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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…
The long-term dynamics of particles involved in an incompressible flow with a small viscosity ($\epsilon>0$) and slow chemical reactions, is depicted by a class of stochastic reaction-diffusion-advection (RDA) equations with a fast…
We consider the Navier--Stokes equations for compressible heat-conducting ideal polytropic gases in a bounded annular domain when the viscosity and thermal conductivity coefficients are general smooth functions of temperature. A…
The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity…
The behaviour of a miniature calorimetric sensor, which is under consideration for catheter-based coronary artery flow assessment, is investigated in both steady and pulsatile tube flow. The sensor is composed of a heating element operated…
A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
New insight into the contribution of the microscale vortex evolution towards convection heat transfer in porous media is presented in this paper. The objective is to determine how the microscale vortices influence convection heat transfer…
A formulation of elliptic boundary value problems is used to develop the first discrete exterior calculus (DEC) library for massively parallel computations with 3D domains. This can be used for steady-state analysis of any physical process…
The fluid flow across an unbounded horizontal plate embedded with uniform mass diffusion is studied in this article together with the impacts of the chemical reaction and parabolic motion, while the temperature and concentration of the…
A Type-I model of a multicomponent system of fluids with non-constant temperature is derived as the high-friction limit of a Type-II model via a Chapman-Enskog expansion. The asymptotic model is shown to fit into the general theory of…
Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterise convection but are still too coarse to fully resolve it. Recently, numerical solutions of…
In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation [Griffin, Fu, & Moin, PNAS, 118:34, 2021] and an algebraic temperature-velocity relation, is developed for high-speed…
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 study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
This paper discusses the convective heat transfer enhancement of non-condensing slug flows by using phase separation for local liquid circulations through a porous-tube insert. Numerical simulations were carried out to study the air-water…
In this paper, we propose a space-dependent eddy thermal diffusivity model for turbulent vertical natural convection in a fluid between two infinite vertical walls at different temperatures. Using this model, we derive analytical results…
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…
Current-carrying conductors inevitably experience resistive heating due to the material's finite electrical conductivity. The resulting temperature distribution within the wire has essential implications for structural integrity,…
In the paper, we investigate the nonlinear thermoelasticity model in two- and three-dimensional convex and bounded domains. We propose new boundary conditions for the displacement. These conditions are not usual in thermoelasticity.…