جستجوی مقالات مرتبط با کلیدواژه "laplace transform" در نشریات گروه "مکانیک"

Nanofluid is an innovative technology that is essential in biomedical applications. A nanofluid study of human blood flow mathematically is more favorable since it provides a hypothesis for complex systems faster and is cost-saving. Academic researchers have expressed interest in investigating the characteristics of Casson nanofluid flow within a cylindrical structure, which serves as a representative model for the flow of blood in constricted human arteries. However, slip velocity boundary conditions were considered by only a certain number of researchers. The goal of this study is to develop mathematical modelling of Casson fluid flow with gold nanoparticles in the slip cylinder. The impacts of convective heat transfer, magnetohydrodynamics (MHD), and porous medium are also investigated. The Tiwari-Das nanofluid model is utilized in the governing equations. Then, the governing equations with the related boundary conditions are transformed into dimensionless form. The analytical solutions were obtained through the use of the Laplace transform and the finite Hankel transform in combination. The results of nanofluid velocity, temperature, skin friction, and Nusselt number are analyzed through the use of graphs and tables containing relevant parameters. Slip velocity causes an increment in blood velocity and a decrement in skin friction. Blood velocity and temperature are enhanced as the nanoparticles' volume fraction is increased. It is significant in cancer treatment to increase the heat transfer rate at targeted cancerous cells.

This paper uses different higher-order shear deformation theories to analyze the axial and transverse dynamic response of carbon nanotube-reinforced composite (CNTRC) beams under moving harmonic load. The governing equations of the CNTRC beam are obtained based on the shear deformation beam theory and the Hamilton principle. The exact solution for dynamic response is presented using the Laplace transform. A comparison of previous studies has been published, where a good agreement is observed. Finally, some examples were used to analyze aspect ratio, other higher-order theories, excitation frequency, the volume fraction of Carbon nanotubes (CNTs), the velocity of a moving harmonic load, and their influence on axial and transverse dynamic and maximum deflections. It was observed that the X-beam is a stronger beam than other CNT patterns, Reddy theory is the lower limit, and HSDT theory is the upper limit. The vibration response and dynamic movement of the structure can be controlled by choosing the appropriate items.

In this paper, we propose a new technique for solving the magnetic hydrodynamic boundary layer equations after converting them to a nonlinear ordinary differential equation using the appropriate similarity transformation. This technique is based on a combination of the q-homotopy analysis method, the Laplace transform, and the Pade´ approximation, named (q-HALPM). To ensure the method's efficiency, we compared the results of q-HALPM with the ones obtained by methods (DTM-Pade´) and M-HPM . Additionally, the effect of the magnetic parameter on the velocity and heat transfer was studied. The results confirm that the new method has high accuracy and efficiency in finding the approximate analytical solution for the current problem. Moreover, the graphs of the new solutions show the validity and usefulness of the proposed method.

The article describes the problem of unsteady vibrations of a Bernoulli-Euler beam taking into account the relaxation of temperature and diffusion processes. The initial mathematical model includes a system of equations for unsteady bending vibrations of the beam with consideration of heat and mass transfer. This model is obtained from the general model of thermomechanodiffusion for continuum using the D'Alembert's variational principle. The solution of the problem is obtained in the integral form. The kernels of the integral representations are Green's functions. For finding of Green's functions the expansion into trigonometric Fourier series and Laplace transform in time are used. The calculation example is investigated for a freely supported three-component beam made of zinc, copper and aluminum alloy under the action of unsteady bending moments, including the interaction of mechanical, temperature and diffusion fields.

Nowadays, the preparation, characterization, and modeling of nanofluids are deliberated in plenty to improve the heat transfer effects. Therefore, this paper centers on the heat transfer effects of three separate hybrid nanoparticles such as Al2O3-SiO2, Al2O3-TiO2, and TiO2-SiO2 with a base fluid such as water to gratify the advances. Analytical investigations for the Marangoni convection of different hybrid nanofluids over the flat surface for the cases such as suction, injection and impermeable were analyzed. A validation table for the comparison between analytical and numerical studies is tabulated. The influence of the hybrid nanoparticles solid volume fraction and the wall mass transfer parameter are mentioned through graphs at the side of the heat transfer rate tabulation. The impact of solid volume fraction decelerates the velocity distribution and raises the temperature distribution for all the three hybrid nanofluids in the cases of suction, impermeable, and injection. While relating the surface velocity and heat transfer rate of the three hybrid nanofluids, Al2O3-SiO2/water has a higher surface velocity, TiO2-SiO2/water has a higher heat transfer rate and Al2O3-TiO2/water has lower surface velocity and heat transfer rate for the increment of wall mass transfer parameter.

The boundary element method is used to analyze the problem of dynamic loading acting inside a cubic cavity located in a partially saturated poroelastic halfspace. Defining relations of a Biot’s porous medium are used, which are written in Laplace representations for unknown functions of displacements of the skeleton and pore pressures of the fillers. Solutions in time are obtained using the stepped method of numerical inversion of Laplace transforms. Dynamic responses of displacements and pore pressures at points on the surface of the halfspace and the cavity have been constructed. The effect of the values of the saturation coefficient and of the depth of the location of the cavity on dynamic responses has been studied.

