Heat Conductivity Coefficient Research Articles

Significant improving magnetic properties and thermal conductivity of FeBSiPCNbCu nanocrystalline powder cores by designing novel ZnO insulating layer

As the application scenarios of soft magnetic composites (SMCs) tend to be high frequency, reducing their high-frequency core loss (Pcv) and improve the heat-sinking capability to avoiding thermal failure of electronic system are still greatly challenging. In present work, we successfully designed and prepared novel ZnO insulating layers on the surface of FeBSiPCNbCu nanocrystalline powders and discussed their growth processes. In addition, we investigated the effects of the ZnO insulating layers on the magnetic properties and heat-sinking capability of the FeBSiPCNbCu nanocrystalline magnetic powder cores (NMPCs) and explored the related mechanisms. The experimental results show that the hydrolysis of 1.75 wt% zinc acetate dihydrate under the coupling of 1 wt% polyvinylpyrrolidone forms uniform and thin ZnO insulating layers on the powders surface. The FeBSiPCNbCu@ZnO NMPCs annealed at 510 °C for 60 min exhibit excellent magnetic properties and superior heat-sinking capability with a low core loss of 698.4 mW/cm3 (20 mT, 2 MHz), high DC bias permeability of 68.3% (100 Oe) and heat conductivity coefficient of 2.22 W/(m•K) as compared with those of 859.8 mW/cm3, 57.1% and 1.86 W/(m•K), respectively, for the NMPCs without ZnO insulating layer.

The Effects of Microstructure on the Thermophysical Properties of the K439B Ni-Based Superalloy

The thermophysical properties of superalloys are critical for the design, fabrication, and service of hot-end components in engines. In this work, the influence of microstructure on the thermophysical parameters including heat conductivity, thermal diffusivity, heat expansion coefficient, and specific heat capacity of the K439B superalloy, which is a prospective cast superalloy for engine casings, were investigated from 100 °C to 900 °C. It has been observed that these properties increase with temperature, especially between 700 °C and 800 °C, for alloys subjected to different heat treatment processes. When compared under the same temperature, these parameters decrease with an increase in the size and volume fraction of the γ′ phase in the alloys. Meanwhile, the interfaces between the γ/γ′ phase and the boundaries between dendrites also impeded the heat treatment. It can be concluded that among the alloys with different heat treatment process, the sequence 1160 °C/4 h + 1080 °C/4 h + 845 °C/20 h exhibited the most stable heat conductivity and lowest heat expansion coefficient, making it advantageous for high-temperature service.

Regularization in space–time topology optimization for additive manufacturing

In additive manufacturing, the fabrication sequence has a large influence on the quality of manufactured components. While planning of the fabrication sequence is typically performed after the component has been designed, recent developments have demonstrated the possibility and benefits of simultaneous optimization of both the structural layout and the corresponding fabrication sequence. This is particularly relevant in multi-axis additive manufacturing, where rotational motion offers enhanced flexibility compared to planar fabrication. The simultaneous optimization approach, called space–time topology optimization, introduces a pseudo-time field to encode the manufacturing process order, alongside a pseudo-density field representing the structural layout. To comply with manufacturing principles, the pseudo-time field needs to be monotonic, i.e., free of local minima. However, explicitly formulated constraints proposed in prior work are not always effective, particularly for complex structural layouts that commonly result from topology optimization.In this paper, we introduce a novel method to regularize the pseudo-time field in space–time topology optimization. We conceptualize the monotonic additive manufacturing process as a virtual heat conduction process starting from the surface upon which a component is constructed layer by layer. The virtual temperature field, which shall not be confused with the actual temperature field during manufacturing, serves as an analogy for encoding the fabrication sequence. In this new formulation, we use local virtual heat conductivity coefficients as optimization variables to steer the temperature field and, consequently, the fabrication sequence. The virtual temperature field is inherently free of local minima due to the physics it resembles. We numerically validate the effectiveness of this regularization in space–time topology optimization under process-dependent loads, including gravity and thermomechanical loads.

