanced by thermal radiation, leading to a promotion of 34.8% in C7H16 concentration in the center region of combustor. The concentration of combustion products, such as H2O and CO2, increases by 13.2% in the reaction region.

NIRwave: A wave-turbulence-driven solar wind model constrained by PSP observations

Aims. We generate a model description of the solar wind based on an explicit wave-turbulence-driven heating mechanism, and constrain our model with observational data. Methods. We included an explicit coronal heating source term in the general 3D magnetohydrodynamic code NIRVANA to simulate the properties of the solar wind. The adapted heating mechanism is based on the interaction and subsequent dissipation of counter-propagating Alfvén waves in the solar corona, accounting for a turbulent heating rate Qp. The solar magnetic field is assumed to be an axisymmetric dipole with a field strength of 1 G. Our model results are validated against observational data taken by the Parker Solar Probe (PSP). Results. Our NIRwave solar wind model reconstructs the bimodal structure of the solar wind with slow and fast wind speeds of 410 km s−1 and 650 km s−1 respectively. The global mass-loss rate of our solar wind model is 2.6 × 10−14 M⊙ yr−1. Despite implementing simplified conditions to represent the solar magnetic field, the solar wind parameters characterising our steady-state solution are in reasonable agreement with previously established results and empirical constraints. The number density from our wind solution is in good agreement with the derived empirical constraints, with larger deviations for the radial velocity and temperature. In a comparison to a polytropic wind model generated with NIRVANA, we find that our NIRwave model is in better agreement with the observational constraints that we derive.

Theoretical and Experimental Analysis of the Thermal Response in Induction Thermography in the Frequency Range of 2.5 Hz to 20 kHz

The one-dimensional propagation of electromagnetic waves and the propagation of the resulting thermal waves in conducting material are analysed in a coherent way. The heat release due to resistive losses has a static and an oscillating part. Both are considered as heat source terms for the thermal diffusion equation. The time dependence of the temperature is described by analytical solutions. Electrically and thermally conducting materials are classified by the ratio of thermal penetration depth to the skin depth. Experiments performed on ferritic steel, stainless steel and carbon-fibre-reinforced polymer show the time dependence of the thermal signal after heating begins, as described by the theory. At low induction frequencies, an oscillating part of the surface temperature at the double of the induction frequency is detected in accordance with the theory. The results point out new opportunities for induction thermography.

Flow and radiation modeling over a Martian entry vehicle

The high-temperature shock layer around re-entry vehicles strongly emits radiation through atomic lines and molecular bands. Radiative heat transfer strongly affects boundary layer flow and heat transfer. A novel spectral model based on k-distribution is implemented and coupled with a hypersonic flow solver in OpenFOAM to simulate heat transfer over a Martian entry vehicle. The Navier-Stokes equations with finite rate chemistry are used to model hypersonic chemically reacting flows. The convective terms in the governing equations are treated with various flux schemes (HLL, AUSM+, Kurganov, and Tadmor). The non-gray radiative properties of shock layer gases were modeled with the Emission-weighted Full Spectrum k-distribution (EFSK) method. The Radiative Transfer Equation (RTE) is solved with the P1 radiative solver to calculate the wall heat flux and radiative heat source term. At a high Mach number, the radiative heat flux is dominant compared to the convective heat flux. The numerical results for Mach number 26 are compared with published data and are found to be in good agreement. All the flux schemes provided results in close agreement, with minor differences, especially near the wall for the AUSM+ flux scheme.

