Related papers: Bilayer one-dimensional Convection-Diffusion-React…
In this work, we study the propagation of wildfires using an advection--diffusion--reaction model which also includes convective and radiative heat loss. An existing model is discussed \cite{asensio_2002} and a physically consistent…
We present a numerical study of convection in a horizontal layer comprising a fluid-saturated porous bed overlain by an unconfined fluid layer. Convection is driven by a vertical, destabilising temperature difference applied across the…
It is necessary to use more general models than the classical Fourier heat conduction law to describe small-scale thermal conductivity processes. The effects of heat flow memory and heat capacity memory (internal energy) in solids are…
This work establishes a closed-form analysis for two-dimensional transient heat transfer in an absorber plate based on the thermal wave model when the collector starts to work. The method of separation of variables is employed to determine…
We numerically investigate turbulent Rayleigh-B\'enard convection within two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $Nu$) in…
Convection-diffusion equations provide the basis for describing heat and mass transfer phenomena as well as processes of continuum mechanics. To handle flows in porous media, the fundamental issue is to model correctly the convective…
We propose a one-dimensional (1D) diffusion equation (heat equation) for systems in which the diffusion constant (thermal diffusivity) varies alternately with a spatial period $a$. We solve the time evolution of the field (temperature)…
The double-skin roofs investigated in this paper are formed by adding a metallic screen on an existing sheet metal roof. The system enhances passive cooling of dwellings and can help diminishing power costs for air conditioning in summer or…
A two-dimensional model is proposed for energy efficiency assessment through the simulation of heat transfer in building envelopes, considering the influence of the surrounding environment. The model is based on the \DF ~approach that…
A new two-layer model has been proposed to study microscale heat transfer associated with a developing flow boundary layer. As an example, a cold, microscale film of liquid impinging on an isothermal hot, horizontal surface has been…
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an internally heated disc. Heat enters via a distributed…
Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due…
Three inverse boundary value problems for the heat equations in one space dimension are considered. Those three problems are: extracting an unknown interface in a heat conductive material, an unknown boundary in a layered material or a…
In the context of the problem of heat conduction in one-dimensional systems, we present an analytical calculation of the instantaneous energy transfer across a tagged particle in a one-dimensional gas of equal-mass, hard-point particles.…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…
We consider a problem of identification of point sources in time dependent advection-diffusion systems with a non-linear reaction term. The linear counterpart of the problem in question can be reduced to solving a system of non-linear…
Previous studies have suggested a crossover from superdiffusive to normal heat transport in one-dimensional (1D) anharmonic oscillator systems with a double-well type interatomic interaction like $V(\xi)=-\xi^2/2+\xi^4/4$, when the system…
Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical…
The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs and how we treated it. It is demonstrated that the Guyer-Krumhansl equation…
A heat exchanger can be modeled as a closed domain containing an incompressible fluid. The moving fluid has a temperature distribution obeying the advection-diffusion equation, with zero temperature boundary conditions at the walls.…