A universal approach by Laplace transform to the variational iteration method for fractional derivatives with the nonsingular kernel is presented; in particular, the Caputo-Fabrizio fractional derivative and the Atangana-Baleanu fractional derivative with the non-singular kernel is considered. The analysis elaborated for both non-singular kernel derivatives is shown the necessity of considering the modified Caputo-Fabrizio fractional derivative and the analogous modifications for the Atangana-Baleanu fractional derivative with non-singular Mittag-Leffler kernel in order to satisfy the initial conditions for some fractional differential equations.

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional derivatives of the Wright’s functions. A semi-analytical solution for the velocity field is obtained by using the Laplace transform coupled with the numerical algorithms for the inverse Laplace transform elaborated by Stehfest and Tzou. Effects of the derivative fractional order and physical parameters on the nanofluid flow and heat transfer are graphically investigated.

In the present paper, an analytical approach is used to study the thermal deflections of a simply supported composite plate with a beam-like stiffener. The results for a plate–beam system exposed to a sinusoidal thermal load is used to study the effects of the low Earth orbit (LEO) thermal conditions on the composite plates, which have been used in the structure of satellites and spacecraft. To solve the governing equations of the system, the Laplace transform method for the time domain is used with the Navier series expansions. As the employed method is completely analytical, the results are exact.

A simple method which is suitable for determining with reasonable precision the parameters of gas flow system has been proposed. An inverse boundary-value problem is considered. The model of gas flow with the Danckwert’s boundary conditions in a real measurement system has been analyzed and solved. The tracer technique was applied to determine axial dispersion coefficient of gas phase and Pèclet number. These parameters are commonly used to characterize the flow behavior of fluids. Axial dispersion coefficients were estimated by comparing model solution with recorded TCD signal (an inverse problem as a method for model parameter estimation) employing the Laplace transform technique. The Gaver-Stehfest algorithm for the solution of the mathematical model has been applied. The proposed model of gas show a good agreement with the experimental data. The obtained results show that under operation conditions in the studied system the flow behaviour is neither plug flow nor perfect mixing. The described method is very fast in both experimental and computational part. Simple and errorless derivation of sophisticated model formulas has been possible by application of the Computer Algebra System-type program. The program also simplifies computations. Mathematical manipulations and computations were performed using program Maple®.

In the present investigation the disturbances in a homogeneous transversely isotropic magneto-Visco thermoelastic rotating medium with two temperature due to thermomechanical sources has been addressed. The thermoelasticity theories developed by Green-Naghdi (Type II and Type III) both with and without energy dissipation has been applied to the thermomechanical sources. The Laplace and Fourier transform techniques have been applied to solve the present problem. As an application, the bounding surface is subjected to concentrated and distributed sources (mechanical and thermal sources). The analytical expressions of displacement, stress components, temperature change and induced magnetic field are obtained in the transformed domain. Numerical inversion techniques have been applied to obtain the results in the physical domain. Numerical simulated results are depicted graphically to show the effect of viscosity on the resulting quantities. Some special cases of interest are also deduced from the present investigation.

In the current study, the effects of interactions of the moving loads and the attached mass-spring-damper systems of the composite plates on the resulting dynamic responses are investigated comprehensively, for the first time, using the classical plate theory. The solution of the coupled governing system of equations is accomplished through tracing the spatial variations using a Navier-type solution and the time variations by means of a Laplace transform. Therefore, the results are exact. The effects of various material, stiffness, and kinematic parameters of the system on the responses are investigated comprehensively and the results are illustrated graphically. Apart from the novelties presented in the modeling and solution stages, some practical conclusions have been drawn such as the fact that the amplitude of vibration increases for both the free and forced vibrations of the plate and the suspended mass, when the magnitude of suspended mass increases.

The present study is the first to analyze the dynamic response of a poroelastic beam subjected to a moving force. Moreover, the influences of attached mass-spring systems and non-ideal supports (with local movements in the supporting points or base due to the presence of factors such as gaps, unbalanced masses, and friction or seismic excitations) on the responses were investigated. Non-ideal support experiences time-dependent deflection and moment. To evaluate the effects of both the theory type and the material properties, three models were investigated for the beam with mass-spring attachment and non-ideal supports: i) elastic Euler-Bernoulli-type beam, ii) elastic Timoshenko-type beam, and iii) poroelastic beam. The governing-coupled PDE equations of the forced vibration of the saturated poroelastic beam were analytically solved via Laplace and finite Fourier transforms. The effects of various parameters on the responses were investigated comprehensively and illustrated graphically. The poroelastic nature of the material properties was found to attenuate the vibration amplitude, and it is assumed that the attached mass can considerably affect the vibration pattern.

In order to solve the velocity profile and pressure gradient of the unsteady unidirectional slip flow of Voigt fluid, Laplace transform method is adopted in this research. Between the parallel microgap plates, the flow motion is induced by a prescribed arbitrary inlet volume flow rate which varies with time. The velocity slip condition on the wall and the flow conditions are known. In this paper, two basic flow situations are solved, which are a suddenly started and a constant acceleration flow respectively. Based on the above solutions, linear acceleration and oscillatory flow are also considered.

The general solution of equations of saturated porous media with incompressible fluid for two dimensional axi-symmetric problem is obtained in the transformed domain. The Laplace and Hankel transforms have been used to investigate the problem. As an application of the approach concentrated source and source over circular region have been taken to show the utility of the approach. The transformed components of displacement, stress and pore pressure are obtained. Numerical inversion technique is used to obtain the resulting quantities in physical domain. Effect of porosity is shown on the resulting quantities. A particular case of interest is also deduced from the present investigation.