Analysis on battery thermal management system based on flat heat pipe at high discharging rate

Power batteries are the core power source for electric vehicles. However, battery thermal management technology for electric vehicles will face more severe challenges in the future. Flat heat pipe has gradually received much attention in the field of battery thermal management due to its high heat conduction coefficient and lightweight structure. This paper focuses on the influence of flat heat pipe structural parameters on battery thermo-electrical performance by establishing simulation model of the battery cooling system, which makes contribution to the flat heat pipe structure design on optimizing battery overall performance. Based on the mechanism of working medium flow effect of flat heat pipe on the battery electrochemical heat generation, a coupled model of flat heat pipe-based battery system is established according to the relationship between battery electrochemical heat generation performance and flat heat pipe heat transfer characteristics. The accuracy of system model is further verified by experiment, and the battery thermo-electrical characteristics under different discharging conditions is simulated. The flat heat pipe-based battery thermal management system can effectively reduce the battery maximum temperature while improving the uniformity of battery temperature and state of charge (SOC). The reduction of the vapor chamber thickness causes the uneven distribution of vapor thermal resistance, so the battery maximum temperature and maximum temperature difference will become larger, which will further cause the uneven distribution of battery internal resistance, and this will finally increase the non-uniformity of battery module discharging current distribution. A structural design method of the flat heat pipe-based battery thermal management system is developed with the battery thermo-electrical coupling performance as the design objective and the flat heat pipe structural parameters (total thickness, vapor chamber thickness, total length) as the optimization variables. Compared with the original scheme, the battery maximum temperature can be reduced by 6.4% under transient high-rate discharging conditions with the modified flat heat pipe based on the proposed design method, while the battery maximum temperature and SOC difference can also be reduced by 18.4% and 16.3%, respectively.

Multifunctional boron nitride nanosheets/fluorinated‐polyimide composites with ultra‐low dielectric constant and high thermal conductivity

AbstractThermally conductive polymeric composites with low dielectric constant are highly promising for the packaging materials in the field of modern communication. Therefore, the synergistic improvement of low dielectric constant and high thermal conductivity has become a current research hotspot. In this work, we propose a one‐step alkylation of boron nitride nanosheet (BNNS) with ultrasonic stratification using 1‐hexanol, and then hot press the films to make Alkyl‐BNNSs orient in the fluorinated polyimide (f‐PI). The resulting Alkyl‐BNNS/f‐PI composite successfully realizes the synergistic improvement of thermal property and dielectric properties, exhibiting a high heat conductivity coefficient of 2.36 Wm−1 K−1 with a filler content of 4.99 wt.%. Moreover, the permittivity and dielectric loss of the film are as low as 1.76 and 0.0065 at 1 MHz, respectively. This work provides a facile strategy for breaking the bottleneck of making polyimide composites simultaneously with high thermal conduction and low dielectric performance.Highlights The composite exhibits a high heat‐conducting coefficient of 2.36 Wm−1 K−1. Ultra‐low dielectric constant of 1.76 was achieved by the modification of film. Excellent breakdown resistance and flexibility were endowed with the composites.

Теплопроводность керамических композитов YAG:Nd + Mo, полученных методом электроимпульсного плазменного спекания

