Thermal Conductivity Ratio Research Articles

Optimum convergence parameters of lattice Boltzmann method for predicting effective thermal conductivity

Lattice Boltzmann method is widely used in predicting effective thermal conductivity of multi-phase composites due to its prominent performances. In this paper, a comparative study between single-relaxation-time model (BGK model) and two-relaxation-time model (TRT model) for predicting effective thermal conductivity is performed. To this end, the local heat flux scheme of TRT model is derived. The intrinsic drawbacks inherent to BGK model may be effectively cured by TRT model. It is interesting that an optimum convergence parameter exists in TRT model, which may maximize the convergence speed without losing computational accuracy. To determine the optimum convergence parameters, the influences of the microstructure distributions, volume fractions, thermal conductivity ratios and grid numbers are investigated in a systematic manner. For application, an empirical formula is developed to estimate the optimum convergence parameters, which may work for various multi-phase media. Under the guidance of this formula, the convergence speed of TRT model may be thousands of times faster the BGK counterpart. The present work may be readily extended to the predictions of effective electrical conductivity and elasticity modulus.

Numerical Simulation for Nanofluid Flow in a Wall Driven Cavity with Solid Hindrance: Impact of Thermal Conductivity Ratio and Heat Generation

The current work performs the heatline revelation for combined convection of nanofluid within an enclosure with two moving walls at several thermal conductivity ratios plus heat generation parameter. A solid obstacle that produces uniform heat q per unit area is positioned at the middle of the domain. Sliding lids are assigned to the opposite side walls. Two cases: (I) vertical lids are moving in the same directions and (II) horizontal lids are moving in the opposite directions are analyzed. The computational fluid throughout the enclosed space is water-alumina nanofluid. The Finite Element Method of Galerkin’s weighted residual technique is used to solve the governing nonlinear partial differential equations. Numerical estimations are conducted for a wide range of solid fluid thermal conductivity ratio (0.2 ≤ K ≤ 50) and heat generation parameter (1 ≤ Q ≤ 4) for both cases. Outcomes are obtained as streamlines, isothermal lines, heatlines, heat transfer rate and average heat flow. The results show that the heat flux magnitude is higher for case II than case I but the rate of heat transfer stays nearly same for both cases which increase for the increment of Q and decrement of K. Finally, correlations have been established between the heatfunction with parameters K and Q. There exist strong correlations between the variables which measured from the R-squared values.

Long-time tails in the SYK chain from the effective field theory with a large number of derivatives

We study nonlinear energy diffusion in the SYK chain within the framework of Schwinger-Keldysh effective field theory. We analytically construct the corresponding effective action up to 40th order in the derivative expansion. According to this effective action, we calculate the first order loop correction of the energy density response function, whose pole is the dispersion relation of energy diffusion. As expected, the standard derivative expansion of the classical dispersion relation breaks down due to the long-time tails. However, we find that the nonlinear contributions are so that one can still derive the dispersion relation in the power series. In fact, due to the long-time tails, the classical dispersion relation is split into two series distinct from the derivative expansion, and we show they are convergent. The radius of convergence is proportional to the ratio of thermal conductivity to diffusion constant.

Asymptotic study of premixed flames in inert porous media layers of finite width: Parametric analysis of heat recirculation phenomena

In this paper, we present an investigation on super-adiabatic premixed flames in an inert porous medium layer of finite length. The combustion process is modeled by a one-step Arrhenius kinetics in which density variations are taken into account. The asymptotic case of large ratio of thermal conductivities of solid to gas phases and the high activation energy limit are explored. The results obtained for these limiting cases are compared to those for finite values of these parameters. The use of the flame sheet model allows us to obtain steady-state solutions in an analytical form thus facilitating the parametric analysis.The investigation focuses on the phenomenon of multiplicity of steady-state solutions. It is shown that two or three (nontrivial) steady-state solutions are possible, depending on the flow rate intensity. The critical values of the parameters for the existence of multiple solutions are also determined. The stability of the obtained solutions is finally investigated by means of time-dependent simulations.