Синхронизация конвективных течений двухкомпонентной жидкости в смежных ячейках пористой среды

In this work, we study the Soret-driven convection of a two-component fluid in adjacent rectangu-lar cells of a porous medium heated from below in the presence of a gravitational field. In each cell, a long-wavelength oscillatory instability is possible; it can be described by means of phase reduction, which makes it possible to study the synchronization of currents. The horizontal bounda-ries of the cells are assumed to be impenetrable (including for impurities), the heat flux is assumed to be fixed. The vertical boundaries have low thermal conductivity. Fluid motions are described by the Darcy-Boussinesq approximation. Additionally, in this system there is a distributed heat source term describing the heat exchange between the cells. In this way, the equations become coupled via the temperature field. The equations within the long-wavelength approximation are derived using the standard method of multiple scales. An analytical description of the system within the frame-work of a weakly nonlinear analysis can only be constructed near the threshold of the convective instability of the system, and the issue of collective effects is relevant for oscillatory modes; there-fore, we restrict our study to the case of an oscillatory instability. On the basis of equations for the amplitudes of the coupled oscillatory modes, we derived equations for the oscillation phases, which are the key equations of the phase description. For these equations, we found the values of the pa-rameters at which the system has the regime of synchronization of currents; the solution for a stable synchronous regime is also reported.

Inverse time-dependent source problem for the heat equation with a nonlocal Wentzell-Neumann boundary condition

<abstract><p>In this work, we consider the problem of recovering the heat source term for the heat equation with a nonlocal Wentzell-Neumann boundary condition subject to an integral overdetermination condition. Conditions for the existence and uniqueness of the classical solution of the inverse problem are revisited, and a numerical method for practical source reconstruction is introduced. Unlike all of the source reconstruction methods found in literature, the method introduced in this work computes regularized solutions from a triangular linear system arising from a semi-discretization in the space of the continuous model. Regularization is introduced by applying the generalized singular value decomposition of a proper matrix pair along with truncation. Numerical results illustrate the effectiveness of the method.</p></abstract>

Thermo-rheological reduced order models for non-Newtonian fluid flows with power-law viscosity via the modal identification method

In the framework of melted polymer flows characterization, this study deals with the formulation, construction and validation of thermo-rheological Reduced Order Models (ROMs) for incompressible flows of pseudoplastic fluids. The dynamic viscosity is described by a shear rate power law defined by consistency index K and pseudoplastic index n. The flow dynamics are assumed to be quasi-static whereas the thermal state is unsteady. Viscous dissipation acts as a heat source term in the energy equation. ROMs are built through the Modal Identification Method (MIM). First, their general form is derived from governing local conservation equations and the viscosity power-law, with an original approach to handle the issues related to the pseudoplastic index n. Then ROMs are identified using Particle Swarm Optimization and Ordinary Least Squares, from simulations coming from a reference Full Order Model (FOM). The approach is applied to a polymer flow in an annular duct, corresponding to an experimental lab apparatus. ROMs allow computing temperature at chosen locations of interest whatever the applied inputs, here parameters K, n and inlet flowrate as well as a time-varying volumetric heat source power in the central axis. Compared to the reference Finite Elements FOM, computing time is considerably reduced with limited loss of accuracy.

Molecular Photothermal Effects on Time-Resolved IR Spectroscopy: Solute-Solvent Intermolecular Energy Transfer.

Time-resolved IR pump-probe (IR-PP) and two-dimensional IR (2D-IR) spectroscopy are valuable tools for studying ultrafast chemical and biological processes in solutions. However, the corresponding signals at long times are obscured by the molecular photothermal effects resulting from the heat dissipation of vibrationally photoexcited molecules to the surroundings. Recently, a phenomenology model was used to describe molecular photothermal effects on IR-PP signals and the diagonal and cross-peaks of 2D-IR spectra at long pump-probe delay times. Here, we consider the thermal diffusion equation with a time-dependent heat source term to describe the solute-solvent energy transfer process. An approximate solution to the nonhomogeneous differential equation shows that the molecular photothermal effect is determined by the mean intermolecular distance between IR-absorbing molecules. We show that the time profile of heat dissipation from a vibrationally excited molecule to the surroundings, which provides information about the mechanisms involved in the solute-solvent intermolecular energy transfer process in solutions, can be directly measured by analyzing the molecular photothermal IR-PP and 2D-IR signals. We anticipate that the present work can be used to interpret local heating-induced time-resolved IR spectroscopic signals and understand the rate of and the mechanisms involved in the conversion from high-frequency molecular vibrational energy to solvent kinetic energy in condensed phases.

