Thermal Conductivity Ratio Research Articles

Mixed convective flow of a Newtonian fluid through a porous medium with a lack of thermal equilibrium

The primary focus of this work is on the effects of thermal radiation and heat generation on mixed convective MHD steady flow of a Newtonian fluid via a porous channel under local thermal non-equilibrium (LTNE) condition. The resulting governing equations are converted into a set of ordinary differential equations (ODEs) using the proper similarity transformation. The shooting method is implemented in MATLAB code, which is then used to solve the set of dimensionless coupled ODEs. In the fluid phase, the external effects of heat generation and thermal radiation are taken into account. The effect of individual parameters on flow and heat transfer phenomena are discussed in detail with the help of plots and tables. From the study, it is noted that LTNE is predominant near the wedge compared to that far away from the wedge and also as heat transfer rate increases for greater values of thermal conductivity ratio parameter.

Thermal Conductivity Model of Porous Media Embedded with a Damaged Tree-like Branching Network Considering the Influence of Roughness

In the study of heat transfer in tree-like branching network, neither the heat convection caused by fluid flow in the tree-like branching network nor the asymmetric structure of the tree-like branching network can be ignored. In this work, we assume the porous media is embedded with a tree-like branching network that are characterized by damaged pipes. We investigated the effects of surface roughness on heat conduction and heat convection in the porous media embedded with the damaged tree-like branching network based on the fractal features of tree-like branching networks and the basic theory of thermodynamics. The proposed model for thermal conductivity can be expressed as a function of micro-structural parameters of the composite, such as the relative roughness, the ratio of thermal conductivity of the wall to that of the fluid in the micro-channel, the diameter ratio, the length ratio, the branching level, the number of damaged channels, the total number of branching levels, and the main tube porosity of the porous media. The effects of the micro-structural parameters of the model on its effective thermal conductivity have been analyzed in detail. It is believed that the joint expression of heat conduction and heat convection could enrich and develop the physical study of heat transport in porous media.

Convectively cooled solidification in phase change materials in different configurations subject to internal heat generation: Quasi-steady analysis

Phase change phenomena involving internal heat generation are of central interest in various applications, including freeze drying, preservation of biological tissues, microwave/Joule heating processes, materials processing using lasers, and nuclear power generation systems. In this work, mathematical models are developed to study the solidification processes driven by convective cooling effects on the exterior surface of phase change materials (PCM) in different geometric configurations, where both the solid and the liquid phases are subject to volumetric heating. By invoking a quasi-steady assumption and performing a simplified unified analysis, new semi-analytical approximate solutions for this unique Stefan problem in planar, cylindrical, spherical, and semi-infinite geometries of the PCM are obtained and studied. The interface evolution depends on the characteristic dimensionless parameters, such as the Biot number, Bi, internal heat generation parameter, Q, Stefan number, St, and the thermal conductivity ratio, κ. The effects of all the dimensionless parameters, viz., Bi, Q, St, and κ are systematically investigated for each geometrical configuration of the PCM. In particular, the results show the significant role of the Biot number on the transient evolution as well as the steady-state thickness of the solidifying front in the presence of an inhibiting internal heat generation. In addition, a simple and unified condition relating the dimensionless internal heating rate (Q) and the external convective cooling rate (Bi) for the onset of remelting for the special case of κ = 1 applicable for all the above geometries of the PCM is deduced.

In-Plane and Out-of-Plane T-Shaped Conductive Cold Plate Networks

Abstract In this study, two configurations for a cold plate designed to cool a heat-generating solid planar material through a small isothermal side-section are considered. The cold plate is originally conceived by distributing (embedding) within the heat-generating material a fixed amount of a high-conductivity material. Prior work has shown a T-shaped network type emerges, under stringent assumptions, as the optimum distribution for minimizing the cold plate maximum temperature. However, this “in-plane” embedded distribution configuration is impractical for being too intrusive. A new and practical “out-of-plane” configuration is proposed with the same optimal high-conductivity material network placed on top of the low-conductivity heat-generating plane instead of being embedded in it. Using realistic considerations and specifications, several different network distributions with increased complexity are designed for both in-plane and out-of-plane configurations. Modeling and numerical simulations are then performed to compare the heat transfer effectiveness achieved by each configuration and to investigate how the high-to-low thermal conductivity ratio influences the cold plate performance. Results show the in-plane and out-of-plane configurations surprisingly yield nearly identical temperature distributions for all configurations tested, and the increase of the thermal conductivity ratio enhances the network cooling role for all cases. The results also establish the robustness of the network design by showing better cooling performance when the network complexity increases, even when some of the stringent assumptions imposed in the original conceiving of the networks are not fully satisfied.