Simultaneous thermoosmotic and thermoelectric responses in nanoconfined electrolyte solutions: Effects of nanopore structures and membrane properties

HypothesisNanofluidic systems provide an emerging and efficient platform for thermoelectric conversion and fluid pumping with low-grade heat energy. As a basis of their performance enhancement, the effects of the structures and properties of the nanofluidic systems on the thermoelectric response (TER) and the thermoosmotic response (TOR) are yet to be explored. MethodsThe simultaneous TER and TOR of electrolyte solutions in nanofluidic membrane pores on which an axial temperature gradient is exerted are investigated numerically and semi-analytically. A semi-analytical model is developed with the consideration of finite membrane thermal conductivity and the reservoir/entrance effect. FindingsThe increase in the access resistance due to the nanopore-reservoir interfaces accounts for the decrease of short circuit current at the low concentration regime. The decrease in the thermal conductivity ratio can enhance the TER and TOR. The maximum power density occurring at the nanopore radius twice the Debye length ranges from several to dozens of mW K−2 m−2 and is an order of magnitude higher than typical thermo-supercapacitors. The surface charge polarity can heavily affect the sign and magnitude of the short-circuit current, the Seebeck coefficient and the open-circuit thermoosmotic coefficient, but has less effect on the short-circuit thermoosmotic coefficient. Furthermore, the membrane thickness makes different impacts on TER and TOR for zero and finite membrane thermal conductivity.

Analytical study on core flow in a novel scheme of cascade heat exchanger intensified with open foam partially filled in an annulus

Due to the importance of energy-saving and efficiency in the industry, a novel scheme for waste heat recovery was utilized in the cascade refrigeration cycle. This system is composed of a cascade heat exchanger combined with a recuperator intensified with open foam. The exhaust air from the heat exchanger is used for the air handling unit. Also, core flow in an annular channel is proposed as an innovation to enhance heat transfer. An analytical study was performed to evaluate the impact of metal foam properties on the performance of the partially filled annular heat exchanger with asymmetric isothermal boundary conditions. The energy equations were decoupled by normalizing, linear combination, and the variable change method. Then by forming the Bessel differential equations, temperature solutions were achieved in terms of the modified Bessel functions of the first and second kinds. In the energy and momentum equations of the porous region, the local thermal non-equilibrium (LTNE) and the Darcy-Brinkman models were used, respectively. The analytical solutions of velocity, pressure drop, mass flow ratio, temperature, and Nusselt numbers were obtained. A hydraulically critical point exists at the nondimensional interfacial radius of 2.86 for Da=10−4. It revealed that the Darcy number and the thermal conductivity ratio are two crucial parameters for improving performance. Based on the Performance evaluation criterion (PEC) definition, the optimal porosity value of 0.91 was determined. Also, a design triangle in the range of metal foams was proposed to select the local Nusselt and Biot numbers. At a particular Biot number, the PEC value increases 3.76 times in the design range of metal foams. Results demonstrated that the core flow in an annular heat exchanger leads to high performance, several times greater than non-core flow.

Conjugate Natural Convection: A Study of Optimum Fluid Flow and Heat Transfer in Eccentric Annular Channels

Laminar natural convection-conduction heat transfer in vertically positioned annular channels with inherent eccentricity is investigated for optimum solid-fluid thermal conductivity ratio and optimum cylinder walls thicknesses allowing maximum induced fluid flow rate and heat transfer under varying geometry parameters, i.e., annulus eccentricity and radius ratio. A finite-difference technique is employed to solve the coupled momentum and energy equations for the cylindrical annulus walls and the annular fluid with Prandtl number 0.7. As part of the results, fluctuations in the induced fluid flow rate and heat transfer in the eccentric annular channel due to the conjugate effect, governed by the ratios of the solid and fluid thermal conductivities and thicknesses of outer and inner circular cylinder walls, are obtained for the boundary conditions of one wall heated isothermally and the other kept adiabatic. Commonly encountered ratios of the solid and fluid thermal conductivities and cylinder walls thicknesses are utilized in the present analysis. Results reveal that the optimum conductivity ratio and cylinder walls thicknesses increase nonlinearly with eccentricity and radius ratio. Such results can be very useful in effectively designing the heat transfer equipment for optimum performance.

