Narrow Results

This paper introduces a theoretical and numerical study for the problem of Casson fluid flow and heat transfer over an exponentially variable stretching sheet. Our contribution in this work can be observed in the presence of thermal radiation and the assumption of dependence of the fluid thermal conductivity on the heat. This physical problem is governed by a system of ordinary differential equations (ODEs), which is solved numerically by using the differential transformation method (DTM). This numerical method enables us to plot figures of the velocity and temperature distribution through the boundary layer region for different physical parameters. Apart from numerical solutions with the DTM, solutions to our proposed problem are also connected with studying the skin-friction coefficient. Estimates for the local Nusselt number are studied as well. The comparison of our numerical method with previously published results on similar special cases shows excellent agreement.

The study of nanofluids and hybrid nanofluids is gaining conceivable importance due to their characteristics of being so useful in various daily life applications. This study deals with the motion of an electro conductive, incompressible magneto-hydrodynamic (MHD) hybrid nanofluid across a stretched surface of variable thickness. The objective of this study is motivated by a number of manufacturing and machine-building applications. However, no attempt has been made to establish MHD flow of hybrid nanofluid along a stretching sheet (a sheet with variable thickness) while keeping an eye on the impact of Hall current. In real-life situations, variable-thickness sheets are crucial in the creation of flexible containers and, additionally, in the layout and production of aerospace wings and auto body components. This study extends our fundamental knowledge of fluid dynamics and heat transmission in intricate systems. Recognizing how magnetic effects, nanofluid traits and heat conduction interplay can help researchers make valuable developments and breakthroughs in the areas of fluid mechanics and heat transfer. Hall effects are vital for applications including conductive fluids or plasma as they provide a more precise understanding of the movement of charged nanoparticles in the presence of a magnetic field. For hybrid nanofluid, we mixed the nanoparticles of titanium dioxide and copper (TiO₂–Cu) into the water. Due to the low noxiousness and chemical strength of titanium dioxide-based nanoparticles, they have great uses in research. We also consider the effects of Cattaneo–Christov heat flux to analyze the heat transfer of nanoparticles and Hall current effects, which make the flow three-dimensional. For both fundamental research and real-world applications, it is of the utmost importance to take into account the Hall effects and Cattaneo–Christov heat flux in the MHD flow analysis of hybrid nanofluid over stretched surface. It makes it possible to describe the phenomenon more precisely and can enhance the effectiveness and efficiency of numerous technical procedures. By using appropriate transformations, the equations that govern the flow are transformed into a system of non-dimensional ordinary differential equations. The non-dimensional system of equations has been solved numerically by using the ND Solve command in Mathematica Software, which is based on a multistep predictor-corrector method. For velocity and temperature profiles, the interplay of numerous developing parameters on flow is depicted graphically. The Hall parameter enhances the axial velocity but reduces the transverse velocity, while the magnetic field has the opposite effects. The temperature increases with the volume fraction of nanoparticles but decreases with the thermal relaxation parameter.

Non-Newtonian materials have been an appealing topic for researchers because of the variety of laboratory and industrial process involving these fluids. There are several kinds of non-Newtonian fluids classified according to their properties. In this study, the Maxwell fluid model is analyzed due to the unique properties and applications of this non-Newtonian material. We have considered the Buongiorno model for nanofluid, which is a two-phase model that accounts for the effects of Brownian motion and thermophoresis on the transport of nanoparticles in a fluid. A stretching surface holding a chemically reactive fluid is assumed. In addition, the study also considers the impacts of heat flux and magnetic fields. The influence of various physical factors on the flow fields is presented and graphically highlighted. Using linear regression and the data point approach, the relationship between the physical parameters, such as rate of heat and mass transfer, at the surface is investigated. The relationship between the various physical parameters was investigated using the t-test approach. The Maxwell fluid parameter influences heat transmission at the surface. As the magnetic field and heat source parameters increases, the rate of heat transfer decreases. Increasing the Deborah number, chemical reaction parameter and magnetic field parameter enhances the mass transfer rate at the surface. The fluid’s velocity decreases with rising magnetic field and Maxwell fluid parameters. The heat source parameter elevates fluid temperature, while inclusion of the chemical reactions parameter reduces nanoparticle concentration.

