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A self-similar solution for time evolution of quasi-spherical, self-gravitating accretion flows is obtained under the assumption that the generated heat by viscosity is retained in the flow. The solutions are parameterized by the ratio of…
The variational heat equation is a nonlinear, parabolic equation not in divergence form that arises as a model for the dynamics of the director field in a nematic liquid crystal. We present a finite difference scheme for a transformed,…
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…
Within the framework of macroscopic quantum electrodynamics and scattering theory, we derive the general expressions for the variance of radiative heat transfer between two arbitrarily shaped objects placed in an arbitrary environment in…
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 is known that a bounded solution of the heat equation in a half-space which becomes zero at some time must be identically zero, even though no assumptions are made on the boundary values of the solutions. In a recent example, Luis…
An analytical model of unsteady heat transfer in a one-dimensional harmonic crystal is presented. A nonlocal temperature is introduced as a generalization of the kinetic temperature. A closed equation determining unsteady thermal processes…
When a physical system is put in contact with a very large thermal bath, it undergoes a dissipative (i.e., an apparently irreversible) process that leads to thermal equilibrium. This dynamical process can be described fully within quantum…
This work investigates heat transport in rotating internally heated convection, for a horizontally periodic fluid between parallel plates under no-slip and isothermal boundary conditions. The main results are the proof of bounds on the mean…
In this paper, we study the partial convexity of smooth solutions to the heat equation on a compact or complete non-compact Riemannian manifold M or Kahler-Ricci flow. We show that under a natural assumption, a new partial convexity…
In the present paper we propose a reduced temperature non-equilibrium model for simulating multicomponent flows with inter-phase heat transfer, diffusion processes (including the viscosity and the heat conduction) and external energy…
We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…
We consider convection in an internally heated layer of fluid that is bounded below by a perfect insulator and above by a poor conductor. The poorly conducting boundary is modelled by a fixed heat flux. Using solely analytical methods, we…
In the present paper we study inverse problems related to determining the time-dependent coefficient and unknown source function of fractional heat equations. Our approach shows that having just one set of data at an observation point…
After a discussion on the state of local equilibrium with temperature inhomogeneity, comparing mixture state reprsentation in statistical mechanics and pure state representation in thermo field dynamics, a simple model is solved to show…
We study a time-reversed hyperbolic heat conduction problem based upon the Maxwell--Cattaneo model of non-Fourier heat law. This heat and mass diffusion problem is a hyperbolic type equation for thermodynamics systems with thermal memory or…
The Initial-Boundary Value Problem for the heat equation is solved by using a new algorithm based on a random walk on heat balls. Even if it represents a sophisticated generalization of the Walk on Spheres (WOS) algorithm introduced to…
We address the well-posedness of the Cauchy problem corresponding to the relativistic fluid equations, when coupled with the heat-flux constitutive relation arising within the relativistic Chapman-Enskog procedure. The resulting system of…
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the…
In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary…