scholarly journals Heat transfer analysis in stretching/shrinking rectangular fin with convection and radiation

2021 ◽  
Author(s):  
Sharif Ullah ◽  
Amir Ali ◽  
Zia Din
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Analytical Solution ◽  
Heat Transfer Analysis ◽  
Combined Effects ◽  
Transform Method ◽  
Differential Transform ◽  
Effects Of Radiation ◽  
The Impact ◽  
Good Agreement

The aim of this work is to enhance the heat transfer and study the efficiency of stretching/shrinking, radiating and rectangular fins. The effect of the dimensionless parameters, that is, radiation-conduction, convection-conduction stretching, thermo-geometric parameters as well as the Peclet number, and surface temperature are investigated on the efficiency of stretching/shrinking and rectangular fins. The considered model is studied analytically using Differential Transform Method (DTM). The result is analyzed with the numerical solution for the accuracy of the semi-analytical solution, where good agreement is obtained. The impact of the considered parameters is studied numerically on the temperature distribution, fin’s tip temperature, and the efficiency of the fin, where the combined effects of radiation and stretching/ shrinking enhance the system in the heat transfer with better efficiency. The shrinking of the fin with radiation increases the efficiency as compared to stretching with radiation is observed, which plays a significant role in mechanical engineering.

scholarly journals A Review: Differential Transform Method for Semi-Analytical Solution of Differential Equations

2020 ◽  
Vol 25 (2) ◽  
pp. 122-129
Author(s):  
M.M. Rashidi ◽  
F. Rabiei ◽  
S. Naseri Nia ◽  
S. Abbasbandy
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Differential Equations ◽  
Analytical Method ◽  
Transformation Method ◽  
Differential Transform Method ◽  
Transform Method ◽  
Differential Transform ◽  
Different Types ◽  
Integral Differential Equations

AbstractIn this article, the semi-analytical method known as the Differential Transform Method (DTM) for solving different types of differential equations is reviewed. First, basic definitions and formulas of DTM and Differential Transform-Padé approximation (DTM-Padé), which are used to increase the convergence and accuracy of DTM approximations, are discussed. Then both techniques of DTM and DTM-Padé, which have been successfully applied to partial differential equations, as well as the application of these methods in fluid mechanic and heat transfer are presented. In addition, the extension of DTM for integral differential equations and the fuzzy differential transformation method (FDTM) for fuzzy problems are discussed.

A Study of Transient Heat Transfer through a Moving Fin with Temperature Dependent Thermal Properties

2020 ◽  
Vol 401 ◽  
pp. 1-13
Author(s):  
Luyanda Partner Ndlovu ◽  
Raseelo Joel Moitsheki
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Heat Dissipation ◽  
Numerical Solutions ◽  
Solution Technique ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Transform Method ◽  
Differential Transform ◽  
Numerical Solver

In this article, heat transfer through a moving fin with convective and radiative heat dissipation is studied. The analytical solutions are generated using the two-dimensional Differential Transform Method (2D DTM) which is an analytical solution technique that can be applied to various types of differential equations. The accuracy of the analytical solution is validated by benchmarking it against the numerical solution obtained by applying the inbuilt numerical solver in MATLAB ($pdepe$). A good agreement is observed between the analytical and numerical solutions. The effects of thermo-physical parameters, such as the Peclet number, surface emissivity coefficient, power index of heat transfer coefficient, convective-conductive parameter, radiative-conductive parameter and non-dimensional ambient temperature on non-dimensional temperature is studied and explained. Since numerous parameters are studied, the results could be useful in industrial and engineering applications.

The Significance of Fin Profile and Convective-Radiative Fin Tip on Temperature Distribution in a Longitudinal Fin

2019 ◽  
Vol 26 ◽  
pp. 93-105
Author(s):  
Partner Luyanda Ndlovu
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Temperature Distribution ◽  
Physical Parameters ◽  
Transform Method ◽  
Wide Range ◽  
Differential Transform ◽  
Nonlinear Transient ◽  
Numerical Solver ◽  
The One

In this article, the one dimensional nonlinear transient heat transfer through fins of rectangular, convex parabolic and concave parabolic is studied using the two dimensional Differential Transform Method (2D DTM). The thermal conductivity and heat transfer coefficient are modeled as linear and power law functions of temperature respectively. The fin tip dissipate heat to the ambient temperature by convection and radiation. A comparison is made between the proposed convectiveradiative fin tip boundary condition and the adiabatic (insulated) fin tip boundary condition which is widely used in literature. It is found that the fin with a convective-radiative tip dissipates heat to the ambient fluid at a faster rate when compared to a fin with an insulated tip. The results further show that the longitudinal fins of parabolic profiles dissipate more heat when compared to the conventional rectangular fin profile. The accuracy of the analytical method is demonstrated by comparing its results with those generated by an inbuilt numerical solver in MATLAB. Furthermore, a wide range of thermo-physical parameters are studied and their impact on the temperature distribution are illustrated and explained.

Semi-analytical treatments of conjugate heat transfer

2012 ◽  
Vol 227 (3) ◽  
pp. 492-503 ◽  
Author(s):  
Mohammad Reza Hajmohammadi ◽  
Seyed Salman Nourazar ◽  
Ali Habibi Manesh
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Temperature Distribution ◽  
Decomposition Method ◽  
Conjugate Heat Transfer ◽  
Adomian Decomposition Method ◽  
Differential Transform Method ◽  
Transform Method ◽  
Adomian Decomposition ◽  
Differential Transform

A new algorithm is proposed based on semi-analytical methods to solve the conjugate heat transfer problems. In this respect, a problem of conjugate forced-convective flow over a heat-conducting plate is modeled and the integro-differential equation occurring in the problem is solved by two lately-proposed approaches, Adomian decomposition method and differential transform method. The solution of the governing integro-differential equation for temperature distribution of the plate is handled more easily and accurately by implementing Adomian decomposition method/differential transform method rather than other traditional methods such as perturbation method. A numerical approach is also performed via finite volume method to examine the validity of the results for temperature distribution of the plate obtained by Adomian decomposition method/differential transform method. It is shown that the expressions for the temperature distribution in the plate obtained from the two methods, Adomian decomposition method and differential transform method, are the same and show closer agreement to the results calculated from numerical work in comparison with the expression obtained by perturbation method existed in the literature.

On Chaotic Behavior of Temperature Distribution in a Heat Exchanger

2017 ◽  
Vol 27 (11) ◽  
pp. 1750168 ◽  
Author(s):  
Morachan Bagyalakshmi ◽  
SaiSundarakrishnan Gangadharan ◽  
Madhu Ganesh
Keyword(s):  
Heat Exchanger ◽  
Temperature Distribution ◽  
Chaotic Behavior ◽  
Temperature Dependent ◽  
Transform Method ◽  
Differential Transform ◽  
Chaotic Nature ◽  
Dependent Transport ◽  
Energy Equations ◽  
Good Agreement

The objective of this paper is to introduce the notion of fractional derivatives in the energy equations and to study the chaotic nature of the temperature distribution in a heat exchanger with variation of temperature dependent transport properties. The governing fractional partial differential equations are transformed to a set of recurrence relations using fractional differential transform method and solved using inverse transform. The approximate analytical solution obtained by the proposed method has good agreement with the existing results.

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