Nonequilibrium Energy Research Articles

Nonequilibrium Monte Carlo simulations of entangled polymer melts under steady shear flow.

We present a nonequilibrium Monte Carlo (MC) methodology based on expanded nonequilibrium thermodynamic formalism to simulate entangled polymeric materials undergoing steady shear flow. Motivated by the standard kinetic theory for entangled polymers, a second-rank symmetric conformation tensor based on the entanglement segment vector was adopted in the expanded statistical-ensemble based MC method as the nonequilibrium structural variable that properly represents the deformed structure of the system by the flow. The corresponding (second-rank symmetric) conjugate thermodynamic force variable was introduced to simulate an external flow field. As a test case, we applied the GENERIC MC to C400H802 entangled linear polyethylene melts in a wide range of shear rates. Detailed analysis of the GENERIC MC results for various structural and rheological properties (such as chain size, chain orientation, mesoscale chain configuration, topological properties, and material functions) was carried out via direct comparison with the corresponding NEMD results. Overall, the GENERIC MC is shown to predict the general trends of the nonequilibrium properties of polymer systems reasonably for a wide range of flow strengths (i.e., 0.5 ≤ De ≤ 540). In conjunction with NEMD, the present MC method can thus be used to extract fundamental thermodynamic information (nonequilibrium entropy and free energy functions) of entangled polymeric systems under various flow types. Despite the general consistency between the GENERIC MC and NEMD results, some quantitative discrepancies appear in the intermediate-to-strong flow regime. This behavior stems from the inherent mean-field nature of the MC force field which is applied to the individual entanglement segments independently and uniformly along the chain, without accounting for any flow-induced structural or dynamical correlations between segments.

Bioelectromagnetic Paradigm of Cancer Treatment—Modulated Electro-Hyperthermia (mEHT)

One of the most frequently applied bioelectromagnetic effects is the deep heating of the living species with EMF energy. Despite its long history, hyperthermia is a rarely applied oncotherapy. The reason is its controversial results and complicated control. One of the solutions is concentrating the electromagnetic energy nanoscopically on the parts of the malignant cells instead of heating up the complete tumor-mass. This approach is a kind of non-uniform energy absorption, providing energy liberation only in the selected regions. The energy-absorption of the malignant cells targets the membranes and creates a situation far from thermal equilibrium. The selection of the malignant cells is based on their decided differences from their healthy counterparts. The distinguishing parameters are the electromagnetic properties of the components of the malignant tissue which are the physiologic differences between the malignant cells and their healthy counterparts. The targets realize nano-range heating, using natural nanoclusters on the cell-membrane without artificially implementing them. This energy absorption generates consequent reactions, like programmed cell-death (apoptosis) continued by immunogenic cell-death involving extended immune reactions. The applied radiofrequency current is amplitude modulated by time-fractal modulation pattern. The accurately matched impedance realizes the self-selective mechanisms which are promoted by stochastic resonances. This complex method is a new kind of hyperthermia, named mEHT. Our objective is to analyze the problems of the selective, non-equilibrium energy absorption, and present a solution by the electromagnetic mechanisms for an effective and controllable hyperthermia in oncology.

Thermal and nonthermal effects of radiofrequency on living state and applications as an adjuvant with radiation therapy

One of the most frequently applied bioelectromagnetic effects is the deep heating of living species with electromotive force energy. Despite its long history, hyperthermia is a rarely applied oncotherapy because of controversial results and complicated control. The challenge in clinical studies of oncological hyperthermia is the disharmony of the local response and local control with overall survival. Both whole-body (complete isothermia for the body) and local (isothermia for the chosen target) heating show excellent local effects; however, this is not followed with the expected elongation of survival time. A possible solution could be nonisothermal heating to the heterogeneity of the malignancy itself. The distinguishing parameters to select the target are the electromagnetic properties of the malignant tissue together with the physiological differences between malignant cells and their healthy counterparts. Selection could allow for cellular targeting, generating natural reactions, such as programmed cell death (apoptosis) followed by immunogenic cell death involving extended immune reactions. This complex method is a new kind of hyperthermia, named modulated electrohyperthermia (tradename oncothermia). The selective, nonequilibrium energy absorption is well synergized with modern radiation therapies, presenting a solution of an active and controllable tumor-specific immune reaction and subsequent abscopal effects.

