Approximate Analytical Solution for Ionizing Cylindrical Magnetogasdynamic Shock Wave in Rotational Axisymmetric Self-Gravitating Perfect Gas: Isothermal Flow

Ontology type: schema:ScholarlyArticle

Article Info

DATE

2021-04-30

AUTHORS ABSTRACT

The propagation of ionizing cylindrical magnetogasdynamic shock wave in rotational axisymmetric self-gravitating perfect gas under isothermal flow condition is investigated. Mathematical model for the considered problem using system of PDEs is presented. The density, magnetic pressure, azimuthal fluid velocity and axial fluid velocity are assumed to be varying according to power law with distance from the axis of symmetry in the undisturbed medium. The flow variables are expanded in power series and using that the zeroth and first order approximations are discussed. Solutions for zeroth order approximation are constructed in approximate analytical form. The effect of flow parameters namely: gravitational parameter G0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{0}$$\end{document}, shock Cowling number C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{0}$$\end{document}, rotational parameter L and ambient density variation index q are studied on the flow variables and total energy of disturbance. Distribution of gasdynamical quantities are discussed. Radial fluid velocity and mass tends to zero near the axis of symmetry in general; but magnetic pressure, axial fluid velocity, non-dimensional components of vorticity vector lθ(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{\theta }^{(0)}$$\end{document} and lz(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{z}^{(0)}$$\end{document} tend to positive infinity near the axis of symmetry. Azimuthal fluid velocity decreases as we move inwards from the shock to the axis of symmetry. Density and pressure vanish near the axis of symmetry thus forming a vacuum there. J0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_{0}$$\end{document} decreases with increase in value of ambient density variation index q or gravitational parameter G0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{0}$$\end{document}; whereas it increases with increase in value of rotational parameter L or shock Cowling number C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{0}$$\end{document}. More... »

PAGES

1-27

References to SciGraph publications

• 2020-08-07. Approximate analytical solution for the propagation of shock waves in self-gravitating perfect gas via power series method: isothermal flow in JOURNAL OF ASTROPHYSICS AND ASTRONOMY
• 2015-12-18. Propagation of a spherical shock wave in mixture of non-ideal gas and small solid particles under the influence of gravitational field with conductive and radiative heat fluxes in ASTROPHYSICS AND SPACE SCIENCE
• 1971-01. Strong cylindrical shocks in a rotating gas in FLOW, TURBULENCE AND COMBUSTION
• 2014-06-05. Unsteady isothermal flow behind a magnetogasdynamic shock wave in a self-gravitating gas with exponentially varying density in JOURNAL OF THEORETICAL AND APPLIED PHYSICS
• 1971-11. Converging spherical and cylindrical shocks with zero temperature gradient in the rear flow field in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
• 1983-09. Self-similar solutions in the theory of flare-ups in novae, I in ASTROPHYSICS AND SPACE SCIENCE
• 2003-07. Self-similar analytical solutions for blast waves in inhomogeneous atmospheres with frozen-in-magnetic field in THE EUROPEAN PHYSICAL JOURNAL B
• 2004-07. Detonation Wave Propagation in Rotational Gas Flows in JOURNAL OF APPLIED MECHANICS AND TECHNICAL PHYSICS
• 2000-07. Propagation of shock waves in a dusty gas with exponentially varying density in THE EUROPEAN PHYSICAL JOURNAL B
• 2018-09. Exact Solution for a Magnetogasdynamical Cylindrical Shock Wave in a Self-Gravitating Rotating Perfect Gas with Radiation Heat Flux and Variable Density in JOURNAL OF ENGINEERING PHYSICS AND THERMOPHYSICS
• 2019-12-02. Cylindrical ionizing shock waves in a self-gravitating gas with magnetic field: Power series method in JOURNAL OF ASTROPHYSICS AND ASTRONOMY
• 2019-12-07. Approximate analytical solution for shock wave in rotational axisymmetric perfect gas with azimuthal magnetic field: Isothermal flow in JOURNAL OF ASTROPHYSICS AND ASTRONOMY
• 2013-10-01. Self-similar solutions for unsteady flow behind an exponential shock in an axisymmetric rotating dusty gas in SHOCK WAVES

