Conduction Equation Research Articles

Topology optimization method for transient heat conduction using the Lyapunov equation

This study presents a novel topology optimization approach for transient heat conduction during the transition period based on the Lyapunov equation. For the problem under consideration, traditional topology optimization methods face computational challenges due to the time dependence of the transient responses. To address this issue, this article introduces a new optimization formulation that contains a modified governing equation for transient heat conduction and a new objective function. The new formulation aims to simplify the evaluation of transient response performance by utilizing the Lyapunov equation, thereby avoiding time-consuming transient analysis during the optimization iteration process. Additionally, this study employs model reduction techniques to reduce the size of the analysis model and further enhance the efficiency of the optimization process. After comparing two classic methods, the Proper Orthogonal Decomposition (POD) method is selected for its higher efficiency. Numerical examples consider both heat conduction and temperature control problems, employing 2D and 3D models to validate the proposed method's effectiveness. The results of the point-to-point heat conduction example indicate that, compared to the conventional design, the optimized topology design obtained using the proposed method successfully reduce the heating time by approximately 35%. Furthermore, the optimized designs display clear distinguishing features from conventional designs, further emphasizing the significance of implementing transient heat conduction topology optimization.

Effect of some solvents, IR characterization and TGA investigation of complexes prepared by reactions between Arginine with some metal ions of Hg(II),Cd(II) and Mn(II)

Arginine complexes were prepared with some metal ions of Hg(II),Cd(II) and Mn(II) in a stoichiometric ratio of 1: 2 (Mn+: L), where Mn+ = Mn2+, Cd2+ and Hg+2 ions. The Complexes were characterized by the physicochemical and spectroscopic techniques as electric conductivity, metal contents, IR, UV–Visible, and molar conductance techniques. Thermal studies were carried out by thermo gravimetric analysis. The stoichiometric ratios of the synthesized complexes were confirmed by using molar ratio method. Solvent effect on the electronic spectra of the arginine ligand was examined using solvents with different polarities.

Design, structural characterization, DFT, molecular docking, and chemotherapeutic activity of novel platinum(II) and palladium(II) complexes derived from Metformin-based Schiff base

Two novel bidentate Schiff bases ligands derived from Metformin with aldehydic molecules, including o-Ethoxy benzaldehyde (L1) and thiophene-2-carbaldehyde (L2) and Pt(II) and Pd(II) complexes were prepared. Numerous techniques were used to study the ligands and their metal complexes, including mass spectroscopy, IR, UV–Vis, molar conductivity, magnetic moment measurement, 1HNMR, PXRD, and 13CNMR. The preceding two Schiff bases were coordinated to Pd (II) and Pt (II) in the molar ratio of (1:1) (M:L) with the molecular structure [MLCl2]. The chemical quantum characteristics were calculated, and Schiff bases' optimized geometric structures and their complexes were revised theoretically. The MCF-7 breast cancer model was used to test the anticancer effects of metformin Schiff bases and their complexes in vitro. Additionally, using the EGFR tyrosine kinase of the selected proteins, a molecular docking study was carried out to learn more about the docking active site interactions. Ultimately, the conventional DPPH method was used to assess the antioxidant activity of the free ligands and their metal chelates. Pt (II) complexes demonstrated greater free radical scavenging activity than ascorbic acid. Furthermore, Pt (II) complexes showed more effective interactions with the selected mTOR protein, which is assumed to help the COVID-19 virus proliferate. Thus, Pt (II) has a bright future in the realm of chemotherapy.

Effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular plate with variable hybrid foundation

Engineering structures' heterogeneity and porous-auxetic features generate some prominent effects on their thermo-mechanical behavior. In addition, initial stress and heat wave propagation also play important roles in the mechanical behavior of FGM structures. Therefore, this paper investigates the effects of heat wave propagation and initial stress on the thermo-elastic behavior of porous-auxetic FG circular/annular plates with variable hybrid foundations. The one-dimensional transient hyperbolic heat conduction equation is modeled using the Cattaneo-Vernotte (C-V) theory and numerically solved using the Crank-sNicolson (C-N) finite difference scheme. Besides, a mathematical model of the other governing equations is extracted based on the classical thermoporoelasticity theory and semi-analytically solved by employing the state-space method and differential quadrature technique. Numerical examples are provided to illustrate the findings of this investigation graphically. The results reveal that the grading indices, and thermal relaxation time have a significant effect on heat wave propagation in the FG circular plate. Initial stress, porosity, and auxeticity also play an important role in its thermoelastic behavior.