The applicability of volume-averaging method to simulate melting in a multi-scaled periodic structure

The additively manufactured multi-scaled periodic structure is considered as a thermal enhancer to accelerate melting rate of a PCM in a storage tank. Simulating this multi-phase problem can be carried out through different techniques each of which offering a unique interplay between accuracy and computational time. Full transient 3D simulations are offered as the most accurate and computationally involved benchmark case. In parallel, porous media models of the periodic structure is offered to save the computational time albeit at the expense of accuracy. Two cases of local thermal equilibrium (LTE) and local thermal non-equilibrium (LTNE) are investigated over a range of porosity for different solid matrix materials being copper, aluminium, nickel and stainless steel. To enable the use of LTE, a theoretical model for the effective thermal conductivity is developed and validated against detailed 3D results. The LTNE model, on the other hand, has to rely on an interfacial heat transfer coefficient which is developed in this study to minimize the error between simplified porous media models and the benchmark case. The LTNE model demonstrated excellent accuracy for higher thermal conductivity ratio and/or lower porosity, on the contrary, the LTE model for lower thermal conductivity ratio (stainless-steel cases) outperforms the LTNE model.

Unsteady Electro-Magneto Hydrodynamic Flow and Heat Transfer of Two Ionized Fluids in a Rotating System with Hall Currents

An unsteady flow and heat transmission of ionized gases via a horizontal channel enclosed by non-conducting plates in a rotating framework with Hall currents is examined using electro-magnetohydrodynamic (EMHD) two-fluid heat flow. The Hall current impact is taken into account by assuming that the gases are totally ionized, the applied transverse magnetic field is very strong. For temperature and velocity distributions in two-fluid flow regions, the governing equations are solved analytically. For numerous physical parameters such as the Hartmann number, Hall parameter, rotation parameter, viscosity ratio, and so on, numerical solutions are visually displayed. It was discovered that an increase in temperature in the two regions is caused by the thermal conductivity ratio. It was also realized that an increase in rate of heat transfer coefficient at the plates is caused by either the Hartman number or the Hall parameter.

Improvement of the heat transfer quality by air cooling of three‐heated obstacles in a horizontal channel using the lattice Boltzmann method

AbstractThis study focuses on the cooling of three heated obstacles with different heights mounted on the bottom of the channel wall using different aspects that influence the enhancement of the heat exchange, as is known in the concept of cooling electronic devices. The lattice Boltzmann method associated with multiple relaxation times (LBM‐MRT) was adopted to simulate the physical configurations of the studied system. In this context, the D2Q9 and D2Q5 models are applied to describe the fluid flow behavior and conjugate heat transfer, respectively. The evaluation of heat exchange between the cold fluid and three‐heated obstacles has been accurately analyzed under the effect of several parameters such as Reynolds number, obstacle spacing, and thermal conductivity ratio. In addition, the setting of two and three fluids flow inlets were also studied. The results are presented in terms of streamlines, isotherms, and local Nusselt curves. The heat transfer increases with increasing solid‐fluid thermal conductivity. It is also more pronounced for large Reynolds numbers. Moreover, the heat transfer significantly enhances for the second and third obstacles when obstacle spacing increases. The improvement of the heat transfer is performed by the implementation of several jet flows in the studied system.

Impact of using single heated obstacle on natural convection inside porous cavity under non-Darcy flow and thermal non-equilibrium model: A comparison between horizontal and vertical heated obstacle arrangements

The current study implements a numerical investigation on natural convection inside non-Darican porous duct to analyse the actions of using a single heated obstacle attached horizontally/vertically at the heated surface under Local thermal non-equilibrium (LTNE). Importance has been given on how the heated obstacle length and its position manipulate the enhancement of natural convection. Solutions confirm that Nu is extremely depends on ratio of thermal conductivity (Kr), obstacle length (Z), obstacle position (X), modified Rayleigh number (Ra*) and inertia coefficient (Fs/Pr*) as compared to heat transfer coefficient (H). Results display that the rising in Z leads to recede free convection activity as compared to the smallest one, where Z and X have extremely impact on Nu. Results displayed that Nus, Nuf and NuT obtained for the horizontal case are higher than vertical case, which reveals a better thermal performance. Optimum enhancement in Nu has been observed when using small Z and it horizontally attached at higher place inside the duct. The density of LTNE regime is extremely reduced with rising in H, Kr and Ra* and reducing in Z and Fs/Pr*. Finally, the horizontal heated obstacle can be advised to be used in heat exchanger for techniques implementing porous media.

