Deflection Analysis of a Nonlocal Euler–Bernoulli Nanobeam Model Resting on Two Elastic Foundations: A Generalized Differential Quadrature Approach

This paper provides a general formularization of the nonlocal Euler–Bernoulli nanobeam model for a bending examination of the symmetric and asymmetric cross-sectional area of a nanobeam resting over two linear elastic foundations under the effects of different forces, such as axial and shear forces, by considering various boundary conditions’ effects. The governing formulations are determined numerically by the Generalized Differential Quadrature Method (GDQM). A deep search is used to analyze parameters—such as the nonlocal (scaling effect) parameter, nonuniformity of area, the presence of two linear elastic foundations (Winkler–Pasternak elastic foundations), axial force, and the distributed load on the nanobeam’s deflection—with three different types of supports. The significant deductions can be abbreviated as follows: It was found that the nondimensional deflection of the nanobeam was fine while decreasing the scaling effect parameter of the nanobeams. Moreover, when the nanobeam is not resting on any elastic foundations, the nondimensional deflection increases when increasing the scaling effect parameter. Conversely, when the nanobeam is resting on an elastic foundation, the nondimensional deflection of the nanobeam decreases as the scaling effect parameter is increased. In addition, when the cross-sectional area of the nanobeam varies parabolically, the nondimensional deflection of the nonuniform nanobeam decreases in comparison to when the cross-sectional area varies linearly

Magnetic Field Effects on Thermal Nanofluid Flowing through Vertical Stenotic Artery: Analytical Study

The present investigation represents the first complete illustration of nanofluids flow. The effectiveness of wall slip and heat transfer on magnetohydrodynamic nanofluids flow over porous media in vertical stenotic artery with catheter has been analyzed. By considering the long-wavelength with low-Reynolds number approximation, a mathematical solution was derived to velocity, stream function, pressure difference, and temperature. The nanoparticle’s concentration, amplitude ratio, catheter size, and flow rate have been used to extract the pressure difference. This study analyzes the interaction effect of slip and thermal conditions on nanoparticles fluid suspension with a catheter in a vertical stenotic artery with/without the presence of magnetic field and porosity. The results are helpful for understanding the role of the engineering applications of nanofluids in biomedicine and some other applications. The results of this paper reveal that the nanoparticles concentration has little effect on the velocity, and the concentration, slipping, and porosity of the nanoparticles decreases the thermal energy

Slip Effects on Peristaltic Transport of a Particle-Fluid Suspension in a Planar Channel

Peristaltic pumping induced by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid mixed with rigid spherical particles is investigated theoretically taking the slip effect on the wall into account. A perturbation solution is obtained which satisfies the momentum equations for the case in which amplitude ratio (wave amplitude/channel half width) is small. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms and the slip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth-order terms yield the Poiseuille flow and the first-order terms give the Orr-Sommerfeld equation. The results show that the slip conditions have significant effect within certain range of concentration. The phenomenon of reflux (the mean flow reversal) is discussed under slip conditions. It is found that the critical reflux pressure is lower for the particle-fluid suspension than for the particle-free fluid and is affected by slip condition. A motivation of the present analysis has been the hope that such theory of two-phase flow process under slip condition is very useful in understanding the role of peristaltic muscular contraction in transporting biofluid behaving like a particle-fluid mixture. Also the theory is important to the engineering applications of pumping solid-fluid mixture by peristalsis

Deflection Analysis of a Nonlocal Euler–Bernoulli Nanobeam Model Resting on Two Elastic Foundations: A Generalized Differential Quadrature Approach

This paper provides a general formularization of the nonlocal Euler–Bernoulli nanobeam model for a bending examination of the symmetric and asymmetric cross-sectional area of a nanobeam resting over two linear elastic foundations under the effects of different forces, such as axial and shear forces, by considering various boundary conditions’ effects. The governing formulations are determined numerically by the Generalized Differential Quadrature Method (GDQM). A deep search is used to analyze parameters—such as the nonlocal (scaling effect) parameter, nonuniformity of area, the presence of two linear elastic foundations (Winkler–Pasternak elastic foundations), axial force, and the distributed load on the nanobeam’s deflection—with three different types of supports. The significant deductions can be abbreviated as follows: It was found that the nondimensional deflection of the nanobeam was fine while decreasing the scaling effect parameter of the nanobeams. Moreover, when the nanobeam is not resting on any elastic foundations, the nondimensional deflection increases when increasing the scaling effect parameter. Conversely, when the nanobeam is resting on an elastic foundation, the nondimensional deflection of the nanobeam decreases as the scaling effect parameter is increased. In addition, when the cross-sectional area of the nanobeam varies parabolically, the nondimensional deflection of the nonuniform nanobeam decreases in comparison to when the cross-sectional area varies linearly