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12591-021-00566-8

DOI

http://dx.doi.org/10.1007/s12591-021-00566-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1137710546

Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service:

[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Pure Mathematics",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, Uttar Pradesh, India",
"id": "http://www.grid.ac/institutes/grid.419983.e",
"name": [
"Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, Uttar Pradesh, India"
],
"type": "Organization"
},
"familyName": "Nath",
"givenName": "G.",
"id": "sg:person.012645561605.23",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012645561605.23"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, Uttar Pradesh, India",
"id": "http://www.grid.ac/institutes/grid.419983.e",
"name": [
"Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, Uttar Pradesh, India"
],
"type": "Organization"
},
"familyName": "Singh",
"givenName": "Sumeeta",
"id": "sg:person.010452553655.21",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010452553655.21"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1023/b:jamt.0000030320.77965.c1",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1025767930",
"https://doi.org/10.1023/b:jamt.0000030320.77965.c1"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s12036-019-9616-z",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1123214816",
"https://doi.org/10.1007/s12036-019-9616-z"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00661159",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1041173841",
"https://doi.org/10.1007/bf00661159"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s12036-019-9615-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1123054383",
"https://doi.org/10.1007/s12036-019-9615-0"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf01590878",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1014810117",
"https://doi.org/10.1007/bf01590878"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10509-015-2615-x",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1047870252",
"https://doi.org/10.1007/s10509-015-2615-x"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1140/epjb/e2003-00218-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1036479916",
"https://doi.org/10.1140/epjb/e2003-00218-0"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s00193-013-0474-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1012448192",
"https://doi.org/10.1007/s00193-013-0474-3"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s12036-020-09638-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1129967008",
"https://doi.org/10.1007/s12036-020-09638-7"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s100510070238",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1022706255",
"https://doi.org/10.1007/s100510070238"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s40094-014-0131-y",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1028548546",
"https://doi.org/10.1007/s40094-014-0131-y"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/bf00413198",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1003044461",
"https://doi.org/10.1007/bf00413198"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s10891-018-1862-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1107643454",
"https://doi.org/10.1007/s10891-018-1862-4"
],
"type": "CreativeWork"
}
],
"datePublished": "2021-04-30",
"datePublishedReg": "2021-04-30",