This paper inspects the combined effects of heat and mass transfers in a hybridized Williamson viscous nanofluid composed of cadmium telluride (CdTe) and silicon carbide (SiC) nanoparticles in RT42 (Rubitherm) as base fluid in the existence of heat source and thermal radiative aspects. Knowing that the base fluid RT42 is a phase change material (PCM), it is also considered that the surface on which the nanofluid flows is an expandable surface with varying thickness. The influence of chemical reactions process and viscous dissipation on the flow and temperature of the hybridized nanofluid is examined. The parameters’ influences on the problem are evaluated after setting appropriate similarity transformations to transform the collection of major partial differential equations (PDEs) into nondimensional ordinary differential equations (ODEs). The study concludes that the presence of hybridized nanoparticles of CdTe and SiC reduces the horizontal and vertical surface frictional forces of the hybrid nanofluid. The integration of nanoparticles in RT42 enhances heat transfer rates and reduces mass transfer. The thermal radiative variable declines the heat transfer of hybridized nanofluid. The results indicate that altering the variable parameter of surface thickness reduces frictional forces in both directions.

In this work the exact axisymmetric vibration frequencies of circular and annular variable thickness plates are found. The solution is obtained using the exact element method developed earlier. It allows for the exact solution of problems with general polynomial variation in thickness using infinite power series. The solution is exact up to the accuracy of the computer. The natural frequencies of vibration are found as the solutions of the frequency equation. Normalized values for the natural frequencies are given for linear, parabolic and cubic variations of the plate thickness, for circular and annular plates, with four types of boundary conditions on the inner and outer boundaries.

This paper is concerned with the axisymmetric vibration problem of polar orthotropic circular plates of quadratically varying thickness and resting on an elastic foundation. The problem is solved by using the Rayleigh–Ritz method with boundary characteristic orthonormal polynomials for approximating the deflection function. Numerical results are computed for frequencies, nodal radii and mode shapes. Three-dimensional graphs are also plotted for the first four normal modes of axisymmetric vibration of plates with free, simply-supported and clamped edge conditions for various values of taper, orthotropy and foundation parameters.

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of complete (not truncated) conical shells with linearly varying thickness. The complete conical shells free or clamped at the bottom edge with a free vertex are investigated. Unlike conventional shell theories, which are mathematically 2D, the present method is based upon the 3D dynamic equations of elasticity. Displacement components u_r, u_θ and u_z in the radial, circumferential and axial directions, respectively, are taken to be periodic in θ and in time, and expressed by algebraic polynomials in the r- and z-directions. Potential (strain) and kinetic energies of the complete conical shell are formulated. The Ritz method is used to solve the eigenvalue problem, yielding the upper bound values of the frequencies by minimization. As the degree of the polynomials is increased, frequencies converge to the exact values, with four-digit exactitude demonstrated for the first five frequencies. The frequencies from the present 3D method are compared with those from other 3D approaches and 2D shell theory by previous researchers.

The modal analysis of rotating cantilevered rectangular Mindlin plates with variable thickness is studied. The Ritz method is used to derive the governing eigenfrequency equation by minimizing the energy functional of the plate. The admissible functions are taken as a product of the Chebyshev polynomials multiplied by the boundary functions, which enable the displacements and rotational angles to satisfy the geometric boundary conditions of the plate. The Chebyshev polynomials guarantee the numerical robustness, while the Ritz approach provides the upper bound of the exact frequencies. The effectiveness of the present method is confirmed through the convergence and comparison studies. The effects of the dimensionless rotational speed, taper ratio, aspect ratio and thickness ratio on modal characteristics are investigated in detail. The frequency loci veering phenomenon along with the corresponding mode shape switching is exhibited and discussed.

This paper is concerned with the axisymmetric free vibration analysis of a rotating annular plate with variable thickness by using the Ritz method. The rotating plate has a constant angular speed and subjected to a tensile centrifugal body force. The annular plate is fixed at the inner edge and free at the outer edge. Exact stresses, strains, and radial displacement of the rotating annular plate are obtained via plane elasticity. Presented herein are the natural frequencies and modes shapes for the rotating, nonuniform annular plate with various angular speeds and different ratios of the inner radius to the outer radius.

