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This paper introduces a Bayesian inference framework for two-dimensional steady-state heat conduction, focusing on the estimation of unknown distributed heat sources in a thermally-conducting medium with uniform conductivity. The goal is to…
We are motivated to model a heat transfer to a multiple layer regime and their optimization for heat energy resources. Such a problem can be modeled by a porous media with different phases (liquid and solid). The idea arose of a geothermal…
A parametric instability of an incompressible, viscous, and Boussinesq fluid layer bounded between two parallel planes is investigated numerically. The layer is assumed to be inclined at an angle with horizontal. The planes bounding the…
To predict the heat diffusion in a given region over time, it is often necessary to find the numerical solution for heat equation. With the techniques of discrete differential calculus, we propose two unconditional stable numerical schemes…
Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the…
This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is…
Developing robust simulation tools for problems involving multiple mathematical scales has been a subject of great interest in computational mathematics and engineering. A desirable feature to have in a numerical formulation for multiscale…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
Modelling the solar Transition Region with the use of an Adaptive Conduction (TRAC) method permits fast and accurate numerical solutions of the field-aligned hydrodynamic equations, capturing the enthalpy exchange between the corona and…
We propose a mechanism of active near-field heat transfer modulation relying on externally tunable metamaterials. A large modulation effect is observed and can be explained by the coupling of surface modes, which is dramatically varied in…
We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a),…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…
The rate of melting of a solid and the rate of deformation of the resulting melt due to capillary forces are comparable in additive manufacturing applications. This dynamic structural change of a melting solid is extremely challenging to…
We design a class of spatially inhomogeneous heat spreaders in the context of steady-state thermal conduction leading to spatially uniform thermal fields across a large convective surface. Each spreader has a funnel-shaped design, either in…
A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…
We present a new approach for the two-temperature molecular dynamics (MD) model for coupled simulations of electronic and phonon heat conduction in nanoscale systems. The proposed method uses a master equation to perform heat conduction of…
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…
We consider the thermal dunking problem, in which a solid body is suddenly immersed in a fluid of different temperature, and study both the temporal evolution of the solid and the associated Biot number -- a non-dimensional heat transfer…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…