Synthesis, characterization and analytical study of new azo ligand driven from benzocaine and its metal complexes

The synthesis and spectrum of of a new azo ligand derived from acetylacetone and benzocaine (Ethyl p-aminobenzoate)). Spectral investigations such as 1H NMR,FT.IR, 13C-NMR and Mass spectra were performed to investigate the azo dye ligand's structure. Several physiochemical approaches, FT-IR, electronic spectra, molar conductivity, atom absorption, and magnetic susceptibility were used to identify new complexes with CO(II), and Zn(II) ions Complexes that are all 1:2 [M:L] were formed using the procedures described, and an tetrahedral geometry with sp3 hybridization. At several pH ranges (2–12), the electronic spectra of these azo dyes have been examined in terms of their acid–base properties, which included determining their isosbestic points and protonation and ionization constants. In the other study, azodye were used as an inductor for acid-base titration.

Synthesis, Spectroscopic, and DFT Studies of Vanadium (III) Hydroxamate Complex with Potential Biological Applications

A new vanadium (III) hydroxamate complex of composition V(4- NO2C6H4CH=CHCONHO)3 has been synthesized by reaction of VCl3 with potassium salt of 4-nitrocinnamohydroxamate (4-NO2C6H4CH=CHCONHO) in 1:3 molar ratio in dry methanol solvent. The newly synthesized complex is characterized by elemental analysis, molar conductivity, magnetic moment measurements and IR, UV-Vis spectral studies and mass spectrometry. DFT calculations were carried out by using Orca 4.2.1 program and the negative values of the energies of EHOMO and ELUMO for the V(III) complex confirm its stability. A distorted-octahedral geometry around vanadium center has been suggested for complex based upon physicochemical, spectroscopic and DFT studies, involving bonding through hydroxylamine and carbonyl oxygens (O O coordination). The cyclic voltammogram of the complex shows single anodic and cathodic peak. The TGA/DTA curve indicates the single step decomposion of complex. The biological potential of the ligand and complex have been tested by in vitro antimicrobial studies and cytotoxicity assay. Antimicrobial activity of complex has been found increased as compare to precursor and ligand. The results of cytotoxicity reveal the complex less toxic as compared to standard drug simvastatin.

Exploring the Anticancer Activity of Gold Complex with Newly Ligand (DDIBM): Synthesis, Spectral Identification and Magnetic Susceptibility of Its Metallic Complexes

The new heterocyclic ligand, 5-(dimethylamino)-2-(((2-((E)-(4,5-diphenyl-1H-imidazol-2-yl)diazenyl)benzyl)imino)methyl)phenol (DDIBM), was synthesized via the condensation of p-aminobenzylamine with 4,5-diphenyl imidazole, and the resultant compound was condensed with 4-(dimethylamino)-2-hydroxybenzaldehyde. Various instrumental techniques such as mass, 1H-NMR, IR, C.H.N elemental analysis, and UV-vis spectroscopy were used to analyze a newly synthesized ligand. A novel series of complexes was prepared by complexing the ligand with Ni(II), Cu(II), Co(II), and Au(III) and characterized using some of the mentioned techniques. Flame atomic absorption spectroscopy was used to measure the metal ion percentages in the complexes. The magnetic susceptibility and molar conductivity were studied. The electronic spectral data and the magnetic measurement predict the octahedral structure of the complexes except Au(III) complex which has square planer geometry. All complexes showed electrolyte properties. This study aimed to conduct an in vitro cytotoxicity comparative study of DDIBM and its Au(III) complex on human breast cancer cells (MCF-7) and other normal cells. The Au(III) complex was found to be highly selective in targeting cancer cells without affecting normal healthy cells, compared to the ligand. Thus, this complex can be considered as a new drug for treating breast cancer cells (MCF-7), and an attempt in the future to study its effect on other types of cancer.