The microstructure and thermophysical properties (specific heat capacity, thermal conductivity coefficient, heat conductivity coefficient) of fine-grained ceramic composites based on yttrium-aluminum garnet Y2.5Nd0.5Al5O12 (YAG:Nd) with different molybdenum content (10, 20, 40 vol. %) are investigated. Submicron Y2.5Nd0.5Al5O12 powders are obtained by co-precipitation method. Powder compositions of YAG:Nd + Mo with the structure “YAG:Nd core – Mo shell” were obtained using wet chemistry techniques and precipitation of the metal phase from salt solutions. Ceramic composite samples were obtained by the Spark Plasma Sintering (SPS) method. The microstructure and phase composition of ceramics were investigated by electron microscopy and X-ray diffraction phase analysis. YAG:Nd + Mo composites have a high relative density (98.1 – 99 %) and a homogeneous fine-grained microstructure with a grain size of 2 – 3 μm. Increased thermal conductivity and heat conductivity of composites is provided with a content of at least 20 vol.% Mo. For composites with 20% and 40% Mo, the heat conductivity coefficient at 1100 °C reaches 7.0 and 8.8 W⋅m–1⋅K–1, respectively. Sintered composites YAG: Nd + Mo at room temperature and elevated temperatures (up to 1100 °C) have a high heat conductivity coefficient, exceeding the heat conductivity coefficient of uranium dioxide UO2. This makes it possible to use ceramics YAG:Nd+Mo as heat-resistant inert fuel matrices.

A theoretical study of Lifshitz transition for 2H-TaS2.

Lifshitz transition was proposed to explain a change of the topology structure in a Fermi surface induced by continuous lattice deformation without symmetry breaking since 1960. It is well known that the anomalies of the kinetic coefficients (the coefficient of heat conduction and electrical conductivity, viscosity, sound absorption, etc.) are usually closely connected with the Lifshitz transition behavior. 2H-TaS2 is a typical representative to study its anomalies of temperature dependence of heat capacity, resistivity, Hall effect, and magnetic susceptibility. Its geometrical structure of the charge density wave (CDW) phase and layer number dependence of carrier-sign alternation upon cooling in the Hall measurements have not been well understood. The geometrical structure (T-Ts) of the CDW phase was predicted through first principles calculations for bulk and mono-layer 2H-TaS2. Driven by electron-lattice coupling, Ta atoms contract to form a partially gapped CDW phase. The CDW phase has a larger average interlayer separation of S-S atoms in the adjacent two layers compared with the metal phase, which results in a weaker chemical bonding among S-S atoms in the adjacent two layers and then a narrower bandwidth of the energy band. The narrower bandwidth of the energy band leads to a larger density of states (DOS) in the out-of-plane direction above the Fermi level for the CDW phase. As the Fermi level continually drops from the DOS region with a negative slope to that with a positive slope on cooling, the reversal of the p → n type carrier and the pocket-vanishing-type Lifshitz transition occur in the bulk 2H-TaS2. However, the Fermi level slightly drops by 6 meV and happens to be at the positions of pseudo band gaps, so the reduction of in-plane DOS and total DOS is responsible for the always p-type carrier in the mono-layer samples. Our CDW vector of the k-space separation between two saddle points is QSP ≈ 0.62 GK and can provide a theoretical support for the "saddle-point" CDW mechanism proposed by Rice and Scott. Our theoretical explanation gives a new understanding of both Lifshitz transition for symmetry breaking and reversal for the p-n carrier sign in the Hall measurements in various two-dimensional transition metal disulfides.

Preparation and characterization of potato crust-based polyurethane foam-I

Polyurethanes (PUs) are polymers obtained by reacting diisocyanates with a group of polyols. The first synthesized PU compounds were prepared using petroleum subproduct compounds. In this research study, biomass-containing polyols, which have been studied by other scientists, were prepared using potato crust and polymerized with diisocyanates to produce PU foam. Polyol reactions were carried out using the microwave heating method. Synthesis reactions and structural properties of polyols have been studied in many aspects. The most available polyol was used for PU synthesis. Different formulations were tried for PU synthesis and as a result, PU foam containing nearly 25% starch-polyol was synthesized. The chemical structure of PU polymer was identified by ATR-FTIR spectroscopy and crystallographic properties by WA-XRD analysis. The physical and mechanical properties of PU foam, which is used as a large number of building and construction materials, including thermal insulation materials, were evaluated by comparing them with a commercial PU foam. According to the results of our research, it was detected that the incorporation of biomass into the structure of PU polymer improved its density, heat conduction coefficient, pressure based mechanical properties. PU foam derived from potato waste has a WA XRD-ray diffraction peak between 13.1-28.5o. This data is between 12.5-23o in synthetic commercial foam and has been positively improved in the product we synthesized as a result of combining biomass into the structure. The synthesized biomass-based PU foam can be used as thermal insulation material. Biomass-based PU foam has been synthesized with features that can be used as a thermal insulation material.

