Thermal Conductivity Gradient Research Articles

Stretching/shrinking impact on the transient heat transfer in a radial moving porous fin of a longitudinal trapezoidal structure

The prime goal of the current pagination is to scrutinize the transient thermal response in a radial porous moving fin of a longitudinal trapezoidal structure. The solution of the constructed problem is heeded by a pdepe solver in Matlab, which works on the centered-finite difference technique. Darcy’s model is utilized to investigate porous nature. A stretching/shrinking mechanism has been incorporated to improve the fin efficiency. Stretching reduces efficiency, whereas shrinking improves fin efficiency indicating major benefits of fin design consideration. The relevant temperature results are shown visually and discussed quantitatively in detail to evaluate the competence of the suggested fin. With a rise in the Peclet number, temperature distribution decreases. A similar nature is noted with respect to the power index of convective heat transfer coefficient, convection and radiation parameters, porous parameter, stretching/shrinking parameter, and thermal conductivity gradient with temperature. The graphical outcomes also show that the fin temperature amplifies with the ambient temperature parameter. Also, it is noticed that thermal distribution is a decreasing function of the power index of the convective heat transfer coefficient such that there is a decrease of 1.64% in temperature distribution as the power index increases. To support the validity of the solutions, a comparison was made with notable results from the existing literature for the specific case of this study. The novelty of the work is to study highly nonlinear boundary value problems and such nonlinearities are more relevant in the system that describes the thermal processing of materials. It is also noted that initial transient heat transfer vanishes quickly under steady-state conditions when the material is exposed to the ambient temperature.

Numerical simulation on pore-scale pool boiling mechanisms of horizontal gradient porous metals

Horizontal gradient porous metals are proposed to solve the problem of nonuniform temperature distribution on the heating surface. The model of horizontal gradient porous metal is established based on the thermal response of metal skeletons. Pool boiling heat transfer performances of horizontal gradient porous metals are studied by phase-change lattice Boltzmann model. Horizontal porous metal layer thickness, wettability and thermal conductivity gradient effects on bubble behavior and heating surface temperature distribution uniformity are statistically analyzed. The results show that porous metals with horizontal thickness gradient can realize liquid-vapor channel separation, reduce the resistance of bubble rising, and improve the fresh liquid supplement. Compared with the uniform porous metal, the horizontal gradient porous metal with lateral hydrophobic surface or higher thermal conductivity has better boiling heat transfer performance and promotes heating surface uniform temperature distribution at low heat fluxes. The results provide a novel solution to improve the chip wall temperature uniformity for the stable operation of electronic equipment.

High strength insulating polymeric composite based on recycled/virgin polyethylene terephthalate (PET) reinforced with hydrous magnesium silicate (talc)

In the current work, post-consumer polyethylene terephthalate (PET) bottles were reclaimed and reinforced with hydrous magnesium silicate, Mg3Si4O10(OH)2 commonly known as talc and with virgin PET (VPET) for the development of high strength polymeric composites. The composite sheets were prepared using the thermomechanical melt processing method followed by a thermal press technique. VPET was mixed during melt processing of recycled PET (RPET) in a specific ratio to suppress thermal degradation and hydrolysis of developed composite. Various blends of the composite samples of VPET and RPET (RPETx - VPET1-x) with a fixed ratio of talc were prepared and investigated for their strength, conductivity and micro-properties. 45 μm talc particle in ratio 1 to 4 was used. The effect of the talc addition on mechanical properties of the composites at the sub-micron scale was investigated through nanoindentation with quasi-continuous stiffness mode (QCSM) to analyze the nano-mechanical properties as a function of contact displacement. Surface morphology and composition were studied through scanning electron microscopy (SEM) and energy dispersive x-ray analysis (EDX), which showed a uniform dispersion of talc particles with no agglomerates on the surface. Compressive strength was determined with the universal testing machine (UTM) that revealed the highest compressive strength of RPET80 – VPET20 blend with a lowest thermal conductivity gradient value of 0.0213 W.m−1 observed, thus making it preferable material for insulation purposes. Load-displacement curves displayed the harder behavior of the composite sheet containing RPET80 – VPET20/talc as it needed 100 μN load to impose a penetration depth of 7.5 μm only. The elastic modulus and hardness of RPET80–VPET20/talc composite was significantly improved as compared to other samples.

Absorption Dominated Directional Electromagnetic Interference Shielding through Asymmetry in a Multilayered Construct with an Exceptionally High Green Index.