Thermal hydraulic performance of micro-channel heat sink with composite metal foam-solid fin design

<p indent="0mm">Three-dimensional (3D) interconnect technology promises significant performance advantages for the next generation of high speed and multi-functional electronic devices, however, the large-scale integration of electronic circuit and vertical stacking of multi-functional dice have been demonstrated to result in substantially increased waste-heat generation rates and localized hotspots. Efficient thermal management solutions are imperative to ensure the operating temperature of components below a reasonable level. Among various cooling techniques, metal foam heat sink has been identified as a promising alternative for electronic cooling, because of the large specific surface area, high effective thermal conductivity and intensive fluid mixing capability that foam material provided. In this study, a novel micro-channel heat sink with combined metal foam-solid fin, namely combined fin heat sink (CFHS), was established for electronics cooling. Numerical simulations based on Brinkman-Darcy extended momentum equation and local thermal non-equilibrium energy equations were carried out to investigate the fluid flow and heat transfer characteristics. To simplify the computations, a single channel was used as the computational domain with a dimension of 20 mm×2.4 mm× <sc>6 mm.</sc> The constant heat flux of <sc>100 W/cm²</sc> was supplied at the bottom wall to simulate the high-powered electronic device. Metal foam and fin were made of high thermal conductivity copper, and pure water was used as the working coolant. It was assumed that the metal foam was fully saturated with fluid in laminar flow state and the thermal resistance between the metal foam and fin was neglected. Effects of combined fin configuration on the flow and heat transfer performances were studied to determine the optimal porosity and dimensionless metal foam layer thickness for designing the CFHS. The thermal performance of the novel heat sink was compared to that of the conventional heat sink, and the total thermal resistance was analyzed based on the simplified thermal resistance network. The results indicate that the CFHS is more favorable in promoting thermal performance that the average Nusselt number of CFHS is 2.53 times higher than that of the conventional heat sink, while accompanied by the high pressure drop as a penalty. The flow resistance and specific area are two conflicting parameters that affect the thermal and hydraulic performances of the CFHS, our results show that there exists a critical dimensionless metal foam thickness and optimal porosity, which are 0.9 and 0.3, respectively. Compared with the conventional heat sink, the total thermal resistance of CFHS is significantly reduced by 56%, and the thermal performance factor of CFHS performs 1.32 times higher. The presented CFHS thus provides a feasible solution for thermal management of electronic devices with high-powered density.

Landau effective Hamiltonian and its application to magnetic systems

The Landau definition of the effective Hamiltonian (of the nonequilibrium free energy) is realized in a microscopic theory. According to Landau remark, the consideration is based on classical statistical mechanics. In his approach nonequilibrium states coinciding with equilibrium fluctuations are taken into account (the Onsager principle). The definition leads to the exact fulfillment of the Boltzmann principle written in the form with the complete free energy. The considered system is assumed to consist of two subsystems. The first subsystem is an equilibrium one. The second subsystem is a nonequilibrium one and its state is described by quantities that are considered as order parameters. The effective Hamiltonian is calculated near equilibrium in the form of a series in powers of deviations of the order parameters from their equilibrium values. The coefficients of the series are expressed through equilibrium correlation functions of the order parameters. In the final approximation correlations of six and more order parameters are neglected and correlations of four parameters are assumed to be small that leads to the corresponding perturbation theory. The developed theory is compared with the phenomenological Landau theory of phase transitions of the second kind. The obtained results are concretized for paramagnetic-ferromagnetic system. The consideration is restricted by paramagnetic phase.

Multiquantum Transitions in Oxygen and Nitrogen Molecules in Hypersonic Nonequilibrium Flows

A computational fluid dynamics analysis was performed with state-to-state kinetics of oxygen and nitrogen for assessing the influence of vibrational excitation and dissociation on hypersonic flowfields in the range of Mach 7–20. Flows around an axisymmetric forebody geometry were considered by using multiquantum vibrational–translation and dissociation rate coefficients from an ab initio database. The nonequilibrium vibrational energy distributions were modeled by the master kinetic equation. Output quantities of interest included shock standoff distance, translational and vibrational temperatures, and population fractions in the quantum energy states. Both a two-temperature model and a state-to-state kinetics model were used to compare with existing experimental data. The objective of the study was to understand the energy exchange process of multiquantum transitions in the shock layer of a blunt body flow and to assess the maximum number of multiquantum jumps required in describing the nonequilibrium behavior. Multiquantum transitions caused an increase in population in upper energy states due to more efficient energy exchanges. The greater dissociation for the higher multiquantum jumps resulted in reduced shock standoff distance. At the higher Mach numbers, population depletion from the upper energy states demonstrated preferential dissociation. At high temperatures, results indicated that multiquantum transitions had a large influence on the macroscopic parameters of the gas flow behind the shock, especially on the temperature profiles as well as on vibrational population distributions in the upper energy states.