An Electrical Parameter Characterizing Solute Heterogeneity: The Mixing Factor M

AbstractQuantitative estimates of hydrological state variables using electrical or electromagnetic geophysical methods are systematically biased by overlooked heterogeneity below the spatial scale resolved by the method. We generalize the high‐salinity asymptotic limit of electrical conduction in porous media at the continuous (e.g., Darcy) scale, by introducing a new petrophysical parameter, the mixing factor M, which accounts for the effect of fluid conductivity heterogeneity on the equivalent electrical conductivity tensor; it is expressed in terms of the volume‐average of the product of mean‐removed fluid conductivity and electric fields. We investigate the behavior of M for static and evolving fluid conductivity scenarios. Considering 2‐D ergodic log‐normal random fields of fluid conductivity, we demonstrate, in absence of surface conductivity, that observing the components of the M‐tensor allows univocally determining the variance and anisotropy of the field. Further, time‐series of the M‐tensor under diffusion‐limited mixing allows distinguishing between different characteristic temporal scales of diffusion, which are directly related to the initial integral scales of the salinity field. Under advective‐diffusive transport and for a pulse injection, the time‐series of M have a strong dependence on the Péclet number. Since M is defined in the absence of surface conductivity, we investigate how to correct measurements for surface conductivity effects. The parameter M provides conceptual understanding about the impact of saline heterogeneity on electrical measurements. Further work will investigate how it can be incorporated into hydrogeophysical inverse formulations and interpretative frameworks.

Study of the Corrosion Inhibition Efficiency by Using New Azo Compounds from Thiazole Derivatives

Azo compounds were prepared by reacting thiazole derivatives with 2-naphthol, o-vanillin, 4-(dimethyl amino) pyridine, and 4-bromo aniline with thiazole derivatives. The molar conductivity of the azo compounds prepared in this study was measured using (ethanol) as a solvent and at room temperature, all compounds showed non-electrolytic behavior. The compounds were characterized by TGA/DTA, studying the thermal stability and calculating the activation energy of azo compounds, where the thermal analyses of the prepared compounds were measured to identify the temperature at which the compound disintegrates, as the compound has more than one degree of disintegration, and this variation in the degrees of disintegration and the remaining materials depends on the nature of the compound and the type of groups present in it, as well as the efficiency of their use as materials. Resistant to corrosion by weight loss method with different concentrations at constant temperature. The higher the concentration, the greater the inhibition efficiency.

New Silver(I) Lawsone-based complexes: Synthesis, characterization, interaction with biological macromolecules, in vitro antineoplastic, antimetastatic, and antimicrobial activity

New silver(I) complexes of formula [Ag(Lw)]2 (1), [Ag(Lw)(B)], where (Lw= lawsonate, B = 2,2`bipyridine (bpy) (2), 1,10-phenanthroline (phen) (3) and [Ag(Lw)(PPh3)2], (PPh3=triphenylphosphine (4)) have been isolated and characterized using elemental analysis (C, H, N), and FTIR, NMR(1H, 13C and 31P), UV–visible spectroscopy along with thermal analysis and molar conductivity measurements. The resulting data showed that the lawsone coordinates to the Ag(I) as a mono-negative O,O-donor ligand. The interaction of the ligand and complexes with (ctDNA, calf thymus DNA, tRNA, yeast RNA, and BSA, bovine serum albumin) has been studied utilizing absorption and fluorescence spectroscopy. The binding constant data (Kb) revealed that the complexes interact with the biomolecules more strongly than the ligand (HLw). Furthermore, in vitro, cytotoxic activity against normal lung cells (WI38), and various malignant cells, including breast (MCF7 and MDA-231), and colon (HCT116) was studied using cisplatin as a standard drug. The IC50 and selective index (SI) data showed that complex (3) is more selective towards the HCT116 cells. Flow cytometric study of complex (3) revealed that cells are arrested in the G0/G1 phase and induced cell death by an apoptotic mechanism rather than necrosis. The anti-metastatic activity (wound healing) of complex (3) indicated its ability to prevent the migration of cancer cells. The antimicrobial activity of the compounds has been also studied against gram +ve, gram -ve bacteria, and yeast (C. Albican), using penicillin and miconazole, respectively as a reference to show that the complexes (1) and (3) possess the highest activity against these microorganisms.

