相关论文: A free boundary problem in thermal insulation with…

The problem of disturbed flow in the laminar boundary layer is investigated when a heating element is located on the surface of the body. The flow is supposed to be laminar one. It is shown that the problem may be solved in terms of free…

An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, of negligible diameter, made up of two consecutive sections of different, isotropic and homogeneous materials. At the…

The problem of a steady forced convection thermal boundary-layer past a flat plate with a prescribed surface heat flux is investigated both analytically and numerically. In view of the present formulation, the governing equations reduce to…

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…

This paper investigates shape optimization problems in the context of heat transfer, with a focus on the stability and non-optimality of round domains under Robin boundary conditions. Using the flow approach and Steklov eigenvalue…

In this paper thermal conductivity and thermal diffusivity of a two layer system is examined from the theoretical point of view. We use the one dimensional heat diffusion equation with the appropriate solution in each layer and boundary…

We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…

Thermal convection in fluid layers heated from below are usually realized experimentally as well as treated theoretically with fixed boundaries on which conditions for the temperature and the velocity field are prescribed. The thermal and…

We study a free boundary optimization problem in heat conduction, ruled by the infinity-Laplace operator, with lower temperature bound and a volume constraint. We obtain existence and regularity results and derive geometric properties for…

We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable…

In the above paper the authors treat the boundary layer flow along a stationary, vertical, permeable, flat plate within a vertical free stream. Fluid is sucked or injected through the vertical plate. The fluid species concentration at the…

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 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…

We study the situation in which the distribution of temperature a body is due to its interaction with radiation. We consider the boundary value problem for the stationary radiative transfer equation under the assumption of the local…

The influence of fixed temperature and fixed heat flux thermal boundary conditions on rapidly rotating convection in the plane layer geometry is investigated for the case of stress-free mechanical boundary conditions. It is shown that…

Various unusual behaviors of artificial materials are governed by their topological properties, among which the edge state at the boundary of a photonic or phononic lattice has been captivated as a popular notion. However, this remarkable…

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 consider a free boundary problem for the heat equation with a given non-negative external heat source. On the free boundary, we impose the zero Dirichlet condition and the fixed normal derivative so that heat escapes from the boundary.…

We study the free boundary in an unstable parabolic problem arising from a model in combustion. We consider the physical situation in which the heat advances and prove that the free boundary is a $C^{1,\alpha/2}$ hypersurface.

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…