A discontinuous Galerkin fast spectral method for the full Boltzmann equation with general collision kernels

The Boltzmann equation, an integro-differential equation for the molecular distribution function in the physical and velocity phase space, governs the fluid flow behavior at a wide range of physical conditions, including compressible, turbulent, as well as flows involving further physics such as non-equilibrium internal energy exchange and chemical reactions. Despite its wide applicability, deterministic solution of the Boltzmann equation presents a huge computational challenge, and often the collision operator is simplified for practical reasons. In this work, we introduce a highly accurate deterministic method for the full Boltzmann equation which couples the Runge–Kutta discontinuous Galerkin (RKDG) discretization in time and physical space (Su et al. (2015) [1]) and the recently developed fast Fourier spectral method in velocity space (Gamba et al. (2017) [2]). The novelty of this approach encompasses three aspects: first, the fast spectral method for the collision operator applies to general collision kernels with little or no practical limitations, and in order to adapt to the spatial discretization, we propose here a singular-value-decomposition based algorithm to further reduce the cost in evaluating the collision term; second, the DG formulation employed has high order of accuracy at element-level, and has shown to be more efficient than the finite volume method; thirdly, the element-local compact nature of DG as well as our collision algorithm is amenable to effective parallelization on massively parallel architectures. The solver has been verified against analytical Bobylev–Krook–Wu solution. Further, the standard benchmark test cases of rarefied Fourier heat transfer, Couette flow, oscillatory Couette flow, normal shock wave, lid-driven cavity flow, and thermally driven cavity flow have been studied and their results are compared against direct simulation Monte Carlo (DSMC) solutions with equivalent molecular collision models or published deterministic solutions.

Ultrafast excitation of conduction-band electrons by high-intensity ultrashort laser pulses in band-gap solids: Vinogradov equation versus Drude model

Heating of conduction-band electrons is one of the major processes of energy absorption and transfer in high-intensity ultrafast laser–solid interactions. It is frequently simulated by assuming a high rate of electron-particle collisions. We explore the approximation of low-rate electron–phonon collisions based on the Vinogradov equation for the intraband absorption rate by conduction-band electrons performing laser-driven oscillations. Band-structure modification by the ponderomotive energy of the ultrafast oscillations is taken into account. The Vinogradov equation combined with the Keldysh formula for the interband transition rate delivers a highly nonequilibrium energy distribution of the conduction electrons. Reported results suggest a substantial revision of the traditional models of ultrafast free-carrier heating by intense laser pulses.

Accurate Calculation of Free Energy Changes upon Amino Acid Mutation.

Molecular dynamics based free energy calculations allow for a robust and accurate evaluation of free energy changes upon amino acid mutation in proteins. In this chapter we cover the basic theoretical concepts important for the use of calculations utilizing the non-equilibrium alchemical switching methodology. We further provide a detailed step-by-step protocol for estimating the effect of a single amino acid mutation on protein thermostability. In addition, the potential caveats and solutions to some frequently encountered issues concerning the non-equilibrium alchemical free energy calculations are discussed. The protocol comprises details for the hybrid structure/topology generation required for alchemical transitions, equilibrium simulation setup, and description of the fast non-equilibrium switching. Subsequently, the analysis of the obtained results is described. The steps in the protocol are complemented with an illustrative practical application: a destabilizing mutation in the Trp cage mini protein. The concepts that are described are generally applicable. The shown example makes use of the pmx software package for the free energy calculations using Gromacs as a molecular dynamics engine. Finally,we discuss how the current protocol can readily be adapted to carry out charge-changing or multiple mutations at once, as well aslarge-scale mutational scans.

Information Thermodynamics of Turing Patterns.

We set up a rigorous thermodynamic description of reaction-diffusion systems driven out of equilibrium by time-dependent space-distributed chemostats. Building on the assumption of local equilibrium, nonequilibrium thermodynamic potentials are constructed exploiting the symmetries of the chemical network topology. It is shown that the canonical (resp. semigrand canonical) nonequilibrium free energy works as a Lyapunov function in the relaxation to equilibrium of a closed (resp. open) system, and its variation provides the minimum amount of work needed to manipulate the species concentrations. The theory is used to study analytically the Turing pattern formation in a prototypical reaction-diffusion system, the one-dimensional Brusselator model, and to classify it as a genuine thermodynamic nonequilibrium phase transition.