"description": "The propagation of ionizing cylindrical magnetogasdynamic shock wave in rotational axisymmetric self-gravitating perfect gas under isothermal flow condition is investigated. Mathematical model for the considered problem using system of PDEs is presented. The density, magnetic pressure, azimuthal fluid velocity and axial fluid velocity are assumed to be varying according to power law with distance from the axis of symmetry in the undisturbed medium. The flow variables are expanded in power series and using that the zeroth and first order approximations are discussed. Solutions for zeroth order approximation are constructed in approximate analytical form. The effect of flow parameters namely: gravitational parameter G0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$G_{0}$$\\end{document}, shock Cowling number C0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C_{0}$$\\end{document}, rotational parameter L and ambient density variation index q are studied on the flow variables and total energy of disturbance. Distribution of gasdynamical quantities are discussed. Radial fluid velocity and mass tends to zero near the axis of symmetry in general; but magnetic pressure, axial fluid velocity, non-dimensional components of vorticity vector l\u03b8(0)\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$l_{\\theta }^{(0)}$$\\end{document} and lz(0)\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$l_{z}^{(0)}$$\\end{document} tend to positive infinity near the axis of symmetry. Azimuthal fluid velocity decreases as we move inwards from the shock to the axis of symmetry. Density and pressure vanish near the axis of symmetry thus forming a vacuum there. J0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$J_{0}$$\\end{document} decreases with increase in value of ambient density variation index q or gravitational parameter G0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$G_{0}$$\\end{document}; whereas it increases with increase in value of rotational parameter L or shock Cowling number C0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$C_{0}$$\\end{document}.",
"genre": "article",
"id": "sg:pub.10.1007/s12591-021-00566-8",
"inLanguage": "en",
"isAccessibleForFree": false,
"isPartOf": [
{
"id": "sg:journal.1136107",
"issn": [
"0971-3514",
"0974-6870"
],
"name": "Differential Equations and Dynamical Systems",
"publisher": "Springer Nature",
"type": "Periodical"
}
],
"keywords": [
"shock Cowling number",
"magnetogasdynamic shock waves",
"azimuthal fluid velocity",
"axis of symmetry",
"Cowling number",
"fluid velocity",
"self-gravitating perfect gas",
"order approximation",
"gravitational parameter",
"index q",
"axial fluid velocity",
"flow variables",
"perfect gas",
"magnetic pressure",
"system of PDEs",
"approximate analytical solution",
"approximate analytical form",
"first-order approximation",
"shock waves",
"undisturbed medium",
"isothermal flow conditions",
"gasdynamical quantities",
"mathematical model",
"power series",
"pressure vanish",
"analytical solution",
"analytical form",
"parameter L",
"positive infinity",
"isothermal flow",
"vorticity vector",
"power law",
"symmetry",
"flow parameters",
"approximation",
"flow conditions",
"velocity",
"total energy",
"waves",
"PDEs",
"parameters",
"solution",
"infinity",
"zeroth",
"vanishes",
"gas",
"propagation",
"axis",
"variables",
"density",
"problem",
"law",
"pressure",
"flow",
"vacuum",
"number",
"vector",
"model",
"distribution",
"disturbances",
"energy",
"quantity",
"system",
"values",
"distance",
"increase",
"conditions",
"form",
"components",
"medium",
"mass",
"inwards",
"effect",
"series",
"shock"
],
"name": "Approximate Analytical Solution for Ionizing Cylindrical Magnetogasdynamic Shock Wave in Rotational Axisymmetric Self-Gravitating Perfect Gas: Isothermal Flow",
"pagination": "1-27",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1137710546"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s12591-021-00566-8"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s12591-021-00566-8",
"https://app.dimensions.ai/details/publication/pub.1137710546"
],
"sdDataset": "articles",
"sdDatePublished": "2022-05-20T07:38",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/article/article_884.jsonl",
"type": "ScholarlyArticle",
"url": "https://doi.org/10.1007/s12591-021-00566-8"
}
]

