The present study is concentrated on the application of electric and magnetic fields on the longitudinal porous fin with power‐law‐dependent heat transfer coefficient, surface emissivity, and heat generation. The porosity parameter controls the amount of empty spaces or voids in the porous fin and its practical value lies in the range
0
∠
ϕ
∠
1. In industrial application, the heat transfer coefficient is governed by a power law and its specific value defines a certain heat transfer process. The heat generation and surface emissivity of the longitudinal porous fin are assumed to be varied according to the power law and the whole fin is under the influence of an external electric field. The resulting nonlinear equation is solved by the classical Adimian decomposition method (ADM) and the obtained solutions are verified further by the finite difference method (FDM). It has been found that both ADM and FDM are in good agreement for lower values of thermophysical parameters. The effects of power index of heat generation, surface emissivity, and heat transfer coefficient parameter on the temperature distribution, heat flux, and efficiency are analyzed at different values of the porosity parameter comprehensively.
This study presents the elastic properties and nonlinear elasticity of the two-dimensional noncarbon nanomaterials of hexagonal lattice structures having molecular structure XY. Four nitride-based and two phosphide-based two-dimensional nanomaterials, having graphene-like hexagonal lattice structure, are considered in the present study. The four empirical parameters associated with the attractive and repulsive terms of the Tersoff-Brenner potential are calibrated for noncarbon nanomaterials and tested for elastic properties, nonlinear constitutive behaviour, bending modulus, bending and torsional energy. The mathematical identities for the tangent constitutive matrix in terms of interatomic potential function are derived through an atomistic-continuum coupled multiscale framework of the extended version of Cauchy-Born rule. The results obtained using newly calibrated empirical parameters for cohesive energy, bond length, elastic properties, and bending rigidity are compared with those reported in the literature through experimental investigations and quantum mechanical calculations. The continuum approximation is attained through the finite element method. Multiscale evaluations for elastic properties and nonlinear stretching of the nanosheets under in-plane loads are also compared with those obtained from atomistic simulations.
Nonlinear dynamic response of some noncarbon nanomaterials, involving material and geometric nonlinearities, under different types of dynamic loads, is investigated using computationally efficient multiscale modelling. Multiscale based finite element model is developed in the framework of the Cauchy-Born rule, which couples the deformation at the atomic scale to deformation at the continuum scale. The Tersoff-Brenner type interatomic potential is employed to model the atomic interactions. The governing finite elemental equations are derived through Hamilton's principle for a dynamic system. The linearization of nonlinear discrete equations is done using the Newton-Raphson method and are solved using Newmark's time integration technique. The effect of material and geometric nonlinearities, inherent damping, different types of dynamic loads, and initial strain on the transient response of noncarbon nanosheets with clamped boundary conditions are reported in detail. The present results obtained from the multiscale-based finite element method are compared with those obtained from molecular static simulation for the free vibration analysis, and the results are found to be in good agreement. The present results are also compared with the results of those obtained Kirchhoff plate model for some cases.
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