Fabricating green electromagnetic interference (EMI) shields is the need of the hour because strong secondary reflections in the vicinity of the shield adversely affect the environment and the reliability of the neighboring devices. To this end, the present work aims to maximize the absorption-based EMI shielding through a multilayered construct comprising a porous structure (pore size less than λ/5), a highly conducting entity, and a layer to match the impedance. The elements of this construct were positioned so that the incoming electromagnetic (EM) radiation interacts with the other layers of the construct before the conducting entity. This positioning of the layers in the construct offers a high green shielding index (gs) and low reflection coefficient (R ∼ 0.1) with an exceptionally high percent absorption (up to 99%). Polyurethane (PU) foams were fabricated using the salt-leaching technique and strategically positioned with carbon nanotube (CNT) papers and polycarbonate (PC)-based films to obtain symmetric and asymmetric constructs. These structures were then employed to gain mechanistic insight into the directional dependency of shielding performance, gs, and heat dissipation ability. Interestingly, maximum total shielding effectiveness (SET) of -52 dB (88% absorption @8.2 GHz) and specific shielding effectiveness/thickness (SSEt) of -373 dB/cm2g were achieved for a symmetric construct whereas, for the asymmetric construct, the SET and SSEt were -37 dB and -280 dB/cm2g, respectively, with an exceptionally high gs of 8.6, the highest reported so far. The asymmetricity in the construct led to directional dependence of the absorption component (% SEA, shielding effectiveness due to absorption) and heat dissipation, primarily governed by the electrical and thermal conductivity gradient, respectively. This study opens new avenues in this field and reports constructs with an exceptionally high green index.

Numerical study of moving fin with thermal properties

AbstractIn the present study, the influence of numerical analysis involves the transfer of heat for moving fin under convection and radiation with fluid properties depending on internal heat generation is considered. The temperature field for the fin is derived based on the defined geometry. This is transformed into a linear model as per the boundary conditions. The dimensionless analysis is performed, and the equations obtained are solved by Runge–Kutta Fehlberg fourth‐order method coupled with the shooting method. The effects of the relative parameters are studied and depicted graphically. Finally, the computational observation indicates that there is an enhancement of temperature variation under the influence of thermal conductivity gradient, heat generation, and opposite behavior results. In understanding the thermal characteristics of various effects, it was seen that thermo geometric film, radiation conduction, and Peclet number were very useful for many industrial applications. To validate the numerical scheme, a comparative study has been done with an earlier result on a few nondimensional parameters and was found in good agreement.

Bond coat composition formed by spark plasma sintering for gradient material with thermal barrier properties

High-temperature materials for thermal barrier coatings (TBC) have important prospects for application in the aircraft engine industry. To increase the service life and reliability of superalloy parts, the bond coat (BC) in the structure of the TBC is of great importance. In this study, the architecture of the BC material between the superalloy and the external ceramics is proposed. It is shown that the BC layer can consist of a sublayer of intermetallic NiAl (VKNA) and a mixture of VKNA with 15 or 30 wt.% zirconium dioxide (8YSZ). This architecture allows us to form by spark plasma sintering (SPS) technique. In the work, samples of a gradient BC VKNA/VKNA+(15% or 30%)YSZ/YSZ were obtained using SPS at 1070 oC, a pressure of 30 MPa and an isothermal exposure of 5 min. In all sintered compositions the porosity did not exceed 2%. The structure of the BC material is characterized by scanning electron microscopy, energy-dispersion spectroscopy, and micro-durometry. It is shown that the SPS provides an adhesive connection of the sublayers in the BC layer and with the external ceramics. The microhardness increases li nearly during the transition from the VKNA layer to the YSZ layer through a BC with different YSZ content in the sublayer. The BC samples demonstrated a thermal conductivity gradient from the Inconel 625 substrate to YSZ and the influence of the YSZ content in the sublayers on the decrease in the coefficient of linear thermal expansion in the temperature range of 800–1000 oC was also determined. Damage to the ceramic surface during thermal cycling in air at 1100 oC, i.e. the appearance and development of cracks, is not more than 10% at 45 cycles.This research was carried out under Basic Scientific Research Assignment No. FSNM-2020-0026 of the Ministry of Education and Science of Russia and was funded by the Russian Foundation for Basic Research, Grant No. 19-48-590007.

