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The theory of thermoelasticity based on the heat conduction equation with the Caputo time-fractional derivative of order α is used to study thermal stress in an infinite medium with a cylindrical hole. Two types of Neumann boundary conditions are considered: the constant value of the normal derivative of the temperature and constant heat flux at the surface of a cavity. The solution is obtained applying Laplace and Weber integral transforms. Numerical results are illustrated graphically. © 2011 Springer Science+Business Media B.V.


Povstenko Y.Z.,Jan Dlugosz University in Czestochowa
Journal of Thermal Stresses | Year: 2013

The problem of fractional heat conduction in a composite medium consisting of two semi-infinite regions being in perfect thermal contact is considered. The heat conduction in each region is described by the time-fractional heat conduction equations with the Caputo derivative of fractional order α and β, respectively. The solution is obtained using the Laplace transform with respect to time and is expressed in terms of the Mittag-Leffler function and Mainardi function. Numerical results are illustrated graphically. © 2013 Copyright Taylor and Francis Group, LLC.


Povstenko Y.,Jan Dlugosz University in Czestochowa
Nonlinear Dynamics | Year: 2010

The paper is concerned with analysis of time-fractional diffusion-wave equation with Caputo fractional derivative in a half-space. Several examples of problems with Dirichlet and Neumann conditions at the boundary of a half-space are solved using integral transforms technique. For the first and second time-derivative terms, the obtained solutions reduce to the solutions of the ordinary diffusion and wave equations. Numerical results are presented graphically for various values of order of fractional derivative. © 2009 Springer Science+Business Media B.V.


Povstenko Y.Z.,Jan Dlugosz University in Czestochowa
Mechanics Research Communications | Year: 2010

The theory of thermal stresses based on the heat conduction equation with the Caputo time-fractional derivative of order α is used to investigate thermal stresses in an infinite body with a circular cylindrical hole. The solution is obtained applying Laplace and Weber integral transforms. Several examples of problems with Dirichlet and Neumann boundary conditions are presented. Numerical results are illustrated graphically. © 2010 Elsevier B.V. All rights reserved.


Povstenko Y.,Jan Dlugosz University in Czestochowa
Computers and Mathematics with Applications | Year: 2012

The generalized telegraph equations with time- and space-fractional derivatives are considered. The corresponding theories of thermal stresses are formulated. The proposed theories interpolate the classical thermoelasticity, the theory of Lord and Shulman, thermoelasticity without energy dissipation of Green and Naghdi, and theories of fractional thermoelasticity proposed earlier. The fundamental solution to the nonhomogeneous space-time-fractional telegraph equation as well as the corresponding thermal stresses are obtained in the axisymmetric case. © 2011 Elsevier Ltd. All rights reserved.


Povstenko Y.,Jan Dlugosz University in Czestochowa
Archive of Applied Mechanics | Year: 2012

The theory of thermal stresses based on the heat conduction equation with the Caputo time-fractional derivative of order 0 < α ≤ 2 is used to investigate axisymmetic thermal stresses in a cylinder. The solution is obtained applying the Laplace and finite Hankel integral transforms. The Dirichlet and two types of Neumann problems with the prescribed boundary value of the temperature, the normal derivative of the temperature, and the heat flux are considered. Numerical results are illustrated graphically. © 2011 The Author(s).


Povstenko Y.Z.,Jan Dlugosz University in Czestochowa
Nonlinear Analysis: Real World Applications | Year: 2012

In this paper, a time-fractional central symmetric diffusion-wave equation is investigated in a sphere. Two types of Neumann boundary condition are considered: the mathematical condition with the prescribed boundary value of the normal derivative and the physical condition with the prescribed boundary value of the matter flux. Several examples of problems are solved using the Laplace integral transform with respect to time and the finite sin-Fourier transform of the special type with respect to the spatial coordinate. Numerical results are illustrated graphically. © 2011 Elsevier Ltd. All rights reserved.


Patent
Jan Dlugosz University in Czestochowa | Date: 2016-12-21

The invention relates to the use of ionic liquids tertiary phosphine oxides derivatives with terminal amino group, represented by the formula [R^(1)R^(2)P(O)[(CH_(2))_(n)NR^(3)R^(4)R^(5)]^(+)A^(-), wherein R^(1) and R^(2) are the same or different and represent independently an alkyl or aryl group, especially phenyl, R^(3)R^(4)R^(5) are the same or different and represent independently hydrogen atom, an alkyl group with C1 to C6 carbon atoms, an aryl group, especially an imidazole ring, wherein at least one substituent is not hydrogen, A^(-) is Cl, (CF_(3)SO_(2))_(2)N, n 4, as a means of herbicidal properties. In the use according to the invention as ionic liquids tertiary phosphine oxides derivatives with a terminal amino group, are used 4-[t-butyl(phenyl)phosphinyl]-n-butyl-N-methylimidazolium chloride, 4-[benzyl-t-butylphosphinyl]-n-butyl-N-methylimidazolium chloride, bis(trifluoromethylsulfonyl) 4-[t-butyl(phenyl)phosphinyl]-n-butyl-N-methylimidazolium imide and bis(trifluoromethylsulfonyl) 4-[benzyl-t-butylphosphinyl]-n-butyl-N-methylimidazolium imide.


Patent
Jan Dlugosz University in Czestochowa | Date: 2015-07-15

The essence of the invention is the use of chiral ionic salts containing a menthoxymethylimidazolium cation and tetrafluoroborate anion as a means of herbicidal properties. In the use according to the invention as ionic salts alkylimidazolium cation and tetrafluoroborate anion is used, preferably 3-[(1R,2S,5R-(-)-menthoxymethyl]-1-methylimidazolium tetrafluoroborate, 3-[(1R,2S,5R-(-)-menthoxymethyl]-1-propylimidazolium tetrafluoroborate, 1-hexyl-3-[(1R,2S,5R-(-)-menthoxymethyl]imidazolium tetrafluoroborate, 3-[(1R,2S,5R-(-)-menthoxymethyl]-1-octylimidazolium tetrafluoroborate, 3-[(1R,2S,5R-(-)-menthoxymethyl]-1-nonylimidazolium tetrafluoroborate, 1-decyl-3-[(1R,2S,5R-(-)-menthoxymethyl]imidazolium tetrafluoroborate, 3-[(1R,2S,5R-(-)-menthoxymethyl]-1-undecylimidazolium tetrafluoroborate.


Patent
Jan Dlugosz University in Czestochowa | Date: 2015-04-01

The essence of the invention is to develop alloys and methods of preparing Li_(2)ZnO_(2) and LiZnO alloys as a means of catalytic properties. In applying according to the invention Li / ZnO is used as the catalyst during thermal decomposition of the grain, particularly rye.

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