Geothermal resource evaluation of the Middle Permian Qixia-Maokou Formation in the southern Sichuan Basin, China

The southern Sichuan Basin is an abnormal area of high present geothermal fields in the Sichuan Basin. It is a favorable area for the development of geothermal resources in the Sichuan Basin. But its evaluation of geothermal resources is lagging, which has severely affected the development of geothermal resources in the southern Sichuan Basin. In the paper, firstly, based on the temperature data of wells, the geothermal gradients and heat flows of typical wells in the study area were calculated, and the temperatures at the top and bottom of the reservoir in the Qixia-Maokou Formation were calculated using a one-dimensional steady-state heat conduction equation. Then, geothermal resource intensities and reserves of the Middle Permian Qixia-Maokou Formation in the southern Sichuan Basin were evaluated by using a method for rapidly calculating geothermal resources in sedimentary basins by multi-data fusion. Finally, suggestions for geothermal development were proposed. The results show that the geothermal gradient and heat flow values in the southern Sichuan Basin range from 15.6 to 33.70 °C/km and 49 to 85 mW/m2, respectively, and the temperature of the reservoir in the Qixia-Maokou Formation ranges from 50 to 120 °C. The geothermal resources are 3.09 × 1021 J, equivalent to 105 billion tons of standard coal, and the recoverable resources are 6.18 × 1020 J, equivalent to 21 billion tons of standard coal. The development of demonstration projects will focus on the mid- to low-temperature geothermal power generation, geothermal grain drying and geothermal agriculture in the southwestern region of the southern Sichuan Basin. The research results can provide a resource basis for the development of geothermal resources in the southern Sichuan Basin.

Cytotoxic Cu(II) Complexes with a Novel Quinoline Derivative Ligand: Synthesis, Molecular Docking, and Biological Activity Analysis.

The utilization of metallodrugs as a viable alternative to organic molecules has gained significant attention in modern medicine. We hereby report synthesis of new imine quinoline ligand (IQL)-based Cu(II) complexes and evaluation of their potential biological applications. Syntheses of the ligand and complexes were achieved by condensation of 7-chloro-2-hydroxyquinoline-3-carbaldehyde and 2,2'-thiodianiline, followed by complexation with Cu(II) metal ions. The synthesized ligand and complexes were characterized using UV-vis spectroscopy, TGA/DTA, FTIR spectroscopy, 1H and 13C NMR spectroscopy, and pXRD. The pXRD diffractogram analysis revealed that the synthesized ligand and its complexes were polycrystalline systems, with nanolevel average crystallite sizes of 13.28, 31.47, and 11.57 nm for IQL, CuL, and CuL 2 , respectively. The molar conductivity confirmed the nonelectrolyte nature of the Cu(II) complexes. The biological activity of the synthesized ligand and its Cu(II) complexes was evaluated with in vitro assays, to examine anticancer activity against the MCF-7 human breast cancer cell line and antibacterial activity against Gram-positive (Staphylococcus aureus) and Gram-negative (Escherichia coli and Pseudomonas aeruginosa) bacterial strains. The CuL complex had the highest cytotoxic potency against MCF-7 breast cancer cells, with an IC50 of 43.82 ± 2.351 μg/mL. At 100 μg/mL, CuL induced the largest reduction of cancer cell proliferation by 97%, whereas IQL reduced cell proliferation by 53% and CuL 2 by 28%. The minimum inhibitory concentration for CuL was found to be 12.5 μg/mL against the three tested pathogens. Evaluation of antioxidant activity using 2,2-diphenyl-1-picrylhydrazyl revealed that CuL exhibited the highest antioxidant activity with IC50 of 153.3 ± 1.02 μg/mL. Molecular docking results showed strong binding affinities of CuL to active sites of S. aureus, E. coli, and estrogen receptor alpha, indicating its high biological activity compared to IQL and CuL 2 .

