Torsional static and vibration analysis of functionally graded nanotube with bi-Helmholtz kernel based stress-driven nonlocal integral model

A torsional static and free vibration analysis of the functionally graded nanotube(FGNT)composed of two materials varying continuously according to the power-law along the radial direction is performed using the bi-Helmholtz kernel based stress-driven nonlocal integral model.The differential governing equation and boundary conditions are deduced on the basis of Hamilton’s principle,and the constitutive relationship is expressed as an integral equation with the bi-Helmholtz kernel.Several nominal variables are introduced to simplify the differential governing equation,integral constitutive equation,and boundary conditions.Rather than transforming the constitutive equation from integral to differential forms,the Laplace transformation is used directly to solve the integro-differential equations.The explicit expression for nominal torsional rotation and torque contains four unknown constants,which can be determined with the help of two boundary conditions and two extra constraints from the integral constitutive relation.A few benchmarked examples are solved to illustrate the nonlocal influence on the static torsion of a clamped-clamped(CC)FGNT under torsional constraints and a clamped-free(CF)FGNT under concentrated and uniformly distributed torques as well as the torsional free vibration of an FGNT under different boundary conditions.

Analysis of Silver Nanoparticles in Engine Oil: Atangana–Baleanu Fractional Model

The present article aims to examine the heat and mass distribution in a free convection flow of electrically conducted,generalized Jeffrey nanofluid in a heated rotatory system.The flow analysis is considered in the presence of thermal radiation and the transverse magnetic field of strength B0.The medium is porous accepting generalized Darcy’s law.The motion of the fluid is due to the cosine oscillations of the plate.Nanofluid has been formed by the uniform dispersing of the Silver nanoparticles in regular engine oil.The problem has been modeled in the form of classical partial differential equations and then generalized by replacing time derivative with Atangana–Baleanu(AB)time-fractional derivative.Upon taking the Laplace transform technique(LTT)and using physical boundary conditions,exact expressions have been obtained for momentum,energy,and concentration distributions.The impact of a number of parameters on fluid flow is shown graphically.The numerical tables have been computed for variation in the rate of heat and mass transfer with respect to rooted parameters.Finally,the classical solution is recovered by taking the fractional parameter approaching unity.It is worth noting that by adding silver nanoparticles in regular engine oil,its heat transfer rate increased by 14.59%,which will improve the life and workability of the engine.

Analysis of thermal injuries using classical Fourier and DPL models for multi-layer of skin under different boundary conditions

In this paper,the temperature distribution in the multi-layer of the skin is studied when the skin surface is subjected to most generalized boundary condition.Our skin model consists of three layers known as the epidermis,dermis,and subcutaneous layers.All layers of skin are assumed to be connected with point of interface condition and taking the barrier in between each of the two layers by symmetric flux condition and analyzing each layer separately.The classical Fourier and non-Fourier(DPL)models are extended to analyze the behavior of heat transfer in the multi-layer of the skin.The Laplace transform technique is used to derive analytical solutions for the multi-layer of skin models.The effects of the variability of different parameters such as relaxation time,layer thickness,and different types of boundary conditions on the behavior of temperature distribution in the multi-layer of skin are analyzed and discussed in detail.All the effects are shown graphically.It has been observed that during temperature distribution in the multi-layer of skin,the measurement of skin damage is less on the DPL model(rq>Tt)in comparison to the classical Fourier model.