Thermal performance of a tandem-dual-channel flat-plate pulsating heat pipe applicable to hypergravity

Thermo-hydrodynamic characteristics of a novel flat-plate pulsating heat pipe (FP-PHP) with a symmetrically tandem dual-serpentine-channel were studied experimentally under the simulated hypergravity by a rotating platform capable of providing an adjustable centrifugal acceleration up to a = 4 g0 (g0 = 9.8 m/s2) on ground. The influences of gravity level, heat load, and orientation (i.e., circumferential orientation (C-O) and radial orientation (R-O)) on thermo-hydrodynamic performance of the FP-PHP were investigated. It is indicated that, similar to the traditional single-serpentine PHPs under the normal gravity, the quasi-steady flow motion in the FP-PHP under the hypergravity could be also classified into five flow patterns, i.e., stop-over, intermittent pulsation, pulsation, pulsation with circulation and circulation. Increasing hypergravity level is not conducive to the start-up process of the FP-PHP, which needs larger start-up heat load and higher start-up temperature. Even so, under a ≤ 4 g0, the FP-PHP can successfully start up within decent temperature level of 58 °C. Growing hypergravity level induces increasing negative influences on the thermo-hydrodynamic performance of the FP-PHP, which is more obvious under the R-O than that under the C-O. Anyway, in general, FP-PHP possesses a good thermal performance uniformity, which has an average coefficients of variation less than 3% in thermal resistance of its two symmetric halves. In addition, FP-PHP has an average equivalent thermal conductivity 4.38 times that of the pure 6063 aluminum alloy plate and a total weight 83.6% of it. The average equivalent thermal conductivity ratio of the FP-PHP under the hypergravity of a ≤ 4 g0 to that under the normal gravity is not smaller than 0.70, indicating a good adaptability of the FP-PHP to hypergravity. Accordingly, the FP-PHP could be regarded as a promising option for modern avionics passive thermal control systems for multiple heat sources.

Accurate prediction of the critical heat flux for pool boiling on the heater substrate

While the influence of liquid qualities, surface morphology, and operating circumstances on critical heat flux (CHF) in pool boiling has been extensively studied, the effect of the heater substrate has not. Based on the force balance analysis, a theoretical model has been developed to accurately predict the CHF in pool boiling on a heater substrate. An analytical expression for the CHF of a heater substrate is obtained in terms of the surface thermophysical property. It is indicated that the ratio of thermal conductivity (k) to the product of density (ρ) and specific heat (c p) is an essential substrate property that influences the CHF. By modifying the well-known force-balance-based CHF model (Kandlikar model), the thermal characteristics of the substrate are taken into consideration. The bias of predicted CHF values are within 5% compared with the experimental results.

Impact of different arrangements of heated elliptical body, fins and differential heater in MHD convective transport phenomena of inclined cavity utilizing hybrid nanoliquid: Artificial neutral network prediction

In the current scenario, the impact of different arrangements of solid heated elliptical body, discrete heater (LH/H), array of fins with different sizes (1×2, 2×1, 2×2), conductivity ratio (r), magnetic field (Hartmann number, Ha), angle of inclination (β), nanoparticle volume fraction (χ) and Rayleigh number (Ra) is investigated for natural transport phenomena in the cavity containing hybrid nanoliquid. The cavity consists of three equally spaced fins on one wall and heated elliptical body inside the cavity. The homogeneous hybrid nanoliquid (Al2O3-Cu/water) model using experimental data is utilized and results are evaluated for different controlling parameters: Rayleigh numbers (Ra=103 to 106), Hartmann number (Ha=0 to 100), discrete heater (LH/H=0.1 to 0.9), angle of elliptical body (ω=0° to 180°) with three different positions (Center, POS I and II), angle of inclination (β=0 to π), thermal conductivity ratio (r=0.01–100), nanoparticle volume fraction (χ=0 to 0.02) using Galerkin Finite Element Method (GFEM). The mesh grid independency test is also performed for different combinations of meshes and a refined mesh with optimal degrees of freedom (DoFs=190275) has been considered for entire convection range (Ra=103−106).The impact of controlling parameters on average Nusselt number evaluated from the numerical heat transfer analysis has been compared and predicted using feed forward neural network model. The Levenberg-Marquardt back propagation algorithm is used for ANN training based on limited simulated data with optimal number of neurons and average R2 of 0.99988. The quadratic regression model, which is also determined using the MATLAB built-in subroutine ’fitlm’, demonstrates the greatest dependency of Nusselt number on nanoparticle concentration.