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s12591-021-00566-8'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s12591-021-00566-8'

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s12591-021-00566-8'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s12591-021-00566-8'

This table displays all metadata directly associated to this object as RDF triples.

187 TRIPLES      22 PREDICATES      112 URIs      91 LITERALS      4 BLANK NODES

Subject Predicate Object
2 anzsrc-for:0101
4 schema:citation sg:pub.10.1007/bf00413198
5 sg:pub.10.1007/bf00661159
6 sg:pub.10.1007/bf01590878
7 sg:pub.10.1007/s00193-013-0474-3
8 sg:pub.10.1007/s100510070238
9 sg:pub.10.1007/s10509-015-2615-x
10 sg:pub.10.1007/s10891-018-1862-4
11 sg:pub.10.1007/s12036-019-9615-0
12 sg:pub.10.1007/s12036-019-9616-z
13 sg:pub.10.1007/s12036-020-09638-7
14 sg:pub.10.1007/s40094-014-0131-y
15 sg:pub.10.1023/b:jamt.0000030320.77965.c1
16 sg:pub.10.1140/epjb/e2003-00218-0
17 schema:datePublished 2021-04-30
18 schema:datePublishedReg 2021-04-30
19 schema:description The propagation of ionizing cylindrical magnetogasdynamic shock wave in rotational axisymmetric self-gravitating perfect gas under isothermal flow condition is investigated. Mathematical model for the considered problem using system of PDEs is presented. The density, magnetic pressure, azimuthal fluid velocity and axial fluid velocity are assumed to be varying according to power law with distance from the axis of symmetry in the undisturbed medium. The flow variables are expanded in power series and using that the zeroth and first order approximations are discussed. Solutions for zeroth order approximation are constructed in approximate analytical form. The effect of flow parameters namely: gravitational parameter G0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{0}$$\end{document}, shock Cowling number C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{0}$$\end{document}, rotational parameter L and ambient density variation index q are studied on the flow variables and total energy of disturbance. Distribution of gasdynamical quantities are discussed. Radial fluid velocity and mass tends to zero near the axis of symmetry in general; but magnetic pressure, axial fluid velocity, non-dimensional components of vorticity vector lθ(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{\theta }^{(0)}$$\end{document} and lz(0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{z}^{(0)}$$\end{document} tend to positive infinity near the axis of symmetry. Azimuthal fluid velocity decreases as we move inwards from the shock to the axis of symmetry. Density and pressure vanish near the axis of symmetry thus forming a vacuum there. J0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$J_{0}$$\end{document} decreases with increase in value of ambient density variation index q or gravitational parameter G0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G_{0}$$\end{document}; whereas it increases with increase in value of rotational parameter L or shock Cowling number C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_{0}$$\end{document}.
20 schema:genre article
21 schema:inLanguage en
22 schema:isAccessibleForFree false
23 schema:isPartOf sg:journal.1136107
24 schema:keywords Cowling number
25 PDEs
26 analytical form
27 analytical solution
28 approximate analytical form
29 approximate analytical solution
30 approximation
31 axial fluid velocity
32 axis
33 axis of symmetry
34 azimuthal fluid velocity
35 components
36 conditions
37 density
38 distance
39 distribution
40 disturbances
41 effect
42 energy
43 first-order approximation
44 flow
45 flow conditions
46 flow parameters
47 flow variables
48 fluid velocity
49 form
50 gas
51 gasdynamical quantities
52 gravitational parameter
53 increase
54 index q
55 infinity
56 inwards
57 isothermal flow
58 isothermal flow conditions
59 law
60 magnetic pressure
61 magnetogasdynamic shock waves
62 mass
63 mathematical model
64 medium
65 model
66 number
67 order approximation
68 parameter L
69 parameters
70 perfect gas
71 positive infinity
72 power law
73 power series
74 pressure
75 pressure vanish
76 problem
77 propagation
78 quantity
80 self-gravitating perfect gas
81 series
82 shock
83 shock Cowling number
84 shock waves
85 solution
86 symmetry
87 system
88 system of PDEs
89 total energy
90 undisturbed medium
91 vacuum
92 values
93 vanishes
94 variables
95 vector
96 velocity
97 vorticity vector
98 waves
99 zeroth
