Related papers: Functional solutions for problems of heat and mass…
We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
We study a parabolic initial-boundary-value problem for a system of two differential equations with two boundary conditions of different orders, the Dirichlet and Neumann ones. It occurs specifically in the heat-mass transfer theory. We…
This article is devoted to inverse problems of recovering point sources in mathematical models of heat and mass transfer. The main attention is paid to well-posedness questions of these inverse problems with pointwise overdetermination…
A physics-informed neural network is developed to solve conductive heat transfer partial differential equation (PDE), along with convective heat transfer PDEs as boundary conditions (BCs), in manufacturing and engineering applications where…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain $D\subset\R^d$ and its weak formulation is in the form of a…
This work shows that a class of astrodynamics problems subject to mission constraints can be efficiently solved using the Theory of Functional Connections (TFC) mathematical framework by a specific change of coordinates. In these problems,…
Solving the fundamental and optical gap problems, which yield information about charged and neutral excitations in electronic systems, is one of the biggest challenge in density-functional theory (DFT). Despite their intrinsic difference,…
We consider the heat equation with spatially variable thermal conductivity and homogeneous Dirichlet boundary conditions. Using the Method of Fokas or Unified Transform Method, we derive solution representations as the limit of solutions of…
This article is proposed to investigate the impacts of heat and mass transfer in magnetohydrodynamic casson fluid embedded in porous medium. The generalized solutions have been traced out for the temperature distribution, mass concentration…
We prove equivalence between nonnegative distributional solutions of the fractional heat equation and caloric functions, i.e., functions satisfying the mean value property with respect to the space-time isotropic $\alpha$-stable process. We…
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…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
Evaluation of effective or macroscopic coefficients of thermal conductivity under coupled heat and moisture transfer is presented. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem…
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…
In this paper we introduce the functional framework and the necessary conditions for the well-posedness of an inverse problem arising in the mathematical modeling of disease transmission. The direct problem is given by an initial boundary…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
We introduce a new method of solution for the convective heat transfer under forced laminar flow that is confined by two parallel plates with a distance of 2a or by a circular tube with a radius of a. The advection-conduction equation is…
We study the global existence and uniform-in-time bounds of classical solutions in all dimensions to reaction-diffusion systems dissipating mass. By utilizing the duality method and the regularization of the heat operator, we show that if…