Numerical studies of the simultaneous development of forced convective laminar flow with heat transfer inside a microtube at a uniform temperature

Abstract Conjugate heat transfer is a complex problem because heat is transferred from a solid medium to a liquid medium through their interfaces. The steady-state laminar flow formed inside the microtubules is subjected to a constant temperature at the outer sidewall surface. These images cover a wide range of wall-to-fluid thermal conductivity ratios (ksf = 1, 2, 3, 4, and 5) and wall thickness-to-inner diameter ratios (δ/Ri = 0.25, 0.5, 0.75, 1, 1.25, and 1.5) and Reynolds numbers (Re = 200, 400, 600, 800, and 1,000). The results are processed by a Fluent program based on the finite volume method to numerically integrate the driver’s differential equations. The results show that increasing the wall-to-fluid thermal conductivity ratio ksf increases the inner wall dimensionless temperature and decreases the average Nusselt number. Conversely, an increase in the ratio of wall thickness to inner diameter results in a decrease in the dimensionless temperature of the inner wall and an increase in the average Nusselt number.

A natural convection conjugate heat transfer of Nano-Encapsulated Phase Change Materials (NEPCMs) in an inclined blocked square enclosure

The current investigation deals numerically with a two-dimensional steady laminar flow natural convection heat transfer of a dilute suspension of a base fluid and suspension of Nano Encapsulated Phase Change Materials (NEPCMs) nanoparticles saturated inside an inclined square enclosure with a centered internal conducting square block with a ratio of 0.5. The enclosure inclination angle varies from 0° to 90° with increments of 15°, and block thermal conductivity to the host fluid has been chosen to be 0.2 and 5. The obtained results are in excellent agreement with those available in the literature for validation. The findings reveal that the heat transfer depends considerably on the inclination angle, block thermal conductivity ratio, and Stefan number for all considered ranges. The present results suggest that the average Nusselt number rate is notably enhanced as the inclination angle rises from 0° to 90° for thermal conductivity KR = 0.2 and KR = 5; this enhancement is more evident as the Rayleigh number is increased. The average Nusselt number improves by 5%, 153%, 558%, and 1120% for Rayleigh numbers of 103, 104, 105, and 106, respectively, when the inclination angle varies from 0° to 90° for a thermal conductivity ratio of 0.2. This improvement is somewhat reduced in the case of a thermal conductivity of 5, where the average Nusselt number grows by around 0.4%, 27%, 213%, and 537% for Rayleigh numbers 103, 104, 105, and 106, respectively. The higher value of the latent heat capacity of encapsulated particles enhances the heat transfer rate; the decreased Stefan number induces a notable improvement in the average Nusselt number. This enhancement is more evident as the inclination angle increases. The findings clearly show a considerable influence on the isotherms and heat capacity ratio distributions for all considered block thermal conductivities and Rayleigh numbers.

Gill's problem in a sandwiched porous slab

The classical Gill's stability problem for stationary and parallel buoyant flow in a vertical porous slab with impermeable and isothermal boundaries kept at different temperatures is reconsidered from a different perspective. A three-layer slab is studied instead of a homogeneous slab as in Gill's problem. The three layers have a symmetric configuration where the two external layers have a high thermal conductivity, while the core layer has a much lower conductivity. A simplified model is set up where the thermal conductivity ratio between the external layers and the internal core is assumed as infinite. It is shown that a flow instability in the sandwiched porous slab may arise with a sufficiently large Rayleigh number. It is also demonstrated that this instability coincides with that predicted in a previous analysis for a homogeneous porous layer with permeable boundaries, by considering the limiting case where the permeability of the external layers is much larger than that of the core layer.