Pore-scale investigation on flow boiling heat transfer mechanisms in gradient open-cell metal foams by LBM

Flow boiling heat transfer mechanisms inside gradient open-cell metal foam are investigated based on the newly proposed metal foam model. This new model considers thermal responses of metal skeletons. The structural effects of gradient metal foam, including porosity gradient, thermal conductivity gradient and wettability gradient, on flow boiling heat transfer performance are studied by pseudopotential lattice Boltzmann method. Reynolds number effect on bubble departure characteristics, such as bubble departure diameter, bubble departure frequency and the corresponding probability density distributions, are investigated based on statistical analysis. The results show that bubble confinement weighs heavily over bubble movement inside pore cell during bubble escaping process in porosity-gradient metal foams. Bubble nucleation is depressed by the highly thermal conductive gradient metal foam at high heat fluxes. The interaction between escaping bubble and pore throat shifts from “complete contact” mode to “thin liquid film” mode in the positive wettability-gradient metal foam. Shear force dominates over buoyant force with increasing Reynolds number, resulting in the sliding motion of premature bubbles.

Steady state heat transfer analysis in a rectangular moving porous fin

In this article, the variation of temperature distribution and fin efficiency in a porous moving fin of rectangular profile is studied. This study is performed using Darcy's model to formulate the governing heat transfer differential equation. The approximate analytical solution is generated using the variational iteration method (VIM). The power series solution is validated by benchmarking it against the numerical solution obtained by applying the Runge-Kutta fourth order method. A good agreement between the analytical and numerical results is observed. The effects of porosity parameter, Peclet number and other thermo-physical parameters, such as the power index of heat transfer coefficient, convective-conductive parameter, radiative-conductive parameter, thermal conductivity gradient and non-dimensional ambient temperature on non-dimensional temperature are also studied and explained. The results indicate that the fin rapidly dissipates heat to the ambient temperature with an increase in the Peclet number, convection-radiation parameters and the porosity parameter.

Effect of Variable Thermal Conductivity Calibration Functions on Fin Temperature Distribution

In this article, we introduce a new thermal conductivity calibration function in modeling heat transfer through extended surfaces. The variable thermal conductivity functions are studied on a stand alone basis and further compared to one another. The calculations are carried out using the Variational Iteration Method (VIM) which is an analytical solution technique. The series solutions are bench-marked against the numerical results obtained by applying the Runge-Kutta fourth order method coupled with shooting technique. The effects of some physical parameters such as the thermogeometric fin parameter and thermal conductivity gradient, on temperature distribution are illustrated and explained.

Predicting the Temperature Distribution in Longitudinal Fins of Various Profiles with Power Law Thermal Properties Using the Variational Iteration Method

In this article, the variational iteration method (VIM) is used to analyze heat transfer in longitudinal fins of various profiles with temperature dependent thermal conductivity and heat transfer coefficient. In order to show the efficiency of the VIM, the results obtained using the VIM are compared with the previously obtained results using the differential transform method (DTM) and Lie group analysis of a fin problem with the rectangular profile. After establishing confidence in VIM, heat transfer is analyzed to determine the temperature profiles in longitudinal fins of various profiles with power law thermal properties. The temperature distribution is compared between various profiles. The effects of some physical parameters such as the thermo-geometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated.

Chemically modified and doped carbon nanotube-based nanocomposites with tunable thermal conductivity gradient

Nitrogen (N)-doped and un-doped MWCNTs grown using a chemical vapor deposition (CVD) process were studied for their surface chemical modification and thermal characteristics. Various surface functional groups developed through acid purification or controlled plasma oxidation of MWCNTs were analyzed using X-ray photoelectron spectroscopy (XPS). High resolution electron microscopy was used to understand the structure and morphology of the surface-modified/unmodified MWCNTs. Thermal conductivities of surface-modified/unmodified MWCNT films were estimated using the shifts in Raman peaks for MWCNTs as a function of incident laser power (1–50mW) and film temperature (60–160°C). The thermal conductivity of pristine un-doped MWCNT films was much higher (∼70W/m-K) than that of N-doped MWCNT films (∼16–27W/m-K). Plasma oxidation or acid treatment further reduced the thermal conductivity (∼8–14W/m-K). Thermal maps or temperature distribution profiles for MWCNT films were theoretically evaluated. Finally, different combinations of doped/un-doped and plasma/acid-treated MWCNTs were stacked and impregnated within a polystyrene matrix to result in a gradient of thermal conductivity across the thickness direction of the nanocomposite.

