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The purpose of this paper is to provide an overview and some recent advances in the models, analysis and simulation of thermal transport of phonons as related to the field of microscale/macroscale heat conduction in solids. The efforts focus upon a fairly comprehensive overview of the subject matter from a unified standpoint highlighting the various approximations inherent in the thermal models. Subsequently, the numerical formulations and illustrations using the current state-of-the-art are provided.

This paper is dedicated to the approximate solution to the relaxation time phonon Boltzmann equation (BE). While original contributions are pointed out and addressed appropriately, the efforts and contributions will be focussed on a relatively complete overview highlighting the field from one unified standpoint and clearly stating all assumptions that go into the approximations inherent to existing models. The contents will be divided as follows: In the first section the authors will give an overview of semi-classical phonon transport physics. Then the authors will discuss the equation of phonon radiative transport (EPRT) and its approximations—the ballistic-diffusive approximation (BDA) and the new heat equation (NHE). Next the authors derive and discuss the C-F model. A numerical discretization method valid for all models is then presented followed by results to numerical simulations and discussion.

From a unified treatment based on the introduction of an energy distribution function, the authors have derived the EPRT and its two well-known approximations: BDA and NHE. For completeness and to provide a vehicle for a general numerical discretization approach, the authors have also included analysis of the C-F model and the parabolic and hyperbolic descriptions of heat transfer along with it. The approximation of angular dependence of phonons in radiation-like descriptions of transport has been given special attention. The assumption of isotropy was found to be of paramount importance in the formulation of position space models for phononic thermal transport. For the thin film problem considered here, the NHE along with the proper boundary condition appears to be the best choice to approximate the phonon BE. Not only does it provide predictions that are in excellent agreement with EPRT, it does not require the discretization of phase space making it far more computationally efficient.

The authors hope this work will help dispel the idea that since Fourier’s law describes diffusion (under limiting assumptions) and it has shown to be ineffective in describing heat transfer for very thin films, that diffusion cannot describe heat transfer in thin films and one should look to a radiative description instead. If one considers diffusion in the sense of random motion, as invisaged by the original builders of the subject (Smoluchowski, Einstein, Ornstein et al.), instead of a temperature gradient, the idea that diffusion can govern thermal transport at this scale is not surprising. Indeed, the NHE is essentially a diffusion equation that describes the motion of particles up to the point of true randomness (isotropy) as well as thereafter.

A numerical study is performed to investigate turbulent Couette flow and heat transfer characteristics in concentric annuli with a slightly heated inner cylinder moving in the flow direction. A two‐equation k‐ε turbulence model is employed to determine the turbulent viscosity and the turbulent kinetic energy. The turbulent heat flux is expressed by Boussinesq approximation in which the eddy diffusivity for heat is given as functions of the temperature variance t^2‐ and the dissipation rate of temperature fluctuations ε_t, together with k and ε. The governing boundary‐layer equations are discretized by means of control volume finite‐difference technique and numerically solved using a marching procedure. It is disclosed from the study that the streamwise movement of the inner core causes substantial reductions in the turbulent kinetic energy and the temperature variance, particularly near the inner wall region, resulting in the deterioration of the Nusselt number, and that an attenuation in heat transfer performance is induced by the velocity ratio of the moving inner cylinder to the fluid flow.

This paper presents a detailed review of the numerical modeling of inductively coupled air plasmas under local thermodynamic equilibrium and under chemical non‐equilibrium. First, the physico‐chemical models are described, i.e. the thermodynamics, transport phenomena and chemical kinetics models. Particular attention is given to the correct modelling of ambipolar diffusion in multi‐component chemical non‐equilibrium plasmas. Then, the numerical aspects are discussed, i.e. the space discretization and iterative solution strategies. Finally, computed results are presented for the flow, temperature and chemical concentration fields in an air inductively coupled plasma torch. Calculations are performed assuming local thermodynamic equilibrium and under chemical non‐equilibrium, where two different finite‐rate chemistry models are used. Besides important non‐equilibrium effects, we observe significant demixing of oxygen and nitrogen nuclei, which occurs due to diffusion regardless of the degree of non‐equilibrium in the plasma.

The purpose of this paper is to analyze the influence of underwear on the microenvironment of human clothing.

Based on the basic laws of energy and mass conservation, the paper combined the theory of heat and mass transfer to establish the simulation of the influence of underwear on human thermal reaction in microclimate and prediction model of human thermal reaction law.

The impact on the microenvironment affected by tighter underwear is less than the effect of loose underwear and computational flow dynamics (CFD) can accurately predict the thermal reaction parameters’ values of the human body.