Validation of the local thermal equilibrium assumption for free convection boundary layer flow over a horizontal cylinder embedded in an infinite saturated porous medium

This study numerically investigated the validity of the local thermal equilibrium model for free convection over a horizontal cylinder embedded in an infinitely packed bed of spherical particles saturated with Newtonian fluid. The local thermal non-equilibrium and Forchhemimer-Brinkman extended Darcy model were used by considering the boundary-layer theory assumptions and were solved with the implicit Keller box finite difference scheme. The governing parameters considered are the porosity, thermal conductivity ratio, Rayleigh number, Prandtl number, the ratio of cylinder diameter to spherical particle diameter and Biot number. The results showed the two parameters of conductivity ratio and Biot number can significantly affect the other parameters. For low Biot number and conduction coefficient ratio, the local thermal non-equilibrium assumption was inapplicable in almost all cases. Significantly, for high values of the conductivity ratio and Biot number, the assumption that the fluid and solid matrix are isothermal, could be used in almost all cases studied. Furthermore, increasing the amount of Rayleigh number, Porosity and Prandtl increased the temperature difference between the solid and fluid phases. In addition, increasing the ratio of cylinder diameter to particle diameter reduced the temperature difference between the two phases. The average temperature difference between fluid and solid can have the most changes as follows: It can experience 200% growth when the Prandtl number changes from 2 to 7. Also, it can reduce by 33% by increasing the Bio number from 0.01 to 10. In addition, the temperature difference of two phases can be increased by 7 and 0.5 times by increasing the porosity from 0.25 to 0.85 and increasing the ratio of cylinder diameter to particle diameter from 20 to 100, respectively.

Thermal Performance and Geometric Optimization of Fractal T-Shaped Highly-Conductive Material for Cooling of a Rectangular Chip

To improve the thermal performance of inserted highly-conductive material (HCM) for the cooling of a chip, the present work numerically investigates the effects of various geometric and structural parameters of a fractal T-shaped branched HCM on the maximum temperature of the chip. These parameters include the length ratios of branches at two consecutive branching levels α, the width ratio of branches at two consecutive branching levels β, the maximum branching level m, the length of the branch at the initial level L0, the thickness of the HCM H, and the total volume of the HCM V. The results indicate that the maximum temperature of the chip first drops and then rises with the increase of β, which means the existence of the optimal geometric structure of the branched HCM for the cooling of the chip. In addition, the maximum temperature of the chip decreases with the increase of m and V, decreases with the decrease of H, while first drops and then rises with the increase of α and L0. Further, the present work investigates the effects of the thermal conductivity ratio of HCM and chip γ on the optimal width ratio βm of the branched HCM with a different length ratio α, maximum branching level m, length of the branch at the initial level L0, thickness H, total volume V, and thermal conductivity of the rectangular chip Kc. It was found that βm increases with the increase of γ and V, and decreases with the increase of α, L0, and H. The present finding is beneficial to the improvement of the thermal performance of the inserted HCM via geometric optimization.

Numerical investigation of microchannel heat sinks with different inlets and outlets based on topology optimization

Topology optimization can generate better structures of microchannel with improved cooling performance. In this paper, microchannel heat sinks with five different inlet and outlet structure combinations are optimized using bi-objective topology optimization based on the density method. The layouts of channels are optimized to minimize the power dissipation and total heat generation at the same time. The results show that the straight line inlet and outlet with extension areas (SE) can reduce 20%-50% power dissipation when realizing the same heat transfer performance compared with traditional one channel inlet and one channel outlet (OC). Effects of Reynolds number, the ratio of solid and fluid thermal conductivity and the dimensionless heat generation coefficient in fluid domains are also investigated. The simple channels can be obtained with higher ratio of solid and fluid thermal conductivity and/or higher dimensionless heat generation coefficient in fluid domains. With optimization further considered in the inlet and outlet regions, better overall performance can be obtained. Finally, the 2D optimized structures are further validated by three-dimensional numerical simulation. It is found that the optimized design can realize 53.28% increment of Nusselt number with 40.89% reduction in pressure drop compared with traditional microchannel heat sinks.

