Analytical Solution for Convective–Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

Abstract

In this article, heat transfer in a moving fin with variable thermal conductivity, which is losing heat by simultaneous convection and radiation to its surroundings, is analyzed. The calculations are carried out by using the differential transformation method (DTM) which is an analytical solution technique that can be applied to various types of differential equations. The effects of parameters such as the Peclet number, Pe, thermal conductivity parameter, a, convection-conduction parameter, N c , radiation-conduction parameter, N r , dimensionless convection sink temperature, θ a , and dimensionless radiation sink temperature, θ s , on the temperature distribution are illustrated and explained. The analytical solution is found to be in good agreement with the direct numerical solution. Moreover, the results demonstrate that the DTM is very effective in generating analytical solutions for even highly nonlinear problems.

Dynamic model of large amplitude vibration of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

“…So, many new techniques have appeared in the open literature such as: variational iteration method (He, 2007a;Barari et al, 2011), homotopy perturbation method Saravi et al, 2013), homotopy analysis method (Liao, 2003;Khan et al, 2012)and some other methods Ghasempoor et al, 2102;Akbarzade and Khan, 2012;Alinia et al, 2011;Ganji, 2012;Torabi et al, 2012; …”

“…So, many new techniques have appeared in the open literature such as: variational iteration method (He, 2007a;Barari et al, 2011), homotopy perturbation method Saravi et al, 2013), homotopy analysis method (Liao, 2003;Khan et al, 2012)and some other methods Ghasempoor et al, 2102;Akbarzade and Khan, 2012;Alinia et al, 2011;Ganji, 2012;Torabi et al, 2012;Sheikholeslami et al, 2012a;2012b;Bayat et al, 2011;Rafieipour et al, 2012;Marinca and Herisanu, 2010;Salehi et al, 2012;Hamidi et al, 2012) The variational iteration method (VIM) and variational approach (VA) which were introduced by 2007a;2007b) are very powerful methods in solving non-linear differential equations and studying nonlinear vibration of beams. The Variational Approach which is also called He's variational approach, as well as the variational iteration method, was utilized here to obtain the analytical expression for the following model of nonlinear oscillations in the structural engineering problems:…”

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

“…For all results reported in Figures 5-11 the DTM results were checked against NS which were in excellent agreement with each other. It would be useful to mention that DTM was tested for moving convective-radiative fins [55] against numerical solution, and results of both methods were in good agreement with each other.…”

Performance of Orthotropic Annular Fins Having Contact Resistance

“…It was compared with the direct numerical solution to validate the accuracy of the analytical results. Torabi and Yaghoobi (2012) studied heat transfer in a moving fin with variable thermal conductivity losing heat by convection and radiation using Differential transformation method (DTM). The results demonstrate that the DTM is very effective in generating analytical solutions for even highly nonlinear problems.…”