A Study on Convective-Radial Fins with Temperature-dependent Thermal Conductivity and Internal Heat Generation

Trushit Patel,Ramakanta Meher

doi:10.1515/nleng-2017-0135

Abstract

Abstract In this paper, the temperature distribution in a convective radial fins is analyzed through a fractional order energy balance equation with the consideration of internal heat generation and temperature dependent thermal conductivity. Adomian decomposition Sumudu transform method is used to study the influence of temperature distribution and the efficiency of radial fins for different values of thermal conductivity and to determine the role of thermal conductivity, thermo-geometric fin parameter as well as fractional order values in finding the temperature distribution and the fin efficiency of the convective radial fins. Finally, the efficiency of this proposed method has been studied by comparing the obtained results with the classical order results obtained by using numerical method and Variational Iteration Method (Coskun and Atay, 2007).

Highlights

Extended surfaces, called ns, are used to elevate the heat transfer rate involving a hot body and its surrounding environment and can be modelled in various geometrical shapes such as rectangular, trapezoidal, triangular, and cylindrical
In this paper, the temperature distribution in a convective radial ns is analyzed through a fractional order energy balance equation with the consideration of internal heat generation and temperature dependent thermal conductivity
Adomian decomposition Sumudu transform method is used to study the in uence of temperature distribution and the e ciency of radial ns for different values of thermal conductivity and to determine the role of thermal conductivity, thermo-geometric n parameter as well as fractional order values in nding the temperature distribution and the n e ciency of the convective radial ns

Summary

Introduction

Extended surfaces, called ns, are used to elevate the heat transfer rate involving a hot body and its surrounding environment and can be modelled in various geometrical shapes such as rectangular, trapezoidal, triangular, and cylindrical. Aziz and Torabi [2] considered the simultaneous variation of surface emissivity with heat transfer coe cient, temperature and thermal conductivity and studied the convective–radiative ns numerically. They [3] employed DTM to analyze the e ciency of a T-shape n of combined radiation, convection and with thermal performance. Patel and Meher [8, 9], introduced ADSTM which is a combination of Adomian Decomposition Method [10] and Sumudu transform method They studied temperature distribution and n e ciency in convective n with internal heat generation and porous n with di erent fractional order values. They [12] carried out induced magnetic eld e ect on stagnation ow of a TiO -Cu/water hybrid nano uid over a stretching sheet Ghadikolaei et al [13] used AGM to analyze unsteady MHD Eyring-Powell squeezing ow in stretching channel with considering Joule heating and thermal radiation effect

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Conclusion