Releasing chemical energy in spatially programmed ferroelectrics

Chemical energy ferroelectrics are generally solid macromolecules showing spontaneous polarization and chemical bonding energy. These materials still suffer drawbacks, including the limited control of energy release rate, and thermal decomposition energy well below total chemical energy. To overcome these drawbacks, we report the integrated molecular ferroelectric and energetic material from machine learning-directed additive manufacturing coupled with the ice-templating assembly. The resultant aligned porous architecture shows a low density of 0.35 g cm−3, polarization-controlled energy release, and an anisotropic thermal conductivity ratio of 15. Thermal analysis suggests that the chlorine radicals react with macromolecules enabling a large exothermic enthalpy of reaction (6180 kJ kg−1). In addition, the estimated detonation velocity of molecular ferroelectrics can be tuned from 6.69 ± 0.21 to 7.79 ± 0.25 km s−1 by switching the polarization state. These results provide a pathway toward spatially programmed energetic ferroelectrics for controlled energy release rates.

Three-dimensional simulation of conjugate heat transfer using the hybrid lattice Boltzmann-finite difference method

This paper presents a three-dimensional numerical study of natural convection and conduction thermal phenomena using MRT-lattice Boltzmann and finite difference approaches. Conduction is examined using a simple conjugate heat transfer technique, which is predicated on the assumption of continuity of heat flux and temperature at the solid/fluid interfaces, instead of utilizing the conventional method based on the solution of the conduction equation. Several parameters such as Rayleigh number and thermal conductivity related to common construction materials are also investigated to explore their effects on the evolution of heat transfer. The obtained results show that augmentation of the Rayleigh number increases the quality of heat transfer by around 35–293% for various values of thermal conductivity ratio (solid/fluid). While the increase in thermal conductivity ratio enhances the heat transfer rate by about 212–685%, where the maximum rate of heat exchange is still the same for the thermal conductivity ratio ≥1000. Entropy generation is also examined in this paper to evaluate the efficiency of our studied system. The performed investigations indicate that the rate of entropy generation due to heat transfer, friction, and total entropy generation varies significantly with increasing Rayleigh number and thermal conductivity of the solid.

New magnesium based half-metallic ferromagnetic chalcogenide MgFe2Z4 (Z = S, Se) spinels; a promising materials for spintronic applications

This article focuses on the physical properties of MgFe2Z4 (Z = S, Se) spinels investigated by employing density functional theory calculations. To explore the magnetic and electronic properties, WIEN2k code was executed whereas thermoelectric properties were studied using the BoltzTraP. The determined negative formation energies and positive phonon frequencies show that the system under investigation is stable. The lowest possible ground state energies clearly indicate that spinels lie in ferromagnetic state. Studied spinels illustrated half-metallic nature upon employing the calculations of density of states (DOS) and spin-polarized band structures (BS). Ferromagnetic (FM) state was found to be stable ground state. Observation of ferromagnetism in these compounds was ensured by exchange energies, Jahn-Teller energy and hybridization and is attributed to electron spin in place of Fe2+ clustering. Curie temperature and spin polarization of these compounds is also comprehensively investigated in this study. Analysis of the thermoelectric properties showed a good fit between the ratio of electrical (σ/τ) and thermal conductivity (κ e/τ). Thermoelectric efficiency of studied compounds is found to be appropriate as demonstrated by the thermoelectric power factors.

Statistical modeling and investigation of thermal characteristics of a new nanofluid containing cerium oxide powder

In this paper, the thermal conductivity (knf) of cerium oxide/ethylene glycol nanofluid is extracted for different temperatures (T = 25, 30, 35, 40, 45, and 50 °C) and the volume fraction of nanoparticles (φ= 0, 0.25, 0.5, 0.75, 1, 1.5, 2 and 2.5%) and then knf is predicted by two methods including Artificial Neural Network (ANN) and fitting method. For both methods, the results have been presented and compared. The experiments showed that with increasing φ and temperature, the thermal conductivity ratio (TCR) of nanofluid increases. It was also observed that when the experiments are performed at high temperatures, the rate of increase in knf is much higher than the change in the same amount of φ change at low temperatures. An ANN with 7 neurons has a correlation coefficient very close to 1 and this proves that the outputs are compatible with experimental results. Also, it can be seen that the ANN could predict the thermal behavior of cerium oxide/ethylene glycol nanofluid more accurately.

