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Improving the heat transfer coefficient is crucial across various energy utilization processes for maintaining device safety and stability with high energy efficiency. However, in scenarios with limited heat capacity flow rates, increasing…
In stars and planets natural processes heat convective flows in the bulk of a convective region rather than at hard boundaries. By characterizing how convective dynamics are determined by the strength of an internal heating source we can…
In high-contrast composites, the electric (or stress) field may exhibit significant amplification in the narrow region between inclusions. The behavior of the solution depends on the distance $\epsilon$ between the inclusions, which tends…
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 show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is…
An uncoupled multi-scale homogenization approach is used to estimate the effective thermal conductivities of plain weave C/C composites with a high degree of porosity. The geometrical complexity of the material system on individual scales…
The detailed mathematical model of heat and mass transfer of steel ingot of curvilinear continuous casting machine is proposed. The process of heat and mass transfer is described by nonlinear partial differential equations of parabolic…
Heat and momentum transfer in wall-bounded turbulent flow, coupled with the effects of wall-roughness, is one of the outstanding questions in turbulence research. In the standard Rayleigh-B\'enard problem for natural thermal convection, it…
This work investigates the two-dimensional thermal behavior of a bilayer medium subject to both internal and external heat sources. The model incorporates diffusion, advection, and temperature-dependent volumetric heat generation or…
The aim of this article is to discuss the estimation of the diffusivity coefficient of a homogeneous metal rod from temperature values at a fixed point in the bar for different time instants. The time-dependent problem of heat conduction is…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
Providing thermal insulation to systems at very low temperature from surroundings, involves blocking the transport of thermal energy regular or enhanced, taking place through radiative, conductive and convective processes. For instance, the…
Our goal is to investigate fundamental properties of the system of internally cooled convection. The system consists of an upward thermal flux at the lower boundary, a mean temperature lapse-rate and a constant cooling term in the bulk with…
We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of total transport by a divergence-free velocity field. Subject…
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…
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…
We investigate the stability and dynamics of natural convection in two dimensions, subject to inhomogeneous boundary conditions. In particular, we consider a Rayleigh-B\`enard (RB) cell, where the horizontal top boundary contains a periodic…
The \emph{in situ} estimation of the thermal properties of existing building wall materials is a computationally expensive procedure. Its cost is highly proportional to the duration of measurements. To decrease the computational cost a…
The thermal properties of a material with a spatio-temporal modulation in both the thermal conductivity and the mass density are studied. The special configuration studied here consists of a modulation in a wave-like fashion. It is found…
We investigate the effective thermal conductivity of a two-phase composite with thermal resistance at the interface. The composite is obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different…