Non-equilibrium electron and vibrational distributions under nanosecond repetitively pulsed CO discharges and afterglows: II. the role of radiative and quenching processes

The non-equilibrium vibrational distributions and electron energy distributions of CO in nanosecond repetitively pulsed discharges and afterglows have been determined from a coupled solution of the time-dependent Boltzmann equation for the electron energy distribution function (eedf) of free electrons, the master equations for vibrational levels of CO and the electronic excited states of CO, O and C atoms. The optically thick plasma conditions have been investigated in a companion paper (part I), while in the present paper we also show the results obtained by allowing radiative emission processes (optically thin plasma) as well as electronic excited state collisional quenching processes. Two case studies, which differ for the duration of the afterglow following each pulse (1 μs and 25 μs case studies) are discussed, and each pulse is characterized by a time-dependent electric field profile in the range 0–20 ns. The results, which depend on the number of pulses considered in the discharge and the corresponding afterglow duration, show several peaks in the eedf due to super-elastic electronic collisions. On the other hand, the quenching process of the a3Π electronic state of CO determines the pumping of vibrational quanta in the v = 27 level, which in turn largely modifies the vibrational distribution function (vdf) of CO. As a consequence, the quenching of the a3Π state increases the reactivity of CO through the Boudouard reaction, and under given conditions, this channel can become more important than the dissociation rates by electron impact collisions.

Electron transfer kinetics of methylviologen included in 4-sulfonatocalix[n]arenes at glassy carbon electrode; adiabaticity and activation energy

Quasi-reversible single electron transfer (ET) kinetics of methylviologen partly-included at the rim of 4-sulfonatocalix[n]arenes (n = 4,6 and 8) has been investigated in aqueous solution. ET rates were measured by Nicholson method with relatively large potential scan rates (0.9 V/s < v < 50 V/s). ET proceeded adiabatically on the direct collision between the MV+/MV2+ and the electrode surface. The host-guest binding equilibrium at the activation state was not established under the high-speed cyclic voltammetry condition. The non-equilibrium stabilization energy was independent of the size of the cavitands. The activation energy of ET under the partly-included condition was 70–80% of that without any inclusion.

Thermodynamics of Modularity: Structural Costs Beyond the Landauer Bound

Information processing typically occurs via the composition of modular units, such as universal logic gates. The benefit of modular information processing, in contrast to globally integrated information processing, is that complex global computations are more easily and flexibly implemented via a series of simpler, localized information processing operations which only control and change local degrees of freedom. We show that, despite these benefits, there are unavoidable thermodynamic costs to modularity---costs that arise directly from the operation of localized processing and that go beyond Landauer's dissipation bound for erasing information. Integrated computations can achieve Landauer's bound, however, when they globally coordinate the control of all of an information reservoir's degrees of freedom. Unfortunately, global correlations among the information-bearing degrees of freedom are easily lost by modular implementations. This is costly since such correlations are a thermodynamic fuel. We quantify the minimum irretrievable dissipation of modular computations in terms of the difference between the change in global nonequilibrium free energy, which captures these global correlations, and the local (marginal) change in nonequilibrium free energy, which bounds modular work production. This modularity dissipation is proportional to the amount of additional work required to perform the computational task modularly. It has immediate consequences for physically embedded transducers, known as information ratchets. We show how to circumvent modularity dissipation by designing internal ratchet states that capture the global correlations and patterns in the ratchet's information reservoir. Designed in this way, information ratchets match the optimum thermodynamic efficiency of globally integrated computations.