Analysis of power-law natural conjugate heat transfer under the effect of magnetic field and heat absorption/production based on the first and second laws of thermodynamics for the entropy via lattice Boltzmann method

The amount of entropy generated during the conjugate heat transfer of a non-Newtonian fluid regarding to natural convection within a two-dimensional cavity under the influence of a magnetic field and heat absorption/production has been appraised. The lattice Boltzmann method (LBM) method is developed to perform numerical simulations. Moreover, the first and second laws of thermodynamics are simulated via LBM for the entropy investigation. The influence of variables such as wall shape and aspect ratio of chamber, thermal conductivity ratio, fluid type, Hartmann number, heat absorption/production coefficient and type of magnetic field are analyzed. The lower the power-law index, the more effective the magnetic field applied. The mean Nusselt number for pseudoplastic fluid is about 52% and for dilatant fluid about 18% decreases to the highest value with enhancement of the Hartmann number. By changing the shape of the wall, the amount of current vigor, heat transfer and entropy produced can be significantly affected. In such a way that by designing the wall diagonally, the amount of heat transfer up to about 11% and the power of flow up to about 32% more than other cases. The effect of increasing the strength of the magnetic field decreases with increasing the chamber aspect ratio, and in this case the lowest heat transfer rate is seen, however the Bejan number increases.

Gaseous slip flow in a porous two-dimensional rectangular microchannel subjected to inclined magnetic field

In this study, two-dimensional, steady, laminar, and compressible gaseous flow of Newtonian fluid in a rectangular porous microchannel affected by an electromagnetic field, and under local thermal equilibrium condition was analytically investigated in the slip flow region (0.001<Kn < 0.1). The porous microchannel is entirely affected by uniform inclined magnetic field with an angle α from the positive x-axis, the range of this angle is 0 ≤ α ≤ 90°. Also, the porous microchannel effected by uniform electric field which points in the positive z-direction. Thermophysical properties of the fluid were assumed to be constant. The normalized governing equations were asymptotically solved and expressions of the flow velocity components, the pressure, and the temperature were provided using first-order velocity slip and temperature jump boundary conditions. The effects of various parameters on the flow were studied, such as Darcy number, the porosity, the thermal conductivity ratio, the electrical conductivity ratio, Hartmann number, Knudsen number, the electric field to magnetic field ratio (0 ≤ K ≤ 1), and the magnetic field inclination angle. It was found that increasing the permeability of the porous medium increases the flow velocity but decreases its temperature. Further, the results reveal that applying a stronger magnetic field in absence of electric field decreases the flow velocity but increases its temperature. On the other hand, the stronger the electric field, the higher the flow velocity and its temperature. Also, as the magnetic field inclination angle increases the flow velocity decreases. The effects of Darcy number and the electrical conductivity ratio on the heat flux were studied as well. A comparison of the analytical solutions with the numerical results were presented as a validation for this study. The comparison showed that the analytical results were in good agreement with the numerical results.

Conjugate MHD natural convection of hybrid nanofluids in a square enclosure containing a complex conductive cylinder

PurposeThe purpose of this study is to investigate the enhancement and suppression of heat transfer for hybrid nanofluids (Cu–Al2O3/water) in a square enclosure containing a thermal-conductive cylinder when the Lorentz force is applied to the hybrid nanofluids.Design/methodology/approachSince the inner conductive cylinder in present research has a complex geometry, an in-house meshless method, namely, the local radial basis function (LRBF) method, is applied to solve the 2 dimensional (2D) incompressible Navier–Stokes equation in the fluid domain and Fourier heat conduction equation in solid domain. The solid–fluid interface remains the physical continuity of temperature and heat flux. Only the Lorentz force is considered for the presence of the magnetic field. The conjugate natural convection is assumed to be steady, thus only fully developed heat exchange from the nanofluids to solid or vice versa is comprehensively investigated.FindingsIt can be concluded that Lorentz force plays a more significant role than hybrid nanofluids in enhancing/suppressing heat transfer when the orientation of magnetic field is the same to the x direction. The thermal conductivity ratio can dramatically change the isotherms and streamlines as well as the mean value of the Nusselt number, resulting in totally different heat transfer phenomena. The included angle of magnetic field also has a significant effect on the heat transfer rate when it changes from horizontal to vertical.Research limitations/implicationsThe constant thermo-physical properties of incompressible fluid and the 2D steady flow are considered in this study.Originality/valueThe conjugate MHD natural convection of hybrid nanofluids is numerically investigated by an in-house meshless LRBF method. The enhancement and suppression of heat transfer under the combined influence of the volume fraction of nanoparticles, Hartmann number and the thermal conductivity ratio are comprehensively investigated.