Improved phase-field-based lattice Boltzmann method for thermocapillary flow.

In this paper, we present an improved phase-field-based lattice Boltzmann (LB) method for thermocapillary flows with large density, viscosity, and thermal conductivity ratios. The present method uses three LB models to solve the conservative Allen-Cahn equation, the incompressible Navier-Stokes equations, and the temperature equation. To overcome the difficulty caused by the convection term in solving the convection-diffusion equationfor the temperature field, we first rewrite the temperature equationas a diffuse equationwhere the convection term is regarded as the source term and then construct an improved LB model for the diffusion equation. The macroscopic governing equationscan be recovered correctly from the present LB method; moreover, the present LB method is much simpler and more efficient. In order to test the accuracy of this LB method, several numerical examples are considered, including the planar thermal Poiseuille flow of two immiscible fluids, the two-phase thermocapillary flow in a nonuniformly heated channel, and the thermocapillary Marangoni flow of a deformable bubble. It is found that the numerical results obtained from the present LB method are consistent with the theoretical prediction and available numerical data, which indicates that the present LB method is an effective approach for the thermocapillary flows.

Effect of coating methods on thermal conductivity of graphene-coated fabrics for welding protective clothing

Blade coating and screen printing methods were used to prepare graphene-modified fabric to study their thermal conductivity and molten metal splashes heating properties in our research. The effect of the coating method on thermal properties was discussed. The fabric with blade coating had lower penetration depth, the in-plane and cross-plane thermal conductivity reached 2.08 W/(m·K) and 0.48 W/(m·K) which meant the anisotropy value was 4.3 while the control fabric was 2.4. The elevated temperature after impacting of molten metal splashes declined about 30% from 27 °C to 19 °C. About screen printing samples, the in-plane to cross-plane ratio of thermal conductivity was 3.5, and the temperature rise was 25 °C.

Wood‐Derived, Vertically Aligned, and Densely Interconnected 3D SiC Frameworks for Anisotropically Highly Thermoconductive Polymer Composites

Construction of a vertically aligned and densely interconnected ordered 3D filler framework in a polymer matrix is a challenge to attain significant thermal conductivity (TC) enhancement efficiency. Fortunately, many biomaterials with unique microstructures can be found in nature. With inspiration from wood, artificial composites can be rationally designed to achieve desired properties. Herein, the authors report a facile and effective approach to fabricate anisotropic polymer composites by biotemplate ceramization technology and subsequent vacuum impregnation of epoxy resin. The hierarchical microstructure of wood is perfectly replicated in the cellular biomass derived SiC (bioSiC) framework by carbothermal reduction. Owing to the anisotropic architecture of bioSiC, the epoxy composite with vertically aligned dense SiC microchannels shows interesting properties, including a high TC (10.27 W m−1K−1), a significant enhancement efficiency (259 per 1 vol% loading), an outstanding anisotropic TC ratio (5.77), an extremely low coefficient of linear thermal expansion (12.23 ppm K−1), a high flexural strength (222 MPa), and an excellent flame resistance. These results demonstrate that this approach is expected to open a new avenue for design and preparation of high performance thermal management materials to address the heat dissipation of modern electronics.