Modeling and experimental characterization of the plasma produced by a velvet cathode in a linear induction accelerator

A high power electron diode is used to generate an intense high quality pulsed electron beam (2.6 kA, 4 MeV) in order to produce a bremsstrahlung radiation pulse for the first axis of the flash radiography facility named Epure. The plasma created by surface flashover of the velvet cathode provides a zero work function emitter used to produce the space-charge-limited electron beam. In order to optimize the design of diodes and to better understand the plasma dynamics, we have developed a 0D Collisional-Radiative Model (CRM) which describes the time-dependent evolution of the density of the plasma species in three plasma compositions: 100% H, 95% H + 5% C, and 64% H + 31% O + 5% C. The non-equilibrium electron energy distribution functions (EEDFs) are pre-calculated for a large range of electron mean energies for each mixture. EEDFs and cross sections of electron impact processes are then used to tabulate the electron rate coefficients needed to simulate the time-dependent plasma species densities. The evolution of the electron mean energy is estimated through the electron beam current density itself inferred from particle-in-cell calculations experimentally validated. Visible emission spectroscopy measurements were performed in order to investigate the plasma composition, to measure the Hα/Hβ intensity ratio, and to estimate the electron density. It was shown that the electron density in our setup is between 1014 and 1016 cm−3. Experimental results were compared to the 0D CRM. Results from the time-dependent CRM show that for the three studied plasma compositions, maximum electron densities range from 0.9 × 1014 cm−3 to 1.7 × 1014 cm−3 and that the electron energy averaged over the time interval of the electronic beam pulse is about 3.5 eV. An estimate of the electron energy inside the plasma during the relaxation provides values ranging from 0.10 eV to 0.12 eV based on comparison between the calculated and measured Hα/Hβ intensity ratio averaged over 5 μs. Moreover, main reactions involved in the evolution of the electron density were pointed out.

Nonequilibrium free energy of colloidal glasses under shear

The free energy of hard-sphere systems provides a direct link between the particle-scale structure and macroscopic thermodynamic properties. Here, we employ this framework to investigate the shear-induced structure of a colloidal glass, and link it to its macroscopic mechanical and thermodynamic state. We measure the nonequilibrium free energy under shear from the free volumes of the particles, and monitor its evolution with the applied strain. Unlike crystals, for which the elastic energy increases quadratically with strain due to affine particle displacements, for glasses the free energy decreases due to non-affine displacements and dissipation, reflecting the ability of the glass to reach deeper free-energy minima. We model this decrease using the nonaffine shear modulus and a standard viscous dissipative term. Our model and measurements allow us to disentangle the complex contributions of affine and nonaffine particle displacements in the transient shear deformation of glasses.

Energy accommodation under non-equilibrium conditions for aluminum-inert gas systems

ABSTRACT Molecular dynamics (MD) simulations are conducted to determine non-equilibrium energy accommodation coefficients for aluminum-inert gas systems for a surface temperature of 300 K and gas temperatures in the range of 1000–3000 K. Three different gases are considered: helium, argon, and xenon. Density functional theory (DFT) simulations are conducted to obtain gas-surface interaction potentials and these are then fed as inputs to MD simulations. Effects of temperature and atomic weight of the gas on the accommodation coefficient are explored. Calculated accommodation coefficients are of the order of 0.1 and it is weakly dependent on gas temperature, in contrast to the predictions of Altman's model. Results suggest that energy accommodation coefficients are greatest for argon and lowest for helium for all temperatures considered in this study. This is explained by independently probing the effects of well depth and mass ratio and determining the relative importance of these two effects for the systems under consideration. Lorentz–Berthelot mixing rules substantially over predict the potential well depth, resulting in higher accommodation coefficients. The underlying physics and mechanisms are unraveled using a simple 1-D collision model.

ZEOLITH Detox for Detoxification of Human Body. Proofs for Anti Inflammatory Effects of Zeolite and Detoxification

We studied the mathematical model of interaction with water of natural mineral and microporous crystalline mineral ZEOLITH detox of LavaVitae Company (Austria). In this report are submitted data about the interaction of ZEOLITH detox with water, obtained by non-equilibrium (NES) and differential-equilibrium energy spectrum (DNES) of water. The average energy (∆EH... O) of hydrogen Н…O-bonds among individual molecules H2O after treatment of ZEOLITH detox with water measured by NES- and DNES-methods is ∆E=-0.0034±0.0011 eV for ZEOLITH detox. The average energy (∆EH... O) of hydrogen Н…O-bonds among individual molecules H2O after treatment of ZEOLITH detox with water measured by NES- and DNES-methods is ∆E=-0.0034±0.0011 eV for ZEOLITH detox. The average energy (∆EH... O) of hydrogen Н…O-bonds among individual molecules H2O after treatment of ZEOLITH detox with water measured by NESand DNES-methods. These results suggest the restructuring of ∆EH... O values among H2O molecules with a statistically reliable increase of local extremums in DNES-spectra. The research is performed for ZEOLITH detox with study of pH and oxidative reduction potential (ORP). The report shows the effects of zeolite for the detoxification of human body. The inflammations are one of the basic reasons for aging process. In this research we show anti inflammatory effects from ZEOLITH detox. Keywords: ZEOLITH detox, anti inflammatory effects, detoxification, mathematical model, NES, DNES.

