Related papers: Numerical solution of the heat conduction problem …
In the present Letter we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario…
The Fourier heat conduction model is valid for most macroscopic problems. However, it fails when the wave nature of the heat propagation or time lags become dominant and the memory or/and spatial non-local effects significant -- in…
We consider the Cauchy problem for a first-order evolution equation with memory in a finite-dimensional Hilbert space when the integral term is related to the time derivative of the solution. The main problems of the approximate solution of…
We consider the thermal dunking problem, in which a solid body is suddenly immersed in a fluid of different temperature, and study both the temporal evolution of the solid and the associated Biot number -- a non-dimensional heat transfer…
This work considers the subdiffusion problem with non-positive memory, which not only arises from physical laws with memory, but could be transformed from sophisticated models such as subdiffusion or subdiffusive Fokker-Planck equation with…
We consider the evolution of the temperature $u$ in a material with thermal memory characterized by a time-dependent convolution kernel $h$. The material occupies a bounded region $\Omega$ with a feedback device controlling the external…
We propose a causal heat conduction model based on a heat kernel violating the fading memory paradigm. The resulting transport equation produces an equation for the temperature. The model is applied to the discussion of two important issues…
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated by differential equations with delay terms. This approach is…
We study the dynamical correlation functions and heat conduction for the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by quadratic and cubic intersite potential. Even in the…
We consider three-dimensional models for rate-independent processes describing materials undergoing phase transformations with heat transfer. The problem is formulated within the framework of generalized standard solids by the coupling of…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in…
We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a),…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
The term material with memory is generally used to indicate materials whose mechanical and/or thermodynamical behaviour depends not only on the process at the present time but also on the history of the process itself. Crucial in heat…
In homogenization theory, mathematical models at the macro level are constructed based on the solution of auxiliary cell problems at the micro level within a single periodicity cell. These problems are formulated using asymptotic expansions…
This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon…
It has been observed in many numerical simulations, experiments and from various theoretical treatments that heat transport in one-dimensional systems of interacting particles cannot be described by the phenomenological Fourier's law. The…