The gravitational field effect on a micro-elongated thermoelastic layer under a fluid load with two theories

Abstract

PurposeThis paper aims to study the gravity effects on a micro-elongated thermoelastic layer under a fluid load, utilizing the Lord–Shulman (L-S) theory and the dual-phase-lag (DPL) model.Design/methodology/approachThe analytical method used was the normal mode which partial differential equations transform into ordinary differential equations.FindingsAluminum epoxy numerical computations are carried out, and the results are graphed. The DPL model and the L-S theory are compared in the complete absence and presence of gravity. Comparisons were also made for three values of and it is observed that the gravity has quite a massive influence on all physical quantities.Originality/valueIn the present paper, the authors shall create the general equation for the energy equation, which includes the two theories (DPL and L-S) as well as the solution of micro-elongated thermoelasticity under fluid load. The problem is pretty important in many dynamical systems.

Study of micro‐elongated thermoelastic medium loaded with a piezoelectric layer under the influence of gravity using the dual‐phase‐lag model

“…In view of Equations () and () for the displacement vector $${\boldsymbol{u}}(x,z,t)=u({u}_{1},0,{u}_{3})$$ and the gravity $$g$$, one may use the equations of motion 34 $$$\mu {\nabla }^{2}{u}_{1}+(\lambda +\mu ){e}_{,x}-{\beta }_{0}{T}_{,x}+{\lambda }_{0}{\varphi }_{,x}+\rho g\frac{\partial {u}_{3}}{\partial x}=\rho {u}_{1,tt},$$$ $$$\mu {\nabla }^{2}{u}_{3}+(\lambda +\mu ){e}_{,z}-{\beta }_{0}{T}_{,z}+{\lambda }_{0}{\varphi }_{,z}-\rho g\frac{\partial {u}_{1}}{\partial x}=\rho {u}_{3,tt}.$$$…”

“…We can obtain the equations that the parameters obey from the previous boundary conditions (34) and (35). As a result, 10…”

Volumetric absorption illumination induced by laser radiation in a 2D thermoelastic microelongated semiconductor body with temperature-dependent properties

“…Microelongated materials can be found in many branches of material science; some examples of microelongated media involve solid-liquid crystals, structural materials reinforced with crushed elastic fibers, and porous materials having pores stuffed to the gills with gases or non-viscous fluid. It should be noted that numerous effects on microelongated thermoelasticity, such as initial stress, and also comparing relaxation times including their effects on all physical parameters, have not received much attention; see [37][38][39][40][41].…”