Numerical simulation of thermo-magnetic convection and entropy production in a ferrofluid filled square chamber with effects of heat generating solid body

Thermo-magnetic convection and entropy production are the most widely used subjects of study in the field of an effective design tools for cooling electronic devices. The present work focuses on numerical simulation of thermo-magnetic convection cooling of the heat-generating solid block placed in a magnetite suspended nanoliquid filled chamber. The surfaces of the horizontal borders of the chamber are thermally insulated whilst the vertical borders are cooled at a constant temperature. The finite volume technique with a simple algorithm on a uniform staggered grid is employed to transform the governing non-linear PDE into a set of discretized equations. The liquid motion, thermal transmission, and entropy production are discussed for various pertinent parameters such as solid volume fractions of the nano-additive (φ=0.01−0.04), aspect ratio of a heat-generating solid body (As=0.25−4), thermal conductivity ratio of the heat generating body (0.1≤k*≤5.0), Hartmann number (Ha=0−50) and irreversibility ratio (Ω=0.001−0.1). Isolines of temperature, stream function, normalized entropy along with profiles of mean Nusselt number and mean entropy production outcomes are demonstrated graphically. The results showed that reduction in aspect ratio increases the cooling efficiency due to the hindrance-free effect and produces a high heat transfer rate. Minimum entropy production occurs at low thermal conductivity ratio (k*=0.1). The thermal performance criterion also justifies that the least aspect ratio manifests better thermal performance.

Natural Convection in Annulus Between Two Concentric Cylinders Partially Filled with Metal Foam Distributed with New Suggested Design

The investigation of natural convection in an annular space between two concentric cylinders partially filled with metal foam is introduced numerically. The metal foam is inserted with a new suggested design that includes the distribution of metal foam in the annular space, not only in the redial direction, but also with the angular direction. Temperatures of inner and outer cylinders are maintained at constant value in which inner cylinder temperature is higher than the outer one. Naiver Stokes equation with Boussinesq approximation is used for fluid regime while Brinkman-Forchheimer Darcy model used for metal foam. In addition, the local thermal equilibrium condition in the energy equation of the porous media is presumed to be applicable for the present investigation. CFD ANSYS FLUENT software package (version 18.2) is used as a solver to this problem. Various parameters are examined; Rayleigh number, Darcy number, and thermal conductivity ratio to study the effect of them on fluid flow and heat transfer inside the annuli space in the suggested design of metal foam layer. current model is compared with the available published results and good agreement is noticed. Results showed that as Rayleigh number increases the dominated of convection mode increases and Nusselt increases. Also, Nusselt is larger at the higher Darcy and thermal conductivity ratio. It was found that at Rayleigh of 106 and thermal conductivity ratio of 104 Nusselt reach its higher value which is 6.69 for Darcy of 0.1 and 6.77 for Darcy of 0.001. A comparison between this design and the traditional design was established for Darcy 0.001 and thermal conductivity ratio 102, and its showed a good enhancement in Nusselt number and the greatest enhancement percentage was 44% at Rayleigh equal 5*104 while the lowest percentage is 6% for Rayleigh equal106.

ASSESSMENT OF CONJUGATE AND CONVECTIVE HEAT TRANSFER PERFORMANCE OVER A PARTITIONED CHANNEL WITHIN BACKWARD-FACING STEP USING THE LATTICE BOLTZMANN METHOD

This research concerns the quality of heat transfer across a two-dimensional backwards-facing step in the presence of vertical or inclined partitions in a rectangular channel. Convective and conjugate heat transfer input using constant temperature and heat flux were successfully achieved for low Reynolds number values. The actual code based on the double multiple relaxation time of the lattice Boltzmann method was employed to model numerically the physical problems related to the fluid flow and heat transfer, where the obtained results had a good agreement with previous experimental research. During this study, parametric variations were carried out according to the inclination and position of the partitions, as well as the thermal conductivity ratio in the case of the conjugate heat transfer problem. The numerical results show that the involvement of the partitions and the thermal conductivity ratio has a significant effect on the fluid flow and heat transfer. This impact controls the evolution of local Nusselt number, bulk temperature, and skin friction coefficient. The improvement of heat transfer is remarkable by the introduction of vertical or inclined partitions such that the quality of heat exchange reaches about 7%. While the presence of two inclined partitions increases the heat transfer by about 6% in case of constant temperature of studied hot wall. The implementation of constant heat flux for the hot wall increases the quality of heat transfer by about 9%-10% by the presence of inclined or vertical walls, 11%-13% with double inclined partitions.