The Mathematic Model and Method for Solving the Dirichlet Heat-Exchange Problem for Empty Isotropic Rotary Body

Mykhailo Berdnyk

doi:10.4028/www.scientific.net/SSP.277.168

Paper Titles

Technological Solutions for the Realization of NGH-Technology for Gas Transportation and Storage in Gas Hydrate Form
p.123

Examination of Phase Transition of Mine Methane to Gas Hydrates and their Sudden Failure – Percy Bridgman’s Effect
p.137

Physical and Chemical Methods of Methane Utilization in Ukrainian Coal Mines
p.147

Classification of Theories about Rock Pressure
p.157

The Mathematic Model and Method for Solving the Dirichlet Heat-Exchange Problem for Empty Isotropic Rotary Body
p.168

Formation of Physic and Mechanical Composition of Dust Emission from the Ventilation Shaft of a Coal Mine as a Factor of Ecological Hazard
p.178

Stress-Strain State of a Flat Tractive-Bearing Element of a Lifting and Transporting Machine at Operational Changes of its Parameters
p.188

Changes in Density of Carbon Atomic Packing in Natural Formations
p.202

Integrated Evaluation of the Worked-Out Area Partial Backfill Effect of Stress-Strain State of Coal-Bearing Rock Mass
p.213

HomeSolid State PhenomenaSolid State Phenomena Vol. 277The Mathematic Model and Method for Solving the...

The Mathematic Model and Method for Solving the Dirichlet Heat-Exchange Problem for Empty Isotropic Rotary Body

Abstract:

It is the first generalized 3D mathematic model, which is created for calculating temperature fields in the empty isotropic rotary body, which is restricted by end surfaces and lateral surface of rotation and rotates with constant angular velocity around the axis OZ, with taking into account finite velocity of the heat conductivity in the form of the Dirichlet problem. In this work, an integral transformation was formulated for the 2D finite space, with the help of which a temperature field in the empty isotropic rotary body was determined in the form of convergence series by the Fourier functions.

You might also be interested in these eBooks

Non-Traditional Technologies in the Mining Industry

View Preview

Info:

Periodical:

Solid State Phenomena (Volume 277)

Pages:

168-177

DOI:

https://doi.org/10.4028/www.scientific.net/SSP.277.168

Citation:

Cite this paper

Online since:

June 2018

Authors:

Mykhailo Berdnyk*

Keywords:

Dirichlet Boundary Problem, Generalized Energy-Transport Equation, Laplace Integral Transformation, Relaxation Time

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] Berdnik, M. H. (2005). Matematichne modeljuvannja temperaturnogo polja v cilіndrі, jakij obertaetsja, z urahuvannjam kіncevoi shvidkostі poshirennja tepla. Pitannja prikladnoї matematiki і matematichnogo modeljuvannja, 37-44.

Google Scholar

[2] Berdnyk, M.H. (2017). Mathematical model of and method for solving the neumann generalized heat-exchange problem for a cylinder with homogeneous layers. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (4), 86-91.

DOI: 10.29202/nvngu/2018-3/18

Google Scholar

[3] Povstenko, Y. (2013). Time-fractional heat conduction in an infinite medium with a spherical hole under Robin boundary condition. Fract. Calc. Appl. Anal, (16), 356-369.

DOI: 10.2478/s13540-013-0022-y

Google Scholar

[4] Kuwashimo Kensuke, & Tominori Yamada. (1978). Temperature distribution within a rotatinq cylindrieal body. Bull. JSME, 21(152), 266-272.

Google Scholar

[5] Markovich, B.M. (2010). Rіvnjannja matematichnoї fіziki. Lvіv.: Vidavnictvo Lvіvskoi polіtehnіki.

Google Scholar

[6] Shajdurov, V.V. (1989). Mnogosetochnye metody konechnyh jelementov. M.: Nauka.

Google Scholar

[7] Lopushanska, G.P. (2014). Peretvorennja Furje, Laplasa: uzagalnennja ta zastosuvannja. Lvіv.: LNU іm. Іvana Franka.

Google Scholar