Unified model modal expansion method for full field reconstruction and inversion under mechanical and thermal loading

In this paper, a novel method termed UMM-T&S (Unified Model Modal reconstruction and inversion method for Temperature field and Structural field under limited sensors) is proposed. This method aims to enhance high-precision structural performance inversion and reconstruction under mechanical and thermal loading conditions, particularly in the context of structural health monitoring within the aviation and aerospace sectors. The approach begins by deriving the “temperature modal” solution of the heat conduction equation, drawing upon the modal expansion techniques used in multi-degree-of-freedom systems. This is followed by constructing a parameter mapping relationship within the unified model, enabling the solution of both the structural field (encompassing strain and displacement) and the temperature field through a single structural model modal expansion. Furthermore, the paper details a numerical validation using two different temperature fields and a thermal loading experimental verification on a stiffened plate under five distinct working conditions. The proposed UMM-T&S method yields lower errors (ranging between 10%-40%) and more stable performance across various complex working conditions, in comparison to existing methods. The analysis also delves into the sources of errors and their cumulative impacts.In conclusion, the innovative UMM-T&S method offers a swift, precise, and robust solution for the intricate task of reconstructing and inverting structural performance under combined mechanical and thermal stresses. The method's efficacy and potential are substantiated through experimental validation and comparative analysis against an established methodology, underscoring its capability to effectively tackle the challenges faced in structural monitoring under such demanding conditions.

Optical characteristics of synthetic Cu2+ complex films derived from 4-chloro-N-(3-(hydroxyimino) butan-2-ylidene) benzohydrazide for optoelectronic and photovoltaic applications

This study focuses on the creation and characterisation of Cu2+ complexes using the ONN tridentate chelating ligand, 4-chloro-N'-(3-(hydroxyimino) butan-2-ylidene) benzohydrazide (H2CIB). Synthetics were structurally investigated using a variety of elemental, molar conductivity, magnetic moment measurements and spectroscopic (1D-NMR, UV−Vis, FT-IR, and E-mass) tools as well as theoretically. The data from these analyses revealed that the hydrazone-oxime ligand acted as a mono-negative or neutral tridentate chelator, bonding the Cu2+ ions through the enolo/ketono carbonyl oxygen, protonated oximatic nitrogen, and azomethine nitrogen atoms, resulting in the formation of a square plane structure. In addition, the optical properties of these synthetics were studied. Based on the measured film reflectance, the index of refraction and extinction (k)/absorption (α) coefficient were determined through Kramers-Kronig (K-K) analysis. The optical band gap Eg value is estimated experimentally by different methods. The hydrazone-oxime ligand has the highest value of Eg where the complexes have Eg = 1.76, 1.83 and 1.76 eV for Cu2+- HCIBCuNO3, HCIBCuCl, and H2CIBCuSO4 samples, respectively. The Eg of CdSe is 1.74 eV which is very close to the Eg value of HCIBCuNO3, and H2CIBCuSO4. Therefore, the HCIBCuNO3, and H2CIBCuSO4 can replace the CdSe in all photovoltaic applications, photosensors and solar cells. With the help of n and k values the complex dielectric constant (ε⌣=εr+iεi)) and conductivity (σ⌣=σr+iσi) have been investigated over the whole spectral range. Furthermore, the first (χ(1)) and third (χ(3)) orders of nonlinear optical susceptibilities and the non-linear index (n2) of refraction has been estimated. According to the estimated values of χ(1), χ(3) and n2 the HCIBCuNO3, HCIBCuCl, and H2CIBCuSO4 can be considered as competitors to be used in optical switching gadgets, optical modulators, and optical signal processing.

