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.

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.

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.

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.

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.

scholarly journals A family of Finch and Skea relativistic stars

2017 ◽  
Vol 26 (03) ◽  
pp. 1750014 ◽  
Author(s):  
S. D. Maharaj ◽  
D. Kileba Matondo ◽  
P. Mafa Takisa
Keyword(s):  
Bessel Functions ◽  
Special Functions ◽  
Graphical Analysis ◽  
System Of Differential Equations ◽  
Elementary Functions ◽  
Relativistic Stars ◽  
Spacetime Geometry ◽  
Special Cases ◽  
Barotropic Equation ◽  
Charged Model

Several new families of exact solution to the Einstein–Maxwell system of differential equations are found for anisotropic charged matter. The spacetime geometry is that of Finch and Skea which satisfies all criteria for physical acceptability. The exact solutions can be expressed in terms of elementary functions, Bessel functions and modified Bessel functions. When a parameter is restricted to be an integer then the special functions reduce to simple elementary functions. The uncharged model of Finch and Skea [R. Finch and J. E. F. Skea, Class. Quantum Grav. 6 (1989) 467.] and the charged model of Hansraj and Maharaj [S. Hansraj and S. D. Maharaj, Int. J. Mod. Phys. D 15 (2006) 1311.] are regained as special cases. The solutions found admit a barotropic equation of state. A graphical analysis indicates that the matter and electric quantities are well behaved.

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 A General Study of Fundamental Solutions in Aniotropicthermoelastic Media with Mass Diffusion and Voids

2020 ◽  
Vol 25 (4) ◽  
pp. 22-41
Author(s):  
Vijay Chawla ◽  
Deepmala Kamboj
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Harmonic Functions ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Mass Diffusion ◽  
Point Heat Source ◽  
General Study ◽  
Elementary Functions ◽  
Special Cases

AbstractThe present paper deals with the study of a fundamental solution in transversely isotropic thermoelastic media with mass diffusion and voids. For this purpose, a two-dimensional general solution in transversely isotropic thermoelastic media with mass diffusion and voids is derived first. On the basis of the obtained general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic thermoelastic material with mass diffusion and voids is derived by nine newly introduced harmonic functions. The components of displacement, stress, temperature distribution, mass concentration and voids are expressed in terms of elementary functions and are convenient to use. From the present investigation, some special cases of interest are also deduced and compared with the previous results obtained, which prove the correctness of the present result.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.

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