Analytical Solution and Numerical Simulation for One-Dimensional Steady Nonlinear Heat Conduction in a Longitudinal Radial Fin with Various Profiles

In this article we consider a model describing the temperature profile in a longitudinal fin with rectangular, concave, triangular, and convex parabolic profiles. Both thermal conductivity and the heat transfer coefficient are assumed to be temperature-dependent, and given by a linear function and by power laws, respectively. In addition, the effects of the thermal conductivity gradient have been investigated. Optimal homotopy analysis method (OHAM) is employed to analyze the problem. The effects of the physical applicable parameters such as thermo-geometric fin, thermal conductivity, and heat transfer mode are analyzed. The OHAM solutions are obtained and validity of obtained solutions is verified by the Runge–Kutta fourth-order method and numerical simulation. A very good agreement is found between analytical and numerical results. Also for investigation of lateral effects on the accuracy of results, numerical simulation (by Ansis software) is compared with the homotopy analysis method (HAM) and numerical solution (by Runge–Kutta) of the energy balance equation. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21104

Application of the two-dimensional differential transform method to heat conduction problem for heat transfer in longitudinal rectangular and convex parabolic fins

In this article, approximate analytical (series) solutions for the temperature distribution in a longitudinal rectangular and convex parabolic fins with temperature dependent thermal conductivity and heat transfer coefficient are derived. The transient heat conduction problem is solved for the first time using the two-dimensional differential transform method (2D DTM). The effects of some physical parameters such as the thermo-geometric parameter, exponent and thermal conductivity gradient on temperature distribution are studied. Furthermore, we study the temperature profile at the fin tip.

Analytical Solutions for Steady Heat Transfer in Longitudinal Fins with Temperature-Dependent Properties

Explicit analytical expressions for the temperature profile, fin efficiency, and heat flux in a longitudinal fin are derived. Here, thermal conductivity and heat transfer coefficient depend on the temperature. The differential transform method (DTM) is employed to construct the analytical (series) solutions. Thermal conductivity is considered to be given by the power law in one case and by the linear function of temperature in the other, whereas heat transfer coefficient is only given by the power law. The analytical solutions constructed by the DTM agree very well with the exact solutions even when both the thermal conductivity and the heat transfer coefficient are given by the power law. The analytical solutions are obtained for the problems which cannot be solved exactly. The effects of some physical parameters such as the thermogeometric fin parameter and thermal conductivity gradient on temperature distribution are illustrated and explained.

STRESS INTENSITY RELAXATION AT THE TIP OF AN EDGE CRACK IN A FUNCTIONALLY GRADED MATERIAL SUBJECTED TO A THERMAL SHOCK

We analyze thermal stresses and the stress intensity factor in an edge-cracked strip of a functionally graded material (FGM) subjected to sudden cooling at the cracked surface. It is assumed that the shear modulus of the material decreases hyperbolically with the higher value at the surface exposed to the thermal shock and that the thermal conductivity varies exponentially. Volume fractions of the constituents in a ceramic-metal FGM are then determined with the assumed shear modulus gradient using a three-phase model of conventional composites. The differences between the other assumed material properties and those predicted by the three-phase model are delineated and the applicability of the assumed FGM is discussed. It is shown that the maximum tensile thermal stress in the strip without cracks is substantially reduced by the assumed thermal conductivity gradient and that the magnitude of the compressive stress is increased. A strong compressive zone just away from the thermally shocked surface is devel...

Thermal fracture of functionally gradient ceramics

An edge crack in a strip of functionally gradient ceramics (FGC) is studied under thermal loading conditions. Two FGC materials are considered, i.e., one with a spatial variation of shear modulus and the other with a spatial variation of thermal conductivity. Thermal stress intensity factors (TSIF) are numerically calculated based on singular integral equations derived for the dislocation density along the crack faces. It is shown that: (a) for the FGC with a graded shear modulus, the TSIF are reduced for crack lengths longer thanl c b and remain approximately the same as those of a homogeneous material for shorter crack lengths, wherel c is about 0.065 andb is the width of the strip; and (b) for the FGC with a thermal conductivity gradient, the TSIF are generally lower compared with those for the bonded two-layer material.

Enhanced Thermal Stress Resistance of Structural Ceramics with Thermal Conductivity Gradient

The hypothesis is presented that the maximum tensile thermal stresses in brittle ceramics can be reduced significantly by a redistribution of the temperature profile using a spatially varying thermal conductivity. On the basis of a hollow circular cylinder subjected to radially inward or outward steady‐state heat flow, it is shown that such a spatially varying thermal conductivity can lead to significant decreases in magnitude of the maximum tensile thermal stress. Possible techniques of creating such thermal conductivity variations are discussed briefly.