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We consider a semi-infinite one-dimensional phase-change material with two unknown constant thermal coefficients among the latent heat per unit mass, the specific heat, the mass density and the thermal conductivity. Aiming at the…
A convection-diffusion problem with a large shift in space is considered. Numerical analysis of high order finite element methods on layer-adapted Duran type meshes, as well as on coarser Duran type meshes in places where weak layers…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
This paper aims at the transient heat transfer analysis on extended surfaces with temperature-dependent thermal conductivity, constant internal heat generation, and five different geometries. The governing equations developed in this work…
We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…
This paper gives similarity transformations for laminar film condensation on a vertical flat plate with variable temperature distribution and finds analytical solutions for arbitrary Prandtl numbers and condensation rates. The work…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
In this paper, we present a theoretical study aimed at investigating the rate-limiting factors in thin-film evaporative heat transfer processes, considering the finite-rate evaporation kinetics. The problems of evaporation of a flat…
We study thermal processes in infinite harmonic crystals having a unit cell with arbitrary number of particles. Initially particles have zero displacements and random velocities, corresponding to some initial temperature profile. Our main…
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…
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…
We consider the heat transfer problem associated with a periodic array of extended surfaces (fins) subjected to convection heat transfer with a uniform heat transfer coefficient. Our analysis differs from the classical approach as (i) we…
The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three…
We consider heat transfer in an infinite two-dimensional square harmonic scalar lattice lying in a viscous environment and subjected to a heat source. The basic equations for the particles of the lattice are stated in the form of a system…
Flow-induced deformation of thin structures coupled with convective heat transfer has potential applications in energy harvesting and is important for understanding functioning of several biological systems. We numerically demonstrate…
A stochastic inverse heat transfer problem is formulated to infer the transient heat flux, treated as an unknown Neumann boundary condition. Therefore, an Ensemble-based Simultaneous Input and State Filtering as a Data Assimilation…
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…
Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic…
In this paper, we propose a multiphysics finite element method for a quasi-static thermo-poroelasticity model with a nonlinear convective transport term. To design some stable numerical methods and reveal the multi-physical processes of…
In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…