scholarly journals Fundamental Solution in Micropolar Viscothermoelastic Solids with Void

2015 ◽  
Vol 20 (1) ◽  
pp. 109-125 ◽  
Author(s):  
R. Kumar ◽  
K.D. Sharma ◽  
S.K. Garg
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Present Article ◽  
System Of Differential Equations ◽  
Elementary Functions ◽  
Basic Properties ◽  
Steady Oscillations

Abstract In the present article, we construct the fundamental solution to a system of differential equations in micropolar viscothermoelastic solids with voids in case of steady oscillations in terms of elementary functions. Some basic properties of the fundamental solution are also established.

scholarly journals Fundamental Solution in the Theory of Thermomicrostretch Elastic Diffusive Solids

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Rajneesh Kumar ◽  
Tarun Kansal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
System Of Differential Equations ◽  
Elementary Functions ◽  
Basic Properties ◽  
Special Cases ◽  
Steady Oscillations

We construct the fundamental solution of system of differential equations in the theory of thermomicrostretch elastic diffusive solids in case of steady oscillations in terms of elementary functions. Some basic properties of the fundamental solution are established. Some special cases are also discussed.

Fundamental solution in the linear theory of thermoviscoelastic mixtures

2007 ◽  
Vol 18 (3) ◽  
pp. 323-335 ◽  
Author(s):  
MERAB SVANADZE ◽  
GERARDO IOVANE
Keyword(s):  
Partial Differential Equations ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Linear Theory ◽  
Elementary Functions ◽  
Partial Differential ◽  
Coupled Partial Differential Equations ◽  
Basic Properties ◽  
Steady Vibrations ◽  
Steady Oscillations

In this article the linear theory of thermoviscoelastic mixtures is considered. The fundamental solution of the system of linear-coupled partial differential equations of steady oscillations (steady vibrations) of the theory of thermoviscoelastic mixtures is constructed in terms of elementary functions and basic properties are established.

A study of plane wave and fundamental solution in the theory of microstretch thermoelastic diffusion solid with phase-lag models

2015 ◽  
Vol 11 (2) ◽  
pp. 160-185 ◽  
Author(s):  
Rajneesh Kumar ◽  
Sanjeev Ahuja ◽  
S.K. Garg
Keyword(s):  
Fundamental Solution ◽  
Plane Wave ◽  
Phase Lag ◽  
Dual Phase ◽  
Elementary Functions ◽  
Thermoelastic Diffusion ◽  
Content Type ◽  
Propagation Technique ◽  
Steady Oscillations ◽  
Phase Velocity And Attenuation

Purpose – The purpose of this paper is to study of propagation of plane wave and the fundamental solution of the system of differential equations in the theory of a microstretch thermoelastic diffusion medium in phase-lag models for the case of steady oscillations in terms of elementary functions. Design/methodology/approach – Wave propagation technique along with the numerical methods for computation using MATLAB software has been applied to investigate the problem. Findings – Characteristics of waves like phase velocity and attenuation coefficient are computed numerically and depicted graphically. It is found that due to the presence of diffusion effect, these characteristics get influenced significantly. However, due to decoupling of CD-I and CD-II waves from rest of other, no effect on these characteristics can be perceived. Originality/value – Basic properties of the fundamental solution are established by introducing the dual-phase-lag diffusion (DPLD) and dual-phase-lag heat transfer (DPLT) models.

Fundamental solution of the system of equations of pseudo oscillations in the theory of thermoelastic diffusion materials with double porosity

2019 ◽  
Vol 15 (2) ◽  
pp. 317-336 ◽  
Author(s):  
Tarun Kansal
Keyword(s):  
Partial Differential Equations ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Volume Fraction ◽  
Displacement Vector ◽  
Double Porosity ◽  
Elementary Functions ◽  
Partial Differential ◽  
Thermoelastic Diffusion ◽  
Content Type

PurposeThe purpose of this paper to construct the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with double porosity.Design/methodology/approachThe paper deals with the study of pseudo oscillations in the generalized theory of thermoelastic diffusion materials with double porosity.FindingsThe paper finds the fundamental solution of partial differential equations in terms of elementary functions.Originality/valueAssuming the displacement vector, volume fraction fields, temperature change and chemical potential functions in terms of oscillation frequency in the governing equations, pseudo oscillations have been studied and finally the fundamental solution of partial differential equations in case of pseudo oscillations in terms of elementary functions has been constructed.

scholarly journals Plane Waves and Fundamental Solutions in Heat Conducting Micropolar Fluid

2016 ◽  
Vol 2016 ◽  
pp. 1-10
Author(s):  
Rajneesh Kumar ◽  
Mandeep Kaur
Keyword(s):  
Fundamental Solution ◽  
Micropolar Fluid ◽  
Plane Waves ◽  
Fundamental Solutions ◽  
Heat Conducting ◽  
System Of Differential Equations ◽  
Specific Loss ◽  
Special Cases ◽  
Velocity Attenuation ◽  
Steady Oscillations

In the present investigation, we study the propagation of plane waves in heat conducting micropolar fluid. The phase velocity, attenuation coefficient, specific loss, and penetration depth are computed numerically and depicted graphically. In addition, the fundamental solutions of the system of differential equations in case of steady oscillations are constructed. Some basic properties of the fundamental solution and special cases are also discussed.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Outflowing Envelopes From Stars at Arbitrary Optical Depths a New Approach to the Problem

1998 ◽  
Vol 11 (1) ◽  
pp. 381-381
Author(s):  
A.V. Dorodnitsyn
Keyword(s):  
Differential Equations ◽  
Massive Star ◽  
System Of Differential Equations ◽  
Continuous Transition ◽  
Satisfactory Description ◽  
Sonic Point ◽  
New Approach ◽  
Star Evolution ◽  
Matter Flux ◽  
Massive Star Evolution

We have considered a stationary outflowing envelope accelerated by the radiative force in arbitrary optical depth case. Introduced approximations provide satisfactory description of the behavior of the matter flux with partially separated radiation at arbitrary optical depths. The obtained systemof differential equations provides a continuous transition of the solution between optically thin and optically thick regions. We analytically derivedapproximate representation of the solution at the vicinity of the sonic point. Using this representation we numerically integrate the system of equations from the critical point to the infinity. Matching the boundary conditions we obtain solutions describing the problem system of differential equations. The theoretical approach advanced in this work could be useful for self-consistent simulations of massive star evolution with mass loss.

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