100 schema:name Approximate Analytical Solution for Ionizing Cylindrical Magnetogasdynamic Shock Wave in Rotational Axisymmetric Self-Gravitating Perfect Gas: Isothermal Flow
101 schema:pagination 1-27
102 schema:productId N269cdf63606f492c9be9cc8fe20c1d38
103 Ne890c4f2c915446c87766908121ecb0f
104 schema:sameAs https://app.dimensions.ai/details/publication/pub.1137710546
105 https://doi.org/10.1007/s12591-021-00566-8
106 schema:sdDatePublished 2022-05-20T07:38
108 schema:sdPublisher Nafb5c1f7ef6b43caba8d6cdfbae369f2
109 schema:url https://doi.org/10.1007/s12591-021-00566-8
111 sgo:sdDataset articles
112 rdf:type schema:ScholarlyArticle
113 N269cdf63606f492c9be9cc8fe20c1d38 schema:name dimensions_id
114 schema:value pub.1137710546
115 rdf:type schema:PropertyValue
117 rdf:rest Na444e639220d441bb871999f3e0f17d2
118 Na444e639220d441bb871999f3e0f17d2 rdf:first sg:person.010452553655.21
119 rdf:rest rdf:nil
120 Nafb5c1f7ef6b43caba8d6cdfbae369f2 schema:name Springer Nature - SN SciGraph project
121 rdf:type schema:Organization
122 Ne890c4f2c915446c87766908121ecb0f schema:name doi
123 schema:value 10.1007/s12591-021-00566-8
124 rdf:type schema:PropertyValue
125 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
126 schema:name Mathematical Sciences
127 rdf:type schema:DefinedTerm
128 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
129 schema:name Pure Mathematics
130 rdf:type schema:DefinedTerm
131 sg:journal.1136107 schema:issn 0971-3514
132 0974-6870
133 schema:name Differential Equations and Dynamical Systems
134 schema:publisher Springer Nature
135 rdf:type schema:Periodical
136 sg:person.010452553655.21 schema:affiliation grid-institutes:grid.419983.e
137 schema:familyName Singh
138 schema:givenName Sumeeta
139 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010452553655.21
140 rdf:type schema:Person
141 sg:person.012645561605.23 schema:affiliation grid-institutes:grid.419983.e
142 schema:familyName Nath
143 schema:givenName G.
144 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012645561605.23
145 rdf:type schema:Person
146 sg:pub.10.1007/bf00413198 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003044461
147 https://doi.org/10.1007/bf00413198
148 rdf:type schema:CreativeWork
149 sg:pub.10.1007/bf00661159 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041173841
150 https://doi.org/10.1007/bf00661159
151 rdf:type schema:CreativeWork
152 sg:pub.10.1007/bf01590878 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014810117
153 https://doi.org/10.1007/bf01590878
154 rdf:type schema:CreativeWork
155 sg:pub.10.1007/s00193-013-0474-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012448192
156 https://doi.org/10.1007/s00193-013-0474-3
157 rdf:type schema:CreativeWork
158 sg:pub.10.1007/s100510070238 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022706255
159 https://doi.org/10.1007/s100510070238
160 rdf:type schema:CreativeWork
161 sg:pub.10.1007/s10509-015-2615-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1047870252
162 https://doi.org/10.1007/s10509-015-2615-x
163 rdf:type schema:CreativeWork
164 sg:pub.10.1007/s10891-018-1862-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1107643454
165 https://doi.org/10.1007/s10891-018-1862-4
166 rdf:type schema:CreativeWork
167 sg:pub.10.1007/s12036-019-9615-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1123054383
168 https://doi.org/10.1007/s12036-019-9615-0
169 rdf:type schema:CreativeWork
170 sg:pub.10.1007/s12036-019-9616-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1123214816
171 https://doi.org/10.1007/s12036-019-9616-z
172 rdf:type schema:CreativeWork
173 sg:pub.10.1007/s12036-020-09638-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1129967008
174 https://doi.org/10.1007/s12036-020-09638-7
175 rdf:type schema:CreativeWork
176 sg:pub.10.1007/s40094-014-0131-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1028548546
177 https://doi.org/10.1007/s40094-014-0131-y
178 rdf:type schema:CreativeWork
179 sg:pub.10.1023/b:jamt.0000030320.77965.c1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025767930
180 https://doi.org/10.1023/b:jamt.0000030320.77965.c1
181 rdf:type schema:CreativeWork
182 sg:pub.10.1140/epjb/e2003-00218-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036479916
183 https://doi.org/10.1140/epjb/e2003-00218-0
184 rdf:type schema:CreativeWork
185 grid-institutes:grid.419983.e schema:alternateName Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, Uttar Pradesh, India
186 schema:name Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Prayagraj, Uttar Pradesh, India
187 rdf:type schema:Organization