Solving fractal steady heat-transfer problems with the local fractional Sumudu transform

The fundamental purpose of this paper is to propose a new Laplace-type integral transform (NL-TIT) for solving steady heat-transfer problems. The proposed integral transform is a generalization of the Sumudu, and the Laplace transforms and its visualization is more comfortable than the Sumudu transform, the natural transform, and the Elzaki transform. The suggested integral transform is used to solve the steady heat-transfer problems, and results are compared with the results of the existing techniques.

Download Full-text

An integral transform applied to solve the steady heat transfer problem in the half-plane

Thermal Science ◽

10.2298/tsci17s1105x ◽

2017 ◽

Vol 21 (suppl. 1) ◽

pp. 105-111

Author(s):

Tongqiang Xia ◽

Shengping Yan ◽

Xin Liang ◽

Pengjun Zhang ◽

Chun Liu

Keyword(s):

Heat Transfer ◽

Half Plane ◽

Laplace Equation ◽

Integral Transform ◽

Transfer Problem ◽

Heat Transfer Problem ◽

Linear Heat ◽

Transfer Problems ◽

Steady Heat

An integral transform operator U[?(t)= 1/? ???? ?(t)?-i?t dt is considered to solve the steady heat transfer problem in this paper. The analytic technique is illustrated to be applicable in the solution of a 1-D Laplace equation in the half-plane. The results are interesting as well as potentially useful in the linear heat transfer problems.

Download Full-text

The integrating factor method for solving the steady heat transfer problems in fractal media

Thermal Science ◽

10.2298/tsci16s3729c ◽

2016 ◽

Vol 20 (suppl. 3) ◽

pp. 729-733

Author(s):

Shan-Xiong Chen ◽

Zhi-Hao Tang ◽

Hai-Ning Wang

Keyword(s):

Heat Transfer ◽

Fractional Derivative ◽

Integrating Factor ◽

Factor Method ◽

Fractal Media ◽

Transfer Equations ◽

Constant Coefficients ◽

Transfer Problems ◽

First Time ◽

Steady Heat

In this paper, we propose the integrating factor method via local fractional derivative for the first time. We use the proposed method to handle the steady heat-transfer equations in fractal media with the constant coefficients. Finally, we discuss the non-differentiable behaviors of fractal heat-transfer problems.

Download Full-text

Connections between Aboodh Transform and Some Effective Integral Transforms

International Journal of Innovative Technology and Exploring Engineering - Special Issue ◽

10.35940/ijitee.a4262.119119 ◽

2019 ◽

Vol 9 (1) ◽

pp. 1465-1470

Keyword(s):

Heat Transfer ◽

Signal Processing ◽

Laplace Transform ◽

Integral Transforms ◽

Research Paper ◽

Electrical Networks ◽

Sumudu Transform ◽

Transfer Problems ◽

Bending Of Beams

Integral transforms are the most useful techniques of the mathematics which are used to finding the solution of heat transfer problems, mixing problems, electrical networks, bending of beams, signal processing problems, which generally appears in the various disciplines of engineering and sciences. In this research paper, connections between Aboodh transform and some effective integral transforms (Laplace transform, Kamal transform, Elzaki transform, Sumudu transform, Mahgoub transform, Mohand transform and Sawi transform) are discussed and integral transforms of some typical functions are given in table form in application section to signify the fruitfulness of connections between Aboodh transform and some effective mention integral transforms.

Download Full-text

A Thermal Resistance Model for Problems Involving Chemical Reactions and Phase Transition

Journal of Heat Transfer ◽

10.1115/1.4036087 ◽

2017 ◽

Vol 139 (8) ◽

Author(s):

Yoash Mor ◽

Alon Gany

Keyword(s):

Heat Transfer ◽

Phase Transition ◽

Thermal Resistance ◽

Chemical Reactions ◽

Heat Sources ◽

Resistance Model ◽

Resistance Approach ◽

Transfer Problems ◽

Thermal Resistors ◽

Steady Heat

This paper formulates a modified thermal resistance model (MTRM) for dealing with heat transfer situations involving heat sources from chemical reactions or phase transition. The modified thermal resistance model describes the various heat transfer mechanisms by three common thermal resistors, radiation, convection, and conduction (in media with no internal mass diffusion), adding a new coupled thermal resistor that stands for conduction and enthalpy flow in the gas phase. Similarly to the classical thermal resistance approach, the present model is valid for one-dimensional, quasi-steady heat transfer problems, but it can also handle problems with an internal chemical heat generation source. The new thermal resistance approach can be a useful modular tool for solving relatively easily and quickly complex problems involving chemical reactions and phase transition, such as combustion problems.

Download Full-text