Related papers: Bilayer one-dimensional Convection-Diffusion-React…
We consider the limit of a linear kinetic equation, with reflection-transmission-absorption at an interface, with a degenerate scattering kernel. The equation arise from a microscopic chain of oscillators in contact with a heat bath. In the…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
We present a numerical study of double-diffusive convection characterized by a stratification unstable to thermal convection while at the same time a mean molecular weight (or solute concentration) difference between top and bottom…
A good understanding of the heat transfer in fused filament fabrication is crucial for an accurate stress prediction and subsequently for repetitive, high quality printing. This work focuses on two challenges that have been presented when…
Wildfires represent a problem for ecosystems, human activities, and economies, driven by the climate crisis and land-use changes. Predicting wildfire propagation through mathematical modelling is essential for damage mitigation and risk…
Comparisons of experimental observation of heat and moisture transfer through porous building materials with numerical results have been presented in numerous studies reported in literature. However, some discrepancies have been observed,…
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…
Thermal rectification can occur when heat is transferred asymmetrically. We consider in this work, the case of a composite wall with one conductive and radiative layer. Both Rosseland and surface radiation approximations are used for taking…
This paper is devoted to the diffusive limit of the nonlinear radiative heat transfer system with curved boundary domain (\textit{two dimensional disk}). The solution constructed in \cite{ghattassi2022convergence} by the leading order…
Using boundary-layer theory, natural convection heat transfer formulas which are accurate over a wide range of Rayleigh numbers ($Ra$) were developed in the 1970s and 1980s for vertical and downward-facing plates. A comprehensive formula…
In the presented paper known (up to the beginning of 2008) Lie- and non-Lie exact solutions of different $(1+1)$-dimensional diffusion-convection equations of form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$ are collected.
This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…
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…
Convection of an internally heated fluid, confined between top and bottom plates of equal temperature, is studied by direct numerical simulation in two and three dimensions. The unstably stratified upper region drives convection that…
We calculate numerically the heat transfer rate between a spatially dispersive sphere and a half-space. By utilising Huygens' principle and the extinction theorem, we derive the necessary reflection coefficients at the sphere and the plate…
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
This work deals with an inverse boundary value problem arising from the equation of heat conduction. We reconstruct small perturbations of the (isotropic) heat conductivity distribution from partial (on accessible part of the boundary)…
We develop a theory of fluctuation-driven phenomena in thermal transport in graphene double-layers. We work in the regime of electron hydrodynamics and focus on the double charge neutrality point. Although at the neutrality point charge…
We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due…