Adaptive simulation of 3D thermometry maps for interventional MR-guided tumor ablation using Pennes’ bioheat equation and isotherms

Minimally-invasive thermal ablation procedures have become clinically accepted treatment options for tumors and metastases. Continuous and reliable monitoring of volumetric heat distribution promises to be an important condition for successful outcomes. In this work, an adaptive bioheat transfer simulation of 3D thermometry maps is presented. Pennes’ equation model is updated according to temperature maps generated by uniformly distributed 2D MR phase images rotated around the main axis of the applicator. The volumetric heat diffusion and the resulting shape of the ablation zone can be modelled accurately without introducing a specific heat source term. Filtering the temperature maps by extracting isotherms reduces artefacts and noise, compresses information of the measured data and adds physical a priori knowledge. The inverse heat transfer for estimating values of the simulated tissue and heating parameters is done by reducing the sum squared error between these isotherms and the 3D simulation. The approach is evaluated on data sets consisting of 13 ex vivo bio protein phantoms, including six perfusion phantoms with simulated heat sink effects. Results show an overall average Dice score of 0.89 ± 0.04 (SEM < 0.01). The optimization of the parameters takes 1.05 ± 0.26 s for each acquired image. Future steps should consider the local optimization of the simulation parameters instead of a global one to better detect heat sinks without a priori knowledge. In addition, the use of a proper Kalman filter might increase robustness and accuracy if combined with our method.

Biological heat and mass transport mechanisms behind nanoparticles migration revealed under microCT image guidance

Background and objectivesBlood perfusion, infusion rate, distribution and heating induced redistribution of magnetic nanoparticles inside tumour interstitium governs the heating protocol designs. This study aims to answer three important questions: Why do magnetic nanoparticles redistributes? What causes their migration? Why it is important to be included in priori-treatment planning simulations? Our aim is to test how the regulation of magnetic nanoparticles affects the temperature distribution and how this temperature change modifies tumour microenvironment. We have tested our hypothesis for two cases: (1) when the nanoparticles are lying in close proximity to the flank position of tumour i.e. near the interface of tumour and healthy tissue and (2) when the nanoparticles are located near the skin surface of tumour. Materials and methodsSAS® and MATLAB programs are used to average micro-CT cross-sectional slices containing three-dimensional clusters of pixels corresponds to nanoparticles as a SAR file and Concentration distribution file import to the COMSOL-Multiphysics® 5.2 FEA software for evaluation of temperature distribution and its resulted collateral thermal damage. The volumetric heat generation rate (qMNH‴) is kept ∼ 0.37 W for infusion rate of 4 μL/min. Pennes bioheat equation is three-way coupled with traditional Arrhenius thermal damage model, modified concentration equation in which heat source term (SAR) varies in a directly proportional relationship with Concentration distribution. All variables i.e. Diffusion coefficient, porosity, blood perfusion, metabolic heat generation are varying as a function of thermal damage for a coupled biophysics problem. ResultsThermal signatures of cell-death were evaluated for two case scenarios. The initial distribution volume is 188.46 mm3. On compare and contrast, 6.24% larger thermal diffusion is seen at outer extremities case than at the interface. However, the treatment times are 12.90% (1.13 fold more) to achieve a Ω ≥ 4.6 with ΔT=10°C for latter case. On evaluation of “Source maps” (before heating) with “Destination maps” (after heating) suggests migration of nanoparticles from the regions of higher concentration to the regions of lower concentration due to cell-necrosis induced enhancement in tumour interstitial space. Thermal-diffusion of nanoparticles suggests an increase in redistribution volumes by 23.44% and 26.30% respectively during 99.6% transformation of cancerous cells. This study precisely elucidate qualitative and quantitative aspects of this issue. One of the possible reasons of nanoparticle migration is that the dead cells release intracellular solution after the rupturing of cell membrane. We speculate that five-fold increase in diffusion coefficient of nanoparticles might have played a significant role in particle migration. ConclusionsCNIDC (Cell necrosis induced diffusivity change) and CNIPE (Cell necrosis induced porosity enhancement) may be the two intricate mechanisms that promotes nanoparticles migration.