Non-equilibrium 3-D simulator applied to air injection EOR in light oil reservoirs

In this paper, a 3-D simulator based on the assumption of both chemical and thermal non-equilibrium is presented for a more realistic view of non-equilibrium process for simulating air injection EOR (enhanced oil recovery). The mathematical model is based on a non-equilibrium stage with dynamic mass transfer process between different fluid phases and energy transfer process between fluid and matrix (solid). The light crude oil oxidation and air injection process are both simulated by this simulator, through which the pore blocking, gas breakthrough and gas override process are presented through the visualization of oil, gas saturation distributions. The crude oil oxidation is refined as in-phase and interphase reactions to investigate the effect of reactant dispersion caused by the gas-liquid mass transfer. The oxygen dissolution and the evaporation of light components in crude oil are considered in the non-equilibrium process. The results without mass transfer, with dynamic mass transfer and with instantaneous mass transfer between gas and liquid phases are compared through multiplying the gas-liquid interface area 0, 1 and 100 times respectively, and the influence of these different mass transfer conditions on the migration of temperature peak front and oil recovery is revealed. In addition, the effect of local chemical and thermal non-equilibrium in different matrix permeability as well as porosity scenarios is also investigated to obtain non-equilibrium behavior in different reservoir conditions when implementing air injection EOR. In the last section, we investigated the result with different simulation timescale to see if the non-equilibrium behavior can be captured in the simulator used in this paper. This study suggests that the non-equilibrium behavior would show obvious influence on oil recovery for air injection in the lower permeability reservoir. The non-equilibrium behavior is desirable to be considered for simulating air injection EOR in light oil reservoirs. The developed 3-D simulator is robust that can better reflect the mechanism of air injection EOR in light oil reservoirs. We hope this work encouraging more investigations for the simulation side of non-equilibrium phase behavior and energy transfer in the air injection process.

Time irreversibility in reversible shell models of turbulence.

Turbulent flows governed by the Navier-Stokes equations (NSE) generate an out-of-equilibrium time irreversible energy cascade from large to small scales. In the NSE, the energy transfer is due to the nonlinear terms that are formally symmetric under time reversal. As for the dissipative term: first, it explicitly breaks time reversibility; second, it produces a small-scale sink for the energy transfer that remains effective even in the limit of vanishing viscosity. As a result, it is not clear how to disentangle the time irreversibility originating from the non-equilibrium energy cascade from the explicit time-reversal symmetry breaking due to the viscous term. To this aim, in this paper we investigate the properties of the energy transfer in turbulent shell models by using a reversible viscous mechanism, avoiding any explicit breaking of the [Formula: see text] symmetry. We probe time irreversibility by studying the statistics of Lagrangian power, which is found to be asymmetric under time reversal also in the time-reversible model. This suggests that the turbulent dynamics converges to a strange attractor where time reversibility is spontaneously broken and whose properties are robust for what concerns purely inertial degrees of freedoms, as verified by the anomalous scaling behavior of the velocity structure functions.

Latent heat thermal storage with variable porosity metal matrix: A numerical study

Abstract In this paper, a novel design of multitube shell and tube latent heat thermal energy storage system (LHTES) with variable porosity metal matrix in PCM is presented. The shell side of the LHTES contains a phase change material, whereas heat transfer fluid (HTF) flows through seven tubes with internal fins. Metal matrix, as a thermal conductivity enhancer (TCE), is used to augment heat transfer in PCM, however the temperature distribution in PCM is found to be non-uniform along the length of the storage system for constant porosity metal matrix in PCM, which affects the thermal performance of the LHTES. A numerical model is developed to investigate the fluid flow and heat transfer characteristics using the momentum equation and the two-temperature non-equilibrium energy equation coupled with the enthalpy method to account for phase change in PCM. The numerical model is first validated with the experimental results and further extended to identify the effects of geometrical parameters on the temperature distribution in PCM. A relationship between porosity and ratio of length to annular diameter of the storage system is developed for porosity varying from 0.95 to 0.85. It is found that the size of LHTES with variable metal matrix porosity can be reduced for the same effectiveness.