Solutions of the heat-conduction model described by fractional Emden-Fowler type equation

Wei, Chengzhou; Wang, Huanhuan

doi:10.2298/tsci17s1113w

Cited by 2 publications

(1 citation statement)

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“…Yilmazer and Kocar [16] solved analytically heat conduction equation for an eccentric spherical annulus. Some efforts have been made to solve differential equations in fluid flow and heat conduction problems [17][18][19][20][21][22]. Tian [23] presented a symmetry analysis of non-linear heat conduction equations.…”

Section: Introductionmentioning

confidence: 99%

Heat conduction in rectangular solids with internal heat generation

Duan

2021

THERM SCI

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A representative steady-state heat conduction problem in rectangular solids with uniformly distributed heat generation has been investigated analytically. An analytical solution is provided by solving a nonhomogeneous partial differential equation. A simple and accurate model is proposed to predict the dimensionless shape factor parameter for the first time. The dimensionless shape factor is obtained in the light of the solution of Poisson equation with constant wall temperature boundary conditions. The area-mean temperature is found by integration on the rectangular cross-section. The model is very concise and nice for quick real world approximations, and it provides acceptable accuracy for engineering practice.

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Section: Introductionmentioning

confidence: 99%

Heat conduction in rectangular solids with internal heat generation

Duan

2021

THERM SCI

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Interaction solutions for the (2+1)-dimensional Ito equation

Tang

Xie

et al. 2019

Mod. Phys. Lett. B

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In this paper, two classes of interaction solutions of the (2[Formula: see text]+[Formula: see text]1)-dimensional Ito equation are studied in the case of Hirota bilinear form. As the results, the interaction solutions between the rational function and a periodic function as well as the interaction solution between the hyperbolic function and a periodic function are obtained. Based on the interaction solutions, a new transformation is proposed to analyze and discuss the influence of parameters. Furthermore, two kinds of lump solutions can be obtained via the limit behavior of the interaction solutions and the dynamical properties of these solutions are also illustrated.

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Solutions of the heat-conduction model described by fractional Emden-Fowler type equation

Abstract: In this paper, we presented a reliable algorithm to solve the singularity initial value problems of the time-dependent fractional Emden-Fowler type equations by homotopy analysis method. The approximate solutions of the problems are obtained.

Cited by 2 publications

References 18 publications

Heat conduction in rectangular solids with internal heat generation

Heat conduction in rectangular solids with internal heat generation

Interaction solutions for the (2+1)-dimensional Ito equation

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