scholarly journals Application of local fractional fourier sine transform for 1-D local fractional heat transfer equation

2018 ◽  
Vol 22 (4) ◽  
pp. 1729-1735
Author(s):  
Cheng-Dong Wei ◽  
Guang-Sheng Chen
Keyword(s):  
Heat Transfer ◽  
Transfer Equation ◽  
New Technology ◽  
Heat Transfer Equation ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Fractal Space ◽  
Fractional Differential

This paper proposes a new method called the local fractional Fourier sine transform to solve fractional differential equations on a fractal space. The method takes full advantages of the Yang-Fourier transform, the local fractional Fourier cosine, and sine transforms. A 1-D local fractional heat transfer equation is used as an example to reveal the merits of the new technology, and the example can be used as a paradigm for other applications.

FOURIER SINE AND COSINE TRANSFORMS ON BOEHMIAN SPACES

2013 ◽  
Vol 06 (01) ◽  
pp. 1350005 ◽  
Author(s):  
R. Roopkumar ◽  
E. R. Negrin ◽  
C. Ganesan
Keyword(s):  
Fourier Transform ◽  
Cosine Transform ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Fourier Cosine Transform ◽  
One To One ◽  
The Fourier Transform

We construct suitable Boehmian spaces which are properly larger than [Formula: see text] and we extend the Fourier sine transform and the Fourier cosine transform more than one way. We prove that the extended Fourier sine and cosine transforms have expected properties like linear, continuous, one-to-one and onto from one Boehmian space onto another Boehmian space. We also establish that the well known connection among the Fourier transform, Fourier sine transform and Fourier cosine transform in the context of Boehmians. Finally, we compare the relations among the different Boehmian spaces discussed in this paper.

Some Results Relating the Behaviour of Fourier Transforms Near the Origin and at Infinity

1969 ◽  
Vol 21 ◽  
pp. 942-950 ◽  
Author(s):  
C. Nasim
Keyword(s):  
Fourier Transforms ◽  
Fourier Inversion Formula ◽  
Fourier Cosine ◽  
Summation Formulae ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Image Position ◽  
Watson Transform ◽  
Special Case

It is known that under special conditions, Fourier sine transforms and Fourier cosine transforms behave asymptotically like a power of x, either as x → 0 or as x → ∞ or both. For example (3),where f(x) = x–αϕ(x), 0 < α < 1, and ϕ(x) is of bounded variation in (0, ∞) and Fc(x) is the Fourier cosine transform of f(x). This suggests that other results connecting the behaviour of a function at infinity with the behaviour of its Fourier or Watson transform near the origin might exist. In this paper wre derive various such results. For example, a special case of these results iswhere f(x) is the Fourier sine transform of g(x). It should be noted that the Fourier inversion formula fails to give f(+0) directly in this case. Some applications of these results to show the relationships between various forms of known summation formulae are given.

scholarly journals A Computational Method for n-Dimensional Laplace Transforms Involved with Fourier Cosine Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-4
Author(s):  
Jafar Saberi-Nadjafi
Keyword(s):  
Laplace Transform ◽  
Laplace Transforms ◽  
Computational Method ◽  
Cosine Transform ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Fourier Cosine Transform

In 2007, the author published some results on n-dimensional Laplace transform involved with the Fourier sine transform. In this paper, we propose some new result in n-dimensional Laplace transforms involved with Fourier cosine transform; these results provide few algorithms for evaluating some n-dimensional Laplace transform pairs. In addition, some examples are also presented, which explain the useful applications of the obtained results. Therefore, one can produce some two- and three- as well as n-dimensional Laplace transforms pairs.

Modeling electro-osmotic flow and thermal transport of Caputo fractional Burgers fluid through a micro-channel

2021 ◽  
pp. 095440892110259
Author(s):  
Mohammed Abdulhameed ◽  
Garba Tahiru Adamu ◽  
Gulibur Yakubu Dauda
Keyword(s):  
Electric Field ◽  
Laplace Transform ◽  
Inverse Laplace Transform ◽  
Micro Channel ◽  
Osmotic Flow ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Burgers Fluid ◽  
Electro Osmotic Flow

In this paper, we construct transient electro-osmotic flow of Burgers’ fluid with Caputo fractional derivative in a micro-channel, where the Poisson–Boltzmann equation described the potential electric field applied along the length of the microchannel. The analytical solution for the component of the velocity profile was obtained, first by applying the Laplace transform combined with the classical method of partial differential equations and, second by applying Laplace transform combined with the finite Fourier sine transform. The exact solution for the component of the temperature was obtained by applying Laplace transform and finite Fourier sine transform. Further, due to the complexity of the derived models of the governing equations for both velocity and temperature, the inverse Laplace transform was obtained with the aid of numerical inversion formula based on Stehfest's algorithms with the help of MATHCAD software. The graphical representations showing the effects of the time, retardation time, electro-kinetic width, and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameters on the temperature distribution in the micro-channel were presented and analyzed. The results show that the applied electric field, electro-osmotic force, electro-kinetic width, and relaxation time play a vital role on the velocity distribution in the micro-channel. The fractional parameters can be used to regulate both the velocity and temperature in the micro-channel. The study could be used in the design of various biomedical lab-on-chip devices, which could be useful for biomedical diagnosis and analysis.

Systems Actuated by Shape Memory Alloys: Identification and Modeling

2021 ◽  
Vol 1 (2) ◽  
pp. 12-20
Author(s):  
Najmeh Keshtkar ◽  
Johannes Mersch ◽  
Konrad Katzer ◽  
Felix Lohse ◽  
Lars Natkowski ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Numerical Simulations ◽  
Shape Memory ◽  
Transfer Equation ◽  
Mechanical Parameters ◽  
Heat Transfer Equation ◽  
The Mathematical Model

This paper presents the identification of thermal and mechanical parameters of shape memory alloys by using the heat transfer equation and a constitutive model. The identified parameters are then used to describe the mathematical model of a fiber-elastomer composite embedded with shape memory alloys. To verify the validity of the obtained equations, numerical simulations of the SMA temperature and composite bending are carried out and compared with the experimental results.

scholarly journals Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 777-780
Author(s):  
Huan Sun ◽  
Xing-Hua Liu
Keyword(s):  
Heat Transfer ◽  
Laplace Transform ◽  
Series Expansion ◽  
Transfer Equation ◽  
Expansion Method ◽  
Cantor Sets ◽  
Heat Transfer Equation ◽  
Local Fractional Calculus ◽  
The Laplace Transform ◽  
Series Expansion Method

In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

scholarly journals Temperature distribution in the three-layered upper mantle beneath a continent

2021 ◽  
Vol 2119 (1) ◽  
pp. 012006
Author(s):  
A G Kirdyashkin ◽  
A A Kirdyashkin ◽  
A V Borodin ◽  
V S Kolmakov
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Convective Heat Transfer ◽  
Upper Mantle ◽  
Lower Mantle ◽  
Transfer Equation ◽  
Horizontal Layer ◽  
Heat Transfer Equation ◽  
Continental Lithosphere ◽  
Conduction Heat Transfer

Abstract Temperature distribution in the upper mantle underneath the continent, as well as temperature distribution in the lower mantle, is obtained. In the continental lithosphere, the solution to the heat transfer equation is obtained in the model of conduction heat transfer with inner heat within the crust. To calculate the temperature distribution in the upper and lower mantle, we use the results of laboratory and theoretical modeling of free convective heat transfer in a horizontal layer heated from below and cooled from above.

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