Generalized integral transform method for the solution of the heat-conduction equation in a region with moving boundaries

1987 ◽  
Vol 52 (3) ◽  
pp. 369-377 ◽  
Author(s):  
�. M. Kartashov
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Integral Transform ◽  
Moving Boundaries ◽  
Conduction Equation ◽  
Transform Method ◽  
Integral Transform Method

scholarly journals Time-Fractional Heat Conduction in a Plane with Two External Half-Infinite Line Slits under Heat Flux Loading

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 689 ◽  
Author(s):  
Yuriy Povstenko ◽  
Tamara Kyrylych
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Graphical Representation ◽  
Integral Transform ◽  
Conduction Equation ◽  
Infinite Plane ◽  
Conservation Of Energy ◽  
Infinite Line ◽  
Fractional Heat Conduction

The time-fractional heat conduction equation follows from the law of conservation of energy and the corresponding time-nonlocal extension of the Fourier law with the “long-tail” power kernel. The time-fractional heat conduction equation with the Caputo derivative is solved for an infinite plane with two external half-infinite slits with the prescribed heat flux across their surfaces. The integral transform technique is used. The solution is obtained in the form of integrals with integrand being the Mittag–Leffler function. A graphical representation of numerical results is given.

MAGNETO-THERMOELASTIC PROBLEM WITH EDDY CURRENT LOSS OF A THERMOSENSITIVE CONDUCTIVE PLATE

2021 ◽  
Vol 10 (1) ◽  
pp. 557-570
Author(s):  
L.C. Bawankar ◽  
G.D. Kedar
Keyword(s):  
Magnetic Field ◽  
Heat Conduction ◽  
Eddy Current ◽  
Heat Conduction Equation ◽  
Integral Transform ◽  
Eddy Current Loss ◽  
Thermoelastic Problem ◽  
Conduction Equation ◽  
Plane State ◽  
Current Loss

In this paper a two dimensional magneto-thermoelastic problem of a thermosensitive finite conducting plate with eddy current loss is considered. It is assumed that the plate is influenced by a time-varying external magnetic field and that the heating is caused by Joule heat. The fundamental equations for magnetic field, heat conduction and elastic fields are formulated. Temperature dependent material properties and heat source as eddy current loss is considered in the heat conduction equation. Kirchhoff's variable transformation is employed to convert nonlinear to linear heat conduction equation. Integral transform technique is used to solve the magnetic field and temperature distribution. The stresses in a plane state are determined by using Airy's stress function. The numerical analysis is carried out and the results are graphically displayed.

Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Yuriy Povstenko
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Linear Combination ◽  
Heat Conduction Equation ◽  
Integral Transform ◽  
Convective Heat Exchange ◽  
Robin Boundary Condition ◽  
Conduction Equation ◽  
Robin Boundary ◽  
Fractional Heat Conduction

AbstractThe central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.

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