# Numerical treatment of nonlinear Fourier and Maxwell-Cattaneo-Vernotte heat transport equations

@article{Kovacs2020NumericalTO, title={Numerical treatment of nonlinear Fourier and Maxwell-Cattaneo-Vernotte heat transport equations}, author={R'obert Kov'acs and Patrizia Rogolino}, journal={International Journal of Heat and Mass Transfer}, year={2020} }

## 17 Citations

The role of the initial states for non-Fourier heat equations

- Physics
- 2022

There are several models for heat conduction non-Fourier equations in the literature that are important for various practical problems. These models manifest themselves in partial differential…

Open Mathematical Aspects of Continuum Thermodynamics: Hyperbolicity, Boundaries and Nonlinearities

- MathematicsSymmetry
- 2020

This work aims to present that each approach has its specific problems, such as how the initial and boundary conditions can be formulated, how the coefficients in the partial differential equations are connected to each other, and how it affects the appearance of nonlinearities.

Lagging heat models in thermodynamics and bioheat transfer: a critical review

- Physics, EngineeringContinuum Mechanics and Thermodynamics
- 2022

The accuracy of the classical heat conduction model, known as Fourier’s law, is highly questioned, dealing with the micro and nanosystems and biological tissues. In other words, the results obtained…

Analytical and numerical modelling of ballistic heat conduction observed in heat pulse experiments

- Physics
- 2020

Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to…

Recent Progresses and Future Directions of Lagging Heat Models in Thermodynamics and Bioheat Transfer

- Physics
- 2021

The accuracy of the classical heat conduction model, known as Fourier’s law, is highly questioned, dealing with the micro/nanosystems and biological tissues. In other words, the results obtained from…

New perspectives for modelling ballistic-diffusive heat conduction

- Physics
- 2021

Among the three heat conduction modes (diffusive, second sound, and ballistic propagation), the ballistic one is the most difficult to model. In the present paper, we discuss its physical…

A State-of-the-Art Review on Integral Transform Technique in Laser–Material Interaction: Fourier and Non-Fourier Heat Equations

- PhysicsMaterials
- 2021

F Fourier and Non-Fourier heat equations have proved their reliability in the case of laser–metallic materials, electron beam–biological and –inorganic materials, laser–semiconducting materials, and laser–graphene material interactions.

A general finite element method: Extension of variational analysis for nonlinear heat conduction with temperature-dependent properties and boundary conditions, and its implementation as local refinement

- PhysicsComput. Math. Appl.
- 2021

Elliptic Equations of Heat Transfer and Diffusion in Solids

- Physics
- 2021

We propose an alternative system of equations for the heat transfer and diffusion in solids, which leads to the second-order elliptical equations describing evolution of temperature and concentration…

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