The impact of density, temperature, moisture, and test direction on the thermal conductivity coefficient in pine wood

The article focuses on the study of the thermal properties of pine wood, a material traditionally used in construction, especially in Poland. The trend towards sustainable construction necessitates a deeper analysis of its properties. Due to the insufficient amount of data in the literature on the thermal conductivity of pine wood, detailed studies were conducted taking into account different wood densities. Seasoned wood samples were subjected to various processes and tests, measuring the heat conduction coefficient under different conditions. These results are relevant in the context of sustainable construction and will assist in further research on wood as a building material. The studies also took into account the effects of temperature and humidity on the thermal properties of wood, which is crucial for its application in various environmental conditions.

Determining patterns in the formation of an insulation layer of foam coke when protecting concrete against fire by reactive coating

An issue related to using concrete for building structures is to ensure their stability and durability during operation within wide limits. Therefore, the object of research was the change in the properties of concrete in case of fire and its protection when applied with a reactive coating capable of forming a foam coke layer under the influence of high temperature on the coating. It has been proven that in the process of thermal action on the fire-resistant coating, the process of heat insulation of concrete involves the formation of soot-like products on the surface of the material. Thus, under the influence of the flame of the burner, a temperature arose on the surface of the sample, which led to the swelling of the coating by more than 18 mm. The measured temperature on the surface of the concrete sample under the layer of foam coke was no more than 140 °C, which indicates the formation of a fire barrier. In this regard, modeling of the process of heat transfer through the formed layer of foam coke in the process of its protection with a reactive coating was carried out and dependence was established, which makes it possible to estimate the coefficients of temperature conductivity and thermal conductivity during high-temperature action. According to the experimental data and the established dependences, the coefficient of temperature conductivity and heat conductivity of foam coke was calculated, which is 9.17·10–7 m2/s and 0.17 W/(m∙K). The assessment of the maximum possible penetration of fire through the layer of foam coke was carried out. A temperature was formed on the surface of the sample, which significantly exceeded the temperature of the destruction of concrete, and on the surface of concrete under the coating it did not reach 250 °C. So, there are reasons to assert the possibility of targeted regulation of concrete fire protection processes by using reactive coatings capable of forming a protective layer on the surface of the material that inhibits the rate of heat transfer

Investigation of mechanical properties and thermal conductivity coefficients of 3D printer materials

The demand for 3D printer technology and products, one of the additive manufacturing methods, is increasing daily in the sectoral and academic fields. Many types of polymer-based filaments are used in 3D printers, pure or filled/reinforcement. Utilizing these specialized materials in places suitable for their mechanical and thermal properties will help efficiently use resources. Using 3D printers, it is possible to manufacture products that provide thermal insulation or good heat conduction in heating and cooling areas. Especially due to the energy requirements for heating and cooling, it is very important to know the thermal performance of materials to ensure and maintain energy efficiency. This study experimentally investigated the mechanical properties and heat conduction coefficients of 3D printed parts. The experiments were conducted with seven different filament materials (PLA, PLA+, PLA-CF, PLA Wood, Tough PLA, ABS+, TPU) and three layer thicknesses (0.1, 0.2, and 0.3 mm). Samples for tensile testing, hardness, and thermal conductivity coefficient measurements were produced, and measurements were performed. In the experiments, the highest tensile strength was obtained in PLA-CF with 0.3 mm layer thickness, and the lowest tensile strength was obtained in PLA Wood with 0.3 mm layer thickness. Tensile strength decreased with an increasing layer thickness in PLA, PLA Wood, ABS+, and TPU, while it increased in PLA-CF. The highest tensile strength of PLA+ was determined to be 0.2 mm and 0.1 mm layer thickness in Tough PLA. Hardness results showed minimal change in hardness values with increasing layer thickness. The thermal conductivity values of the samples varied according to the additives and layer thicknesses. The highest thermal conductivity increase was measured in PLA-CF with 11.84%, and the lowest thermal conductivity decrease was measured in Tough PLA with 9.44%.

