General Solution and Fundamental Solution in Anisotropic Micropolar Thermoelastic Media with Mass Diffusion

2021 ◽  
pp. 603-621
Author(s):  
Vijay Chawla ◽  
Sanjeev Ahuja
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Mass Diffusion

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.

Fundamental solution for a two-dimensional problem in transversely isotropic micropolar thermoelastic media

2017 ◽  
Vol 13 (3) ◽  
pp. 409-423 ◽  
Author(s):  
Vijay Chawla ◽  
Sanjeev Ahuja ◽  
Varsha Rani
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Heat Source ◽  
Harmonic Functions ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Two Dimensional ◽  
Point Heat Source ◽  
Content Type ◽  
Thermoelastic Material

Purpose The purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general solution in transversely isotropic thermoelastic media is derived. Design/methodology/approach On the basis of the general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions. Findings The components of displacement, stress, temperature distribution and couple stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained. Practical implications Fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions. Originality/value Fundamental solutions for a steady point heat source acting on the surface of a micropolar thermoelastic material is obtained by seven newly introduced harmonic functions. From the present investigation, some special cases of interest are also deduced.

scholarly journals General solution and fundamental solution for two-dimensional problem in orthotropic thermoelastic media with voids

2014 ◽  
Vol 41 (4) ◽  
pp. 247-265
Author(s):  
Rajneesh Kumar ◽  
Vijay Chawla
Keyword(s):  
General Solution ◽  
Fundamental Solution ◽  
Heat Source ◽  
Harmonic Functions ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Point Heat Source ◽  
Elementary Functions ◽  
Thermoelastic Material ◽  
Special Case

The aim of the present paper is to study the fundamental solution in orthotropic thermoelastic media with voids. With this objective, firstly the two-dimensional general solution in orthotropic thermoelastic media with voids is derived. On the basis of general solution, the fundamental solution for a steady point heat source on the surface of a semiinfinite orthotropic thermoelastic material with voids is constructed by six newly introduced harmonic functions. The temperature and voids distribution and components of displacement and stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained. Since all the components are expressed in terms of elementary functions, it is convenient to use them.

The Role of VLBI in the Establishment of Coordinate Systems

1975 ◽  
Vol 26 ◽  
pp. 293-295 ◽  
Author(s):  
I. Zhongolovitch
Keyword(s):  
General Solution ◽  
Future Development ◽  
Rational Approach ◽  
Radio Telescopes ◽  
Coordinate Systems ◽  
Tectonic Plates ◽  
Astronomical Observations ◽  
Optical Instruments ◽  
Fundamental Polyhedron

Considering the future development and general solution of the problem under consideration and also the high precision attainable by astronomical observations, the following procedure may be the most rational approach:1. On the main tectonic plates of the Earth’s crust, powerful movable radio telescopes should be mounted at the same points where standard optical instruments are installed. There should be two stations separated by a distance of about 6 to 8000 kilometers on each plate. Thus, we obtain a fundamental polyhedron embracing the whole Earth with about 10 to 12 apexes, and with its sides represented by VLBI.

Burgers fluid flow in perspective of Buongiorno’s model with improved heat and mass flux theory for stretching cylinder

2020 ◽  
Vol 92 (3) ◽  
pp. 31101
Author(s):  
Zahoor Iqbal ◽  
Masood Khan ◽  
Awais Ahmed
Keyword(s):  
Diffusion Process ◽  
Mathematical Formulation ◽  
Thermal Relaxation ◽  
Mass Diffusion ◽  
Stretching Cylinder ◽  
Discussion Section ◽  
Buongiorno’S Model ◽  
Homotopy Analysis ◽  
Burgers Fluid ◽  
Diffusion Phenomena

In this study, an effort is made to model the thermal conduction and mass diffusion phenomena in perspective of Buongiorno’s model and Cattaneo-Christov theory for 2D flow of magnetized Burgers nanofluid due to stretching cylinder. Moreover, the impacts of Joule heating and heat source are also included to investigate the heat flow mechanism. Additionally, mass diffusion process in flow of nanofluid is examined by employing the influence of chemical reaction. Mathematical modelling of momentum, heat and mass diffusion equations is carried out in mathematical formulation section of the manuscript. Homotopy analysis method (HAM) in Wolfram Mathematica is utilized to analyze the effects of physical dimensionless constants on flow, temperature and solutal distributions of Burgers nanofluid. Graphical results are depicted and physically justified in results and discussion section. At the end of the manuscript the section of closing remarks is also included to highlight the main findings of this study. It is revealed that an escalation in thermal relaxation time constant leads to ascend the temperature curves of nanofluid. Additionally, depreciation is assessed in mass diffusion process due to escalating amount of thermophoretic force constant.

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

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