Transient, Sub-Continuum, Heat Conduction in Irregular Geometries

Phonon transfer in irregular shapes is important for assessing the influence of shape effect on thermal transport characteristics of low-scale films. It becomes critical for evaluating the contribution of the scattering phonons to the phonon intensity distribution inside the film. Hence, the sub-continuum ballistic-diffusive model is incorporated to formulate the phonon transport in an irregular geometry of low-size film adopting the transient, frequency-independent, equation of phonon radiative transfer. The discrete ordinate method is used in the numerical discretization of the governing transport equation. It is demonstrated that the geometric feature of the film influences the phonon intensity distribution within the film material. The transport characteristics obtained from the Fourier and the ballistic-diffusive models are markedly different in their spatial and temporal behavior. This is true when the device sizes are of the same order of magnitude as the mean-free path of the heat carriers.

Significance of Entropy Generation and the Coriolis Force on the Three-Dimensional Non-Darcy Flow of Ethylene-Glycol Conveying Carbon Nanotubes (SWCNTs and MWCNTs)

Nanofluids based on CNTs/ethylene glycol have a potential role in contributing to industrial applications like heat exchangers, domestic refrigerator, electronics cooling, etc. The aim and novelty of the present research is to communicate the significance of the Coriolis force and Darcy-Forchheimer stretched flow of ethylene glycol (EG) conveying carbon nanotubes (CNTs) in a rotating frame. Furthermore, entropy analysis is the main focus in this study. Two types of CNTs known as multiwalled (MWCNT) and single-walled (SWCNT) carbon nanotubes are considered. Ethylene glycol (EG) is treated as the base liquid. Xue’s model is utilized for the physical aspects of specific heat, density and thermal conductivity. The heat transfer mechanism is modeled through nonlinear thermal radiation, viscous dissipation and convective condition. The governing flow problems have been computed numerically via the NDSolve method. Outcomes for single-walled and multi-walled CNTs are arranged and compared. Our findings reveal that entropy generation is accompanied by an increasing trend in the Brinkman number and temperature ratio parameter. Temperature increases with the intensification of radiative and convective variables. Moreover, the temperature gradient has marginally larger values in the case of SWCNT, when compared with MWCNT.

Over-Equilibrium as a Result of Conservatively-Perturbed Equilibrium (Acyclic and Cyclic Mechanisms)

The effect of over-equilibrium, i. e., the effect at which the concentration of some substance is higher than the corresponding equilibrium value, is demonstrated for two types of ideal chemical reactors, continuously stirred tank reactor (CSTR) and plug-flow reactor (PFR), respectively, under conditions of conservatively perturbed-equilibrium (CPE). Two types of complex chemical mechanisms are analyzed, acyclic and cyclic ones. Using numerical experiments and the same residence times, it is shown that for the steady-state PFR this effect is more pronounced that for the steady-state CSTR, and it is true both for acyclic and cyclic reactions. In the studied mechanisms, cyclic and acyclic, the initial concentration of some substance is taken as the equilibrium one, and two other concentrations are the nonequilibrium ones. The greater the difference between the two initially nonequilibrium concentrations, the greater the concentration of the third substance, which was taken initially as the equilibrium one. At the specific values of kinetic parameters considered here, the sensitivity of the occurrence time of the B-concentration extremum for the different reactors (PFR and CSTR) at the fixed mechanism is small, but for the different mechanisms (acyclic and cyclic) at the fixed reactor is significant.

Maximum Work Rate Extractable from Energy Fluxes

A general formalism is developed to evaluate the amount of work extractable from energy fluxes. It covers nonequilibrium cases when the concept of exergy is not relevant. The rate of work deficiency, which has been previously introduced as the total loss of exergy, is defined here as the total loss of work, which would have resulted if all the work were lost to the environment. New performance indicators are proposed. First, the work content factor gives the proportion of extractable work in a given amount of energy. Second, the work deficiency factor is a measure of the potential of improvement for the operation of energy conversion systems. Previous results reported in literature are particular cases of the general results obtained here. The formalism is used to evaluate the work rate extractable from the solar energy flux. Results are shown in cases where solar radiation interacts with materials without energy bandgap (metals) and with energy bandgaps (semiconductors), respectively.

Spectral Properties of Dissipation

The novel concept of spectral diffusivity is introduced to analyze the dissipative properties of continua. The dissipative components of a linear system of evolution equations are separated into noninteracting parts. This separation is similar to mode analysis in wave propagation. The new modal quantities characterize dissipation and are best interpreted as effective diffusivities, or, in case of the heat conduction, as effective heat conductivities of the material.

Theoretical Analysis of Activation Energy Effect on Prandtl–Eyring Nanoliquid Flow Subject to Melting Condition

This study models the convective flow of Prandtl–Eyring nanomaterials driven by a stretched surface. The model incorporates the significant aspects of activation energy, Joule heating and chemical reaction. The thermal impulses of particles with melting condition is addressed. The system of equations is an ordinary differential equation (ODE) system and is tackled numerically by utilizing the Lobatto IIIA computational solver. The physical importance of flow controlling variables to the temperature, velocity and concentration is analyzed using graphical illustrations. The skin friction coefficient and Nusselt number are examined. The results of several scenarios, mesh-point utilization, the number of ODEs and boundary conditions evaluation are provided via tables.

A case study of non-Fourier heat conduction using internal variables and GENERIC

Applying simultaneously the methodology of non-equilibrium thermodynamics with internal variables (NET-IV) and the framework of General Equation for the Non-Equilibrium Reversible–Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier’s law and its various extensions—the Maxwell–Cattaneo–Vernotte, Guyer–Krumhansl, Jeffreys type, Ginzburg–Landau (Allen–Cahn) type and ballistic–diffusive heat conduction equations—are derived in both formulations. Along these lines, a comparison of NET-IV and GENERIC is also performed. Our results may pave the way for microscopic/multiscale understanding of beyond-Fourier heat conduction and open new ways for numerical simulations of heat conduction problems.

Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach

A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.