Numerical investigation on the effects of axial-stress loads on the temperature-programmed oxidation characteristics of loose broken coal

This work innovatively explored the qualitative and quantitative effect of axial stress loads on the low-temperature oxidation behaviors of loose broken coal using a multi-field coupled numerical simulation. To achieve this purpose, a global numerical model for simulating the multi-field coupling temperature-programmed oxidation behavior of coal subjected to axial stress was established. We first acquired the evolution of the temperature, gas concentrations, axial-deformation behaviors, and seepage-heat transfer parameters of coal oxidation under axial stress loads based on the numerical model validation. Subsequently, the influence of various axial stress loads on the temperature-programmed oxidation behaviors was qualitatively and quantitatively evaluated. Results indicate that the numerical model exhibited excellent reliability. In addition, the entire oxidation process comprised temperature-dominated, temperature- and oxygen-dominated, and oxygen-consumption-dominated stages. Moreover, under axial stress conditions, both the porosity and permeability of coal samples decreased, whereas the heat conductivity coefficient increased, indicating an intensifying trend in oxidation reactions. Additionally, there was a critical stress that promoted the coal oxidation process; both the permeability and temperature of the coal demonstrated significant differences as the axial stress reached this critical point. The axial stress affected the oxidation behavior by changing the permeability and heat-transfer characteristics of the coal. This study is significant for predicting, preventing, and mitigating spontaneous fire disasters of stress-loaded coal.

A wellbore fluid performance parameters–temperature–pressure coupling prediction model during the managed pressure cementing injection stage

AbstractManaged pressure cementing (MPC) is a new technology based on managed pressure drilling, which has a greater advantage in facing narrow density window formations. However, the existing pressure prediction models during MPC injection stage consider fewer factors and have lower accuracy. To this end, combined with the characteristics of the injection stage, a predictive model of the distribution of annular fluid type was first proposed. Then, based on the experimental results, fluid density and rheology as a function of temperature and pressure were fitted. The governing equation of temperature‐pressure field was established. Eventually the fluid performance parameters–temperature–pressure coupling prediction model was developed in this paper. By comparing the predicted pump pressure with the measured pump pressure, the maximum relative error is not more than 10%. Using this model, the fluid type distribution, temperature field distribution, and pressure field distribution were investigated. The results indicated that the distribution of fluid types in the wellbore presented a complex variation, with up to 10 fluids in the casing and up to five fluids in the annulus. The trend of temperature field is complex, with three turning points. The larger the formation temperature gradient, the higher the fluid temperature in the annulus. The influence law of fluid heat conduction coefficient is reversed at 6750 m. Decreasing drilling fluid density will trigger gas channeling, while increasing drilling fluid density will increase the risk of fracturing formation, and safe operation can be realized by MPC. The variation of the static pressure in the casing is more complicated than in the annulus and the annular circulation pressure in the eccentric casing is smaller than that of the concentric casing, which is due to the smaller annular friction pressure. This study can provide a theoretical basis for the prediction of hydrodynamic parameters during the MPC injection stage.

