Related papers: Splitting schemes for hyperbolic heat conduction e…
Additive manufacturing and welding processes are highly sensitive to heat dissipation, where improper thermal management leads to residual stresses, distortions, and cracking. Existing heat transfer models, such as Rosenthal's solutions,…
There are various situations where the classical Fourier's law for heat conduction is not applicable, such as heat conduction in heterogeneous materials or for modeling low-temperature phenomena. In such cases, heat flux is not directly…
The heat equation, based on Fourier's law, is commonly used for description of heat conduction. However, Fourier's law is valid under the assumption of local thermodynamic equilibrium, which is violated in very small dimensions and short…
The effects of MHD boundary layer flow of non-linear thermal radiation with convective heat transfer and non-uniform heat source/sink in presence of thermophortic velocity and chemical reaction investigated in this study. Suitable…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
A new lattice Boltzmann scheme associated with flexible specific heat ratio is proposed. The new free degree is introduced via the internal energy associated with the internal structure. The evolution equation of the distribution function…
A theory of temperature dynamics in many-body systems driven by time-dependent external sources is introduced. The formalism based on the combination of the perturbation theory and the fluctuational-electrodynamics approach in many-body…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
We study numerically the standard one pressure model of two fluid flows with energy equations. This system is not solved in time derivative. It has been transformed into an equivalent system solved in time derivative. We show that the…
We perform non-equilibrium simulations to study heat conduction in two-dimensional strongly coupled dusty plasmas. Temperature gradients are established by heating one part of the otherwise equilibrium system to a higher temperature. Heat…
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow can not be computed exactly. Instead, we use a numerical…
A new quasilinear mathematical model of heat conduction with finite velocity of heat front movement is offered.
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
We investigate the radiative heat transfer and spatial distributions of stationary temperatures in periodic many-body systems composed of alternating slabs of two different materials. We show that temperature distributions exhibit an…
I revisit the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] and describe, for one-dimensional systems of arbitrary sizes whose ends are in contact with thermal baths at different…
We use the hyperbolic subdiffusion equation with fractional time derivatives (the generalized Cattaneo equation) to study the transport process of electrolytes in media where subdiffusion occurs. In this model the flux is delayed in a…
We review the near-field radiative heat flux between hyperbolic materials focusing on multilayer hyperbolic meta-materials. We discuss the formation of the hyperbolic bands, the impact of ordering of the multilayer slabs, as well as the…
It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
A heat equation with uncertain domains is thoroughly investigated. Statistical moments of the solution is approximated by the counterparts of the shape derivative. A rigorous proof for the existence of the shape derivative is presented.…