Study on the structure, elasticity, and thermal conductivity of orthocarbonate Sr2CO4

Orthocarbonate Sr2CO4 is a recently discovered Sr-carbonate that plays a crucial role in understanding the global long-term carbon cycle. In this work, the structure, equation of state, elasticity, and thermal conductivity of Sr2CO4 were studied by first-principles calculations. The results show that the surfaces of the SrO9 and SrO11 polyhedrons, which make up Sr2CO4, are composed of triangles and quadrangles. By comparison with other alkaline earth metal orthocarbonates, SrCO3 polymorphs, and the Preliminary Reference Earth Model (PREM), Sr2CO4 is found to be a carbonate with high density, low wave velocity, low anisotropy, and low thermal conductivity in the entire Earth’s mantle. This study may help to understand the high-pressure behavior of alkaline earth metal orthocarbonates in the Earth’s interior.

TEMPLATE-ENGINEERED TRIVALENT IRON AND CHROMIUM CONTAINING MACROCYCLIC COMPLEXES: CHARACTERIZATION AND IN VITRO STUDIES

A novel series of tetraaza macrocyclic complexes of biological importance was synthesized by “in situ” template reaction between triethylenetetramine and dibenzoylmethane in the presence of trivalent Fe and Cr metal salts in 1:1:1 molar ratio. These complexes are represented by molecular formula [M(C[Formula: see text]H[Formula: see text]N[Formula: see text]X]X2; [Formula: see text](III) and Cr(III); [Formula: see text], NO[Formula: see text], −OAc; C[Formula: see text]H[Formula: see text]N[Formula: see text] ligand. The reported complexes were characterized by using various physicochemical and spectroscopic techniques including elemental analyses, molar conductance, thermo-gravimetric analysis, FTIR, UV–Visible and mass spectral studies. The results obtained from analytical techniques and spectroscopic techniques together suggested the complexes have a square pyramidal geometry. Various computational studies were performed including molecular docking and modeling. Further, macrocyclic complexes were also screened for their “in vitro” antimicrobial activity against selected bacterial and fungal strains. The antioxidant activity of these complexes was also evaluated. Some of the complexes were found to possess remarkable antimicrobial activity and antioxidant activity. However, complex [Fe(C[Formula: see text]H[Formula: see text]N[Formula: see text](NO[Formula: see text]](NO[Formula: see text] was found to be most potent against selected bacterial and fungal strains. On the other hand, complex [Cr(C[Formula: see text]H[Formula: see text]N[Formula: see text](NO[Formula: see text]](NO[Formula: see text] was found to show best antioxidant activity with lowest value of IC[Formula: see text].

A new method for solving multidimensional heat conduction problems

In this study, we propose an efficient boundary-type method named the half boundary method (HBM) for solving multidimensional heat conduction equations. Unlike conventional numerical methods, the core idea behind the HBM is to concentrate variables along half of the boundary and employ them to represent node variables within the solution domain. This approach streamlines the solving process by dealing with smaller-order matrices, substantially reducing storage requirements. We derived the fundamental equations of the HBM for solving multidimensional heat conduction differential equations. Furthermore, by introducing the Cayley–Hamilton formula, we optimize the program to enhance computational efficiency. Additionally, we explored heat conduction problems in solution domains differing from rectangular regions. Notably, we pioneer the application of the HBM to address three-dimensional (3-D) problems for the first time, ensuring its accuracy through rigorous validation.

Equivalent Thermal Conductivity of Topology-Optimized Composite Structure for Three Typical Conductive Heat Transfer Models