This paper presents modeling and free vibration analysis of variable stiffness system for the truncated sandwich conical shell made of porous aluminum foam core with variable thickness and carbon fiber face sheets under the simply supported boundary condition. The thickness of the core layer varies along the longitudinal direction. Five different types of porosity distribution of the aluminum foam core, which contains Type-X, Type-O, Type-U, Type-V and Type-$\mathrm{\Lambda }$ along the direction of thickness, are considered. Considering the effect of thermal environment, we derive the nonlinear dynamic equations based on first-order shear deformation theory and Hamilton’s principle, and obtain the natural frequencies of the system by employing the Galerkin method. The comparison and validation are conducted by contrast with the determined results of the literature. The influences of porosity distribution pattern, porosity coefficient, the total number of layers, temperature increment, semi-vertex angle, the exponent of thickness function, the minimum radius-thickness and length-thickness ratio of the core layer on the natural frequencies, modal and mode shapes are studied comprehensively.

This study focuses on the vibration characteristics of the functionally graded materials (FGMs) porous plate. The plate is to be supported on different boundary constraints with linearly varying thicknesses. Existence of different porosity (void) pattern, within the materials, are taken into consideration using the power (P-FGM) and sigmoidal (S-FGM) gradation laws. The current methodology was developed utilizing the FSDT (first-order shear deformation theory) under thermal environmental conditions. Variations of temperature like as uniform, linearly varying, and nonlinear distribution patterns were examined by including temperature-dependent and independent material properties. The equations of motion including all the effects are derived from Hamilton’s principle and, subsequently solved using the Galerkin’s Vlasov method for various plate boundary conditions. Finally, the analytical outcomes are verified numerically, with the existing works. Furthermore, the study demonstrates that the fundamental frequency of porous FGM tapered plate is very close to the result obtained by the other researchers. Moreover, a detailed examination has been carried out to reveal the effect of various factors such as volume exponent index ($\mathbb{N})$, side-to-thickness ratio ($a$/$h)$, and temperature effect ($T)$. In addition to this, some new benchmark results are obtained for free vibration analysis of tapered plates under a thermal environment.

This paper presents elastic solutions of a disk made of functionally graded material (FGM) with variable thickness subjected to rotating load. The material properties are represented by combination of two sigmoid FGM (S-FGM) namely aluminum–ceramic–aluminum and the disk's different thickness profiles are assumed to be represented by power law distributions. Hollow disks are considered and the solutions for the displacements and stresses are given under appropriate boundary conditions. The effects of the material grading index n and the geometry of the disk on the displacements and stresses are investigated. The results are compared with the known results in the literature on metal–ceramic–metal FGMs. Also the solutions are compared S-FGM versus FGM and non FGM and variable thickness versus uniform thickness. It is found that a sigmoid functionally graded disk with concave thickness profile has smaller displacements and stresses compared with concave or linear thickness profile. It is also observed that an S-FGM rotating functionally graded disk with metal–ceramic–metal combination can be more efficient than the one with ceramic–metal or metal–ceramic.

The author considers a linearly elastic shallow shell with variable thickness and shows that, as the thickness of the shell goes to zero, the solution of the three-dimensional equations converges to the solution of the two-dimensional shallow shell equations with variable thickness.

Inelastic stresses and displacements in rotating solid disks of exponentially varying thickness have been investigated using Tresca's and von Mises' yield criteria. In both criteria, linear strain hardening material behavior is assumed. A previously obtained analytical solution is adopted in the analysis when Tresca criterion is used. An efficient numerical solution procedure has been designed to obtain the solution of von Mises. Plastic limit angular velocities have been calculated for different values of the geometric parameters. In all the cases investigated the difference between Tresca and von Mises, in finding plastic limit angular velocities was less than 3%. The inelastic stresses, displacement and strains have been calculated for disks of different profiles and the results presented in graphical forms.

In this paper, free vibration of two-dimensional functionally graded (2D-FG) sectorial plate with variable thickness resting on Winkler–Pasternak elastic foundation has been studied. It is assumed that the plate properties vary continuously through its both circumference and thickness according to power law distribution of the volume fraction. Primarily, the motion equations have been derived based on first order shear deformation theory (FSDT). The numerical two-dimensional differential quadrature method (2D-DQM) has been employed to solve the motion equations. Four different kinds of boundary condition are considered. The effects of geometrical and elastic foundation parameters along with 2D-FG power indices effects on the natural frequencies have been studied. Also the frequency parameters of the sectorial plate with uniform, linear and nonlinear variation of thickness for various boundary conditions have been computed and the effects of variable thickness parameters on natural frequency have been investigated.