A new semi-analytic method for calculating the thermal–mechanical coupling stress intensity factor of interfacial crack

The interfacial crack thermal–mechanical coupling stress intensity factor (SIF) calculation plays an important role in anti-cracking design and safety assessment of compressed air energy storage (CAES) multi-layer cavern. In current SIF calculation method, there is no consideration of thermal–mechanical coupling effect caused by the difference between the singularity of stress field (λ) and temperature field (λT). In this study, a new semi-analytic method for calculating the thermal–mechanical coupling SIF of interfacial crack is established based on a new thermal–mechanical coupling Williams expansion for the cases of both insulated and constant temperature. The singularity index of temperature field at the crack-tip is dependent on the material parameters (heat conduction coefficient ki) for the crack perpendicular to and terminated at the interface, but independent on the material parameters (ki) for the crack located at the interface. The larger the difference of bi-material's heat conduction coefficient (ki), the larger the value of stress field when the crack is located on the side of larger Young's modulus (Ei) or on the side of lower ki. The semi-analytic method is degenerately verified by available literature results (without thermal–mechanical coupling term) and completely verified by finite element results (with thermal–mechanical coupling term), which can provide a theoretical basis for anti-cracking optimal design of CAES multi-layer caverns under thermal–mechanical loading condition.

Some existence results for the Brinkman-Fourier system

In this paper, we prove the existence of weak solutions to the Brinkman-Fourier system under suitable conditions on the pressure. The main novelty of this paper lies in the fact that the viscosity and heat conductivity coefficients are functions of the temperature, furthermore, the viscosity coefficients may be degenerate in the sense that it may vanish as the temperature goes to zero. The key points to achieve the main results rely on the Galerkin method, the De Giorgi method and some compactness arguments.

Solid chamber for satellite electronic modules and evaluation of its heat conduction behavior

A novel solid chamber configuration for cooling satellite electronic modules enduring high heat is proposed. Solid chamber modules with different inner structures and solid materials with high thermal conductivity are designed, and their thermal performances were experimentally studied. The equivalent heat conduction coefficient and contact thermal resistance of a solid chamber module are defined and the estimation methods for the thermal behavior are proposed. It is found that the thermal performances of the two solid chamber modules with the inner structures respectively composed of Graphite/Al 630/30 composites and graphite plate are obviously better than those of the other modules. Based on the assessment of the thermal resistance and cracks generated in the modules after thermal tests, it is found that the powder metallurgy technology makes the interlayers bonded more tightly than diffusion welding in the manufacture of solid chamber, and the tightness of the interlayer interface plays a key role in the contact thermal resistance.

Effects of viscous dissipation and activation energy for the MHD Eyring-powell fluid flow with Darcy-Forchheimer and variable fluid properties

The study of flow, heat and mass transference of Eyring-Powell fluid flowing in the existence of micro cantilever sensor is useful to create enhancement in the field of non-Newtonian fluid. The Darcy-Forchheimer porosity medium is considered for the flow analysis. The impressions of thermal radiation, viscous dissipation, heat generation, activation energy, Soret and Dufour effects are taken here to investigate the transference analysis of heat and mass rate. The flow phenomena are inspected under the influence of variable fluid properties. The motivation arises to work in this type of study is due to their applications in various industries such as steam generators, chemical reactors, system of dying package beds, several cooling and heating process and treatment of various diseases. The flow equations are occurred in the form of PDEs and then we utilize suitable similarity transformations to convert them into ODEs. These ODEs are numerically solved by the numerical technique namely, ‘shooting method’. The result reveals that the fluid velocity upsurges due to Hartman number and fluid coefficient whereas opposite impact is illustrious due to porosity coefficient, inertia coefficient and viscosity parameter. The finding indicated that we can upturns the temperature within the flow system due to thermal radiation, thermal conduction coefficient, Eckert number, heat generation and Dufour number. The rate of mass transference enhances for higher inputs of heat conduction coefficient, activation energy and Soret number while reverse behavior is seen due to temperature difference coefficient.