Local to continental scale coupled fire-atmosphere simulation of large industrial fire plume

This paper presents an approach to model the multiscale smoke dispersion following industrial fires, based on the atmospheric code Meso-NH coupled with the ForeFire surface fire code. Meso-NH can solve explicitly micro to meso-scale meteorology, while ForeFire allows for an efficient parametrization of the injected heat and vapour fluxes. The combination of these two models allows for a straightforward implementation of the heat source term and simultaneously accounts for its effect on local meteorology (as convection and latent heat), thus leading to a prognostic representation of the developing plume. In addition to its multiscale reach, the main contribution of the proposed approach is the explicit modelling of the effects of released heat and vapour on the local meteorological conditions which determine the height and the near-to-far scale development of the rising fireplume. The context of the study imposed to set model parameters that allow for faster than real time forecast along with a qualitatively realistic representation of the plume. Quantitative assessments on the physio-chemical properties of the plume require finer physical models which are available at the expense of an increased computational time and require quantitative estimates of the chemicals involved in the combustion, and are let to future developments. Model evaluation in the proximity of the fire is performed by comparing results with a combustion CFD solver on an idealized situation, followed by a mesh sensitivity study. Then, the proposed coupled method is applied to a real-case multi-scale simulation of smoke dispersion from the local (city) to the continental scale, with a twice faster than real-time computation time.

Exact solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

Exact solution for non-classical one-phase Stefan problem with variable thermal coefficients and two different heat source terms

A point source model to represent heat distribution without calculating the Joule heat during radiofrequency ablation

Numerous liver cancer oncologists suggest bridging therapies to limit cancer growth until donors are available. Interventional radiology including radiofrequency ablation (RFA) is one such bridging therapy. This locoregional therapy aims to produce an optimal amount of heat to kill cancer cells, where the heat is produced by a radiofrequency (RF) needle. Less experienced Interventional Radiologists (IRs) require a software-assisted smart solution to predict the optimal heat distribution as both overkilling and untreated cancer cells are problematic treatments. Therefore, two of the big three partial differential equations, 1) heat equation (Pennes, Journal of Applied Physiology, 1948, 1, 93–122) to predict the heat distribution and 2) Laplace equation (Prakash, Open Biomed. Eng. J., 2010, 4, 27–38) for electric potential along with different cell death models (O’Neill et al., Ann. Biomed. Eng., 2011, 39, 570–579) are widely used in the last three decades. However, solving two differential equations and a cell death model is computationally expensive when the number of finite compact coverings of a liver topological structure increases in millions. Since the heat source from the Joule losses Qr = σ|∇V|2 is obtained from Laplace equation σΔV = 0, it is called the Joule heat model. The traditional Joule heat model can be replaced by a point source model to obtain the heat source term. The idea behind this model is to solve σΔV = δ0 where δ0 is a Dirac-delta function. Therefore, using the fundamental solution of the Laplace equation (Evans, Partial Differential Equations, 2010) we represent the solution of the Joule heat model using an alternative model called the point source model which is given by the Gaussian distribution.Qrx=∑xi∈Ω1K∑icie−|x−xi|22σ2where K and ci are obtained by using needle parameters. This model is employed in one of our software solutions called RFA Guardian (Voglreiter et al., Sci. Rep., 2018, 8, 787) which predicted the treatment outcome very well for more than 100 patients.