Composite materials and structural optimization are important research topics in heat transfer enhancement. The current evaluation parameter for the conductive heat transfer capability of composites is effective thermal conductivity (ETC); however, this parameter has not been studied or analyzed for its applicability to different heat transfer models and composite structures. In addition, the optimized composite structures of a specific object will vary when different optimization methods and criteria are employed. Therefore, it is necessary to investigate a suitable method and parameter for evaluating the heat transfer capability of optimized composites under different heat transfer models. Therefore, this study analyzes and summarizes three typical conductive heat transfer models: surface-to-surface (S-to-S), volume-to-surface (V-to-S), and volume-to-volume (V-to-V) models. The equivalent thermal conductivity (keq) is proposed to evaluate the conductive heat transfer capability of topology-optimized composite structures under the three models. A validated simulation method is used to obtain the key parameters for calculating keq. The influences of the interfacial thermal resistance and size effect on keq are considered. The results show that the composite structure optimized for the V-to-S and V-to-V models has a keq value of only 79.4 W m−1 K−1 under the S-to-S model. However, the keq values are 233.4 W m−1 K−1 and 240.3 W m−1 K−1 under the V-to-S and V-to-V models, respectively, which are approximately 41% greater than those of the in-parallel structure. It can be demonstrated that keq is more suitable than the ETC for evaluating the V-to-S and V-to-V heat transfer capabilities of composite structures. The proposed keq can serve as a characteristic parameter that is beneficial for heat transfer analysis and composite structural optimization.

Synthesis, structural characterisations, electrochemical behavior and antibacterial activities of a chromium(III) resorcinolate complex

The integration and implementation of transition metal complexes as working electrode for surface modifications has become an area of research interest now a days. Based on this, a novel anionic complex having a formula of Na3[Cr(HR)4Cl2] (HR- = resorcinolate) with octahedral geometry, was prepared and characterized by elemental analysis, molar conductance, vibrational spectra. Electropolymerization of the ligand, salt, and complex was done on glassy carbon electrodes with effective surface area 0.15, 0.17, and 0.2 cm2 for poly(NaHR)/GCE, Cr(0)/GCE, and poly(Na3[Cr(HR)4(Cl2)]/GCE respectively. The presence of a redox polymer film on the surface of the electrode was indicated by the experimental changes observed for a solution containing Na3[Cr(HR)4Cl2]. Specifically, the anodic peak currents, which represent the oxidation process, showed significant increases at different potential values compared to the ligand and salt. These potential values were approximately + 114 mV and + 573 mV. Additionally, the cathodic peak current, which is corresponding to the reduction process, exhibited changes at − 230 mV as the scan cycles were increased. These variations strongly suggested the formation of a film composed of a redox polymer on the electrode's surface. Further, the resistance to charge transfer (Rct) of the compound is in the lower voltage compared to the free ligand, CrCl3•6H2O, and the unmodified GCE. This indicates that the modified compound exhibits improved conductivity due to its reduced charge transfer resistance. The antibacterial activity assessed against two Gram-positive bacteria strains (Staphylococcus aureus and Streptococcus epidermis) and two Gram-negative bacteria strains (Escherichia coli and Klebsiella pneumoniae), indicate that the Cr(III) complex exhibit higher antibacterial activity compared to the ligand and the metal salt but lower than the reference. The synthesized is a highly conductive material suitable for potential applications in sensors and catalysis, especially in situations that require efficient and rapid electron transfer process

Vibrations of skew cylindrical shells made of FG-GPLRCs under rapid surface heating

An analysis is performed in this research to examine the thermally induced vibrations in skew cylindrical shells. It is assumed that shell is made from a composite laminated material where each layer is reinforced with graphene platelets (GPLs). The amount of GPLs in the layers may be different which results in a piecewise functionally graded media. The one-dimensional transient heat conduction equation is established through the thickness of the shell. Heat conduction equation is solved using the finite difference method for each layer and continuity of temperature and heat flux is applied between the layers. Crank Nicolson algorithm is implemented to obtain the temperature profile at each time step and after that thermally induced force and moment are evaluated. The kinematics of the shell are estimated following the first order shear deformation shell theory. Also it should be noted that an oblique coordinates system in addition to orthogonal system is defined which make it easier to apply the boundary conditions. The definition of strain and kinetic energies are constructed and Following the Ritz method whose shape functions are estimated by Chebyshev polynomials, energies are provided in discrete form of the governing equations. Results of this study are provided to explore the effects of thermal and mechanical boundary conditions, geometry of the shell, weight fraction and distribution patterns of GPLs. It is highlighted that thermally induced vibrations indeed exist especially in thin class of shells.