The multi-factor influence of frost resistance and prevention effect of tunnel thermal insulation layer in cold areas

To figure out the thermal insulation effect of tunnel thermal insulation layer under the action of different factors in cold areas, the heat transfer analysis module in ABAQUS software was used for the Jiangluling Tunnel to numerically simulate the temperature change of the lining. The said thermal insulation effect under different insulation layer laying methods, insulation material heat conductivity coefficients, insulation layer thickness values, and air temperature conditions was analyzed based on the range of Heat Regulation Circle (HRC), and the empirical equation proposed by Japanese Scholar Kurokawa Yoshinori was employed to calculate the laying length of thermal insulation layer, which was then verified by the safety coefficient of tunnel lining structure. The research results showed that, after the thermal insulation layer had been set, the radial depth of annulus of HRC decreased significantly, indicating that the convective heat transfer of cold air had been suppressed; from high to low, the thermal insulation performance of thermal insulation layer installed by different laying methods was: double-layer style, wall-attaching style, composite filler style, and wall-detaching style. When installing thermal insulation layer for the Jiangluling Tunnel, the wall-attaching style thermal insulation layer is suggested; the thickness of thermal insulation layer should not be less than 5.5 cm; the thermal insulation material should take a thermal conductivity coefficient between 0.025 and 0.04 (W/m.k) and be laid throughout the entire tunnel; when the temperature drops below −17 °C, extra thermal insulation measures should be taken to ensure the frost resistance and prevention ability of the tunnel structure.

On a Method of Solving the Thermal Conductivity Equation of an Inhomogeneous Isotropic Body

Key words: coefficient of internal heat conductivity, classical problems, Cauchy problem, small parameter method, second-order partial differential equation, inhomogeneity function Classical problems in various formulations have been solved by many authors (Cauchy, Dirichle, Neumann and others) for isotropic homogeneous bodies in the theory of elasticity. Such boundary value problems have been reduced to solving differential equations with constant coefficients [1-3; 5]. The paper considers the problem of thermal conduction of an inhomogeneous isotropic body, which leads to the solution of a second-order partial differential equation with variable coefficients (1.3). With sufficient smoothness of the variable coefficients, through transformations, as well as the characteristic equation, this second-order differential equation in a given region can be reduced to one of the following forms; elliptic, hyperbolic and parabolic. Here, the boundary value problem is reduced to solving a second order differential equation with variable parabolic coefficients. A small physical parameter is introduced, and a recurrent sequence of boundary value problems for the Cauchy boundary value problem is obtained in the article. When solving these boundary value problems, the general solution is represented as a series by formula (2.2) and under certain conditions depending on δ and σ the convergence of the series is proved and the solution is reduced to (5.4). In case of varying the inhomogeneity function f (x,y,z), a small physical parameter δ and a constant σ, a set of inhomogeneous isotropic bodies is obtained, the results of which will be compared with the results of homogeneous isotrpic bodies.

Effect of Cryo-Treated Cutting Tool End Milling on Custom 450 Stainless Steel.

Custom 450 stainless steel is the most desirable material across industries due to its widespread application in the aerospace, defense and marine industries. Stainless-steel materials are challenging to deal with and fall into the list of hard-to-process materials due to their low heat conduction coefficient and high mechanical properties. In this research work, end milling was carried out on Custom 450 stainless steel machined using TiAlN coated with tungsten carbide inserts that have been cryo-treated (CT) for 24 h (24 h) and 36 h (36 h), as well as untreated (UT) inserts. The inserts were evaluated in terms of feed force, feed rate and consistent depth of cut (ap) at various spindle speeds (S). Also examined were the tool morphology, chip anatomy and surface morphology of cryo-treated material compared to untreated inserts at various responses to cutting force (Fx, Fy, Fz), cutting temperature (Tc), vibration and surface abrasion. For inserts that have been cryo-treated for 36 h, the feed force (Fx) value was 44% and 5% less compared to inserts treated for 24 h and in UT inserts, respectively. Furthermore, for 24-h and 36-h CT inserts, feed force (Fx) was 12% and 20% less compared to a UT insert. Using 24-h cryo-treated inserts as opposed to UT inserts significantly reduced the surface roughness by 20%. Cutting inserts that have undergone cryogenic treatment have been observed to exhibit longer cutting tool life due to less wear and friction on the cutting edges.