Control of thermal and fluid flow characteristics of an oscillating cylinder by porous media

The present research aims to study the effect of variables including permeability and thickness of porous media on the thermal and hydrodynamic behavior of an oscillating cylinder at a constant temperature. The finite volume technique is employed to model the flow field for various thicknesses of the porous layer and Darcy numbers at low Reynolds numbers. According to the results, raising the Reynolds number and decreasing the Darcy number will reduce the length of the wakes created behind the cylinder. The separation point occurs earlier as the permeability decreases. Additionally, increasing the porous media thickness and decreasing the Darcy number leads to a decline in the amplitude of oscillation of lift and drag coefficient and amplitude of oscillation in lateral and longitudinal directions. Using the porous layer, the amplitude of the displacement of the cylinder is reduced by about 55 %. Thickness, Darcy number, and the thermal conductivity ratio influence the average variation of the Nusselt number in porous media. For any Darcy number with a specific thermal conductivity ratio, the Nusselt number of the cylinder with a porous layer is larger than the one without porous media. For the oscillating cylinder with Da = 0.001, Re = 90, ks/kf = 1000 and a 0.3 porous layer thickness, it has been taken for a 25 % augment in heat transfer.

Improving the thermophysical properties of hybrid nanocellulose-copper (II) oxide (CNC-CuO) as a lubricant additives: A novel nanolubricant for tribology application

The primary objective of the present analysis is to investigate the thermophysical properties of hybrid nanocellulose and copper (II) oxide nanoparticles added to engine oil as a lubricant for piston ring-cylinder liner application. Kinematic viscosity, viscosity index (VI) and dynamic viscosity have been performed for measurement of properties at varying temperatures (ranging from 30 °C to 90 °C) and different concentrations (ranging from 0.1 % to 0.9 % volume concentration). Thermal characteristics have been measured using similar temperatures and concentrations to determine thermal conductivity and specific heat capacity. In the results, as the concentration of the CNC-CuO nanoparticle increases, the VI also increases. This proves the combination of CNC-CuO particles with engine oil improves the lubricity of the base oil concerning its viscosity by 44.3 %-47.12 %. The lowest and highest improvements in the dynamic viscosity were 1.34 % and 74.81 %. The highest increment of thermal conductivity ratio for the selected nanolubricant was 1.80566 % in the solid concentration of 0.1 % at 90 °C. The specific heat capacity of nanolubricant tends to reduce slightly with an increase in temperature. Overall, the addition of CNC-CuO nanoparticle in the engine improved thermophysical properties behaviour's performance at 0.5 % concentration. The results can benefit the heat transfer application, especially tribological.

Generalized correlation for effective thermal conductivity of high porosity architectured materials and metal foams

This paper presents a numerical study on the effective thermal conductivity (keff) of architectured materials typically realized through additive manufacturing. Four different unit cell topologies- Cube, Octet, Face-diagonal Cube, and Tetrakaidecahedron, were simulated for a range of porosity values, and both solid- and fluid-phase thermal conductivities. Numerically predicted keff values were validated against the in-house experiments carried out on single-cell thick 5 × 5 unit cell arrangement samples. These simulations led to a correlation for keff as a function of lattice porosity and thermal conductivities of solid- and fluid-phase materials. For the solid-to-fluid thermal conductivity ratio (ks/kf) greater than 300, the keff showed dependence on only the solid thermal conductivity for any given porosity and unit cell topology. The proposed correlation for the keff of architectured materials is applicable to all the four unit cell topologies with porosities > 0.8, and ks/kf ranging from 102 to 104. For these parameters, the correlation can also predict the keff of high-porosity metal foams obtained via foaming process with an accuracy of ±10%.