Related papers: Third Boundary-Value Problem of the Heat Conductio…
In this work we find a solution to problem of the heat equation which is annihiliated at a cubic boundary $f$. The solution turns out to be the convolution between the fundamental solution of the heat equation and a function $\phi$ which…
We study Rayleigh-Benard convection in the high-Rayleigh-number and high-Prandtl-number regime, i.e., we consider a fluid in a container that is exposed to strong heating of the bottom and cooling of the top plate in the absence of inertia…
A semi-infinite material under a solidification process with the Solomon-Wilson- Alexiades's mushy zone model with a heat flux condition at the fixed boundary is considered. The associated free boundary problem is overspecified through a…
We study temperature distribution in a heat conducting problem, for a system of p-Laplace equation, giving rise to a free boundary.
We consider a new Stefan-type problem for the classical heat equation with a latent heat and phase-change temperature depending of the variable time. We prove the equivalence of this Stefan problem with a class of boundary value problems…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…
The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting…
We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
We consider a boundary-value problem describing the steady motion of a two-component mixture of viscous compressible heat-conducting fluids in a bounded domain. We make no simplifying assumptions except for postulating the coincidence of…
In this article, we present the governing equations for the temperature field upstream and downstream of the periodically developed flow region in channels with arrays of periodic solid structures. From the ansatz that the temperature field…
The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs and how we treated it. It is demonstrated that the Guyer-Krumhansl equation…
An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary…
Mathematical model of the turbulent flux in the three-layer boundary system is presented. Turbulence is described as a presence of the nonzero vorticity. Generalized advection-diffusion-reaction equation is derived for arbitrary number…
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…
We derive the solution representation for a large class of nonlocal boundary value problems for linear evolution PDEs with constant coefficients in one space variable. The prototypical such PDE is the heat equation, for which problems of…
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…
Motivated by recent experimental observations, we consider a steady-state Prandtl-Blasius boundary layer flow with polymers above a slightly heated horizontal plate and study how the heat transport might be affected by the polymers. We…
The heat equation is considered in the complex medium consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies an impedance boundary condition is imposed. An equation for the limiting…
We study the heat equation on a half-space with a linear dynamical boundary condition. Our main aim is to show that, if the diffusion coefficient tends to infinity, then the solutions converge (in a suitable sense) to solutions of the…