In this paper, buckling analysis of thick radially functionally graded circular/annular sector plates with variable thickness resting on two-parameter elastic foundations is studied. The material properties vary along radial direction according to either an exponential or a power-law distribution. The stability equations are derived using the adjacent equilibrium criterion and are based on a higher order shear deformation theory. The generalized differential quadrature method is employed to discretize the stability equations and convert them into a system of algebraic eigenvalue problem. The formulation and method of solution are validated by performing comparison studies with the available results in the open literature. Then, the effects of power-law index, boundary conditions, thickness variation and coefficients of foundation on the critical buckling load of the circular/annular sector plates subjected to different types of in-plane compressions or in-plane shear are investigated in detail.

In the present study, a theoretical solution for thermomechanical creep analysis of functionally graded (FG) thick cylindrical pressure vessel with variable thickness based on the first-order shear deformation theory (FSDT) and multilayer method (MLM) is presented. To the best of the researchers’ knowledge, in the literature, there is no study carried out into FSDT and MLM for creep response of cylindrical pressure vessels with variable thickness under thermal and mechanical loadings. The vessel is subjected to a temperature gradient and nonuniform internal pressure. All mechanical and thermal properties except Poisson’s ratio are assumed to vary along the thickness direction based on a power-law function. The thermomechanical creep response of the material is described by Norton’s law. The virtual work principle is applied to extract the nonhomogeneous differential equations system with variable coefficients. Using the MLM, this differential equations system is converted into a system of differential equations with constant coefficients. These set of differential equations are solved analytically by applying boundary and continuity conditions between the layers. In order to verify the results of this study, the finite element method (FEM) has been used and according to the results, good agreement has been achieved. It can be concluded that the temperature gradient has significant influence on the creep responses of FG thick cylindrical pressure vessel.

A semi-analytical method is presented to investigate time-dependent thermo-elastic creep behavior and life assessment of thick truncated conical shells with variable thickness subjected to internal pressure and thermal load. Based on the first-order shear deformation theory (FSDT), equilibrium equations and boundary conditions are derived using the minimum total potential energy principle. To the best of the researcher’s knowledge, in previous studies, thermo-elastic creep analysis of conical shell with variable thickness based on the FSDT has not been investigated. Norton’s law is assumed as the material creep constitutive model. The multilayered method is proposed to solve the resulting equations, which yields an accurate solution. Subsequently, the stresses at different creep times can be obtained by means of an iterative approach. Using Robinson’s linear life fraction damage rule, the creep damages of conical shells are determined and Larson–Miller parameter (LMP) is employed for assessing the remaining life. The results of the proposed approach are validated with those of the finite element method (FEM) and good agreement was found. The results indicate that the present analysis is accurate and computationally efficient.

In this study, axisymmetric elastic deformation analysis of rotating disks with variable thickness is conducted using an improved Adomian decomposition method (IADM). Variation of thickness is assumed as hyperbolic and different variations are employed for each case considered. Several analytical approximate solutions in different orders are obtained for radial stress, tangential stress, radial displacement and are compared with exact solutions. Results show that IADM can effectively be used in the deformation analysis of rotating variable thickness disks providing the solution as an analytical continuous function in the solution domain.

In this paper, an analytical solution is presented to study the buckling analysis of the composite sandwich conical shells with variable skin thickness and reinforced with lattice cores. This problem involves the filament wound conical shells, where the skin thickness varies through the length of the shell. First, the reinforced core is converted to a layer by analyzing smeared moments and forces on a unit cell. Next, superimposing the stiffness contribution of the stiffeners with those of the inner and outer shells, the equivalent stiffness of the whole structure is achieved. The power series method based on the first-order shear deformation theory (FSDT) is employed to solve the buckling load of the laminated sandwich conical shell. Numerical solution is conducted to verify analytical results by preparing finite element models. Furthermore, using the analytical model, the impact of several design parameters like buckling load, specific buckling load, stiffener orientation, value of stiffeners angle, lamination angle and semi-vertex angle is investigated, and presented based on the results of this study.