It can be effectively used for the prediction of heat exchange between human body and environment in high-temperature environment and human thermophysiological parameters, and overcomes the individual differences of human experiments and the danger and repeatability of high-temperature environmental experiments.

The classical advection-dispersion equation (ADE) model cannot accurately depict the gas transport process in natural geological formations. This paper aims to study the behavior of CO₂ transport in fractal porous media by using an effective Hausdorff fractal derivative advection-dispersion equation (HFDADE) model.

Anomalous dispersion behaviors of CO₂ transport are effectively characterized by the investigation of time and space Hausdorff derivatives on non-Euclidean fractal metrics. The numerical simulation has been performed with different Hausdorff fractal dimensions to reveal characteristics of the developed fractal ADE in fractal porous media. Numerical experiments focus on the influence of the time and space fractal dimensions on flow velocity and dispersion coefficient.

The physical mechanisms of parameters in the Hausdorff fractal derivative model are analyzed clearly. Numerical results demonstrate that the proposed model can well fit the history of gas production data and it can be a powerful technique for depicting the early arrival and long-tailed phenomenon by incorporating a fractal dimension.

To the best of the authors’ knowledge, first time these results are presented.

This paper aims to investigate the comfort properties of modern functional clothing, such as moisture and heat transport. Transport properties are evaluated for real barrier membrane clothes for sport application, under real weather conditions in Middle Europe.

The different combination of functional clothing, with barrier membrane, were investigated under different temperatures and relative moistures inside and outside clothing layers. Water vapour permeability was measured under the steady‐state conditions, by sweating guarded‐hotplate test.

This paper describes the theoretical analysis of moisture transport, and its influence on thermal conductivity; the paper investigates various barrier fabrics for sport apparel, and their ranges of water vapour transport ability under real weather conditions.

All received results are based on the transport of water vapour through a semi‐permeable membrane and are supposed to be conducted mainly within a process of diffusion.

This paper is focused on the theoretical analysis of transport by diffusion of water vapour through porous semi‐permeable barrier textile material, and evaluates the real possibilities for sport applications. The level of transport is limited and mainly depends on the difference of the partial pressures of water vapours outside and inside the porous clothing material.

Accuracy of hydrodynamic transport equations using the energy‐dependent relaxation times has been studied for electron transport in Si 〈100〉. The concept of the hydro‐kinetic transport model is used to describe non‐equilibrium electron transport phenomena and to examine the validity for the assumption of energy‐dependent relaxation times. It has been shown that under the influence of a drastic increase in field the relaxation times might also strongly depend on the average velocity near the peak of strong velocity overshoot. In addition, the velocity dependence is found to be more pronounced at lower temperatures in Si 〈100〉.

Thermo-magnetic convective flow analysis under the impact of thermal radiation for heat and entropy generation phenomena is an active research field for understanding the efficiency of thermodynamic systems in various engineering sectors. This study aims to examine the characteristics of convective heat transport and entropy generation within an inverted T-shaped porous enclosure saturated with a hybrid nanofluid under the influence of thermal radiation and magnetic field.

The mathematical model incorporates the Darcy-Forchheimer-Brinkmann model and considers thermal radiation in the energy balance equation. The complete mathematical model has been numerically simulated through the penalty finite element approach at varying values of flow parameters, such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), radiation parameter (Rd) and porosity value (e). Furthermore, the graphical results for energy variation have been monitored through the energy-flux vector, whereas the entropy generation along with its individual components, namely, entropy generation due to heat transfer, fluid friction and magnetic field, are also presented. Furthermore, the results of the Bejan number for each component are also discussed in detail. Additionally, the concept of ecological coefficient of performance (ECOP) has also been included to analyse the thermal efficiency of the model.

The graphical analysis of results indicates that higher values of Ra, Da, e and Rd enhance the convective heat transport and entropy generation phenomena more rapidly. However, increasing Ha values have a detrimental effect due to the increasing impact of magnetic forces. Furthermore, the ECOP result suggests that the rising value of Da, e and Rd at smaller Ra show a maximum thermal efficiency of the mathematical model, which further declines as the Ra increases. Conversely, the thermal efficiency of the model improves with increasing Ha value, showing an opposite trend in ECOP.

Such complex porous enclosures have practical applications in engineering and science, including areas like solar power collectors, heat exchangers and electronic equipment. Furthermore, the present study of entropy generation would play a vital role in optimizing system performance, improving energy efficiency and promoting sustainable engineering practices during the natural convection process.

To the best of the authors’ knowledge, this study is the first ever attempted detailed investigation of heat transfer and entropy generation phenomena flow parameter ranges in an inverted T-shaped porous enclosure under a uniform magnetic field and thermal radiation.

In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.

Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.

The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.

The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.

For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).