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Efficient Iterative Method for Investigation of Convective–Radiative Porous Fin with Internal Heat Generation Under a Uniform Magnetic Field

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Abstract

This paper is aimed at presenting an efficient iterative approach using Daftardar-Gejiji and Jafari method (DJM) for the analysis of thermal behaviour of convective–radiative porous fin with internal heat generation under a uniform magnetic field. The developed heat transfer models are used to investigate the effects of convective, radiative, and magnetic parameters on the thermal performance of the porous fin. From the study, we establish that increase in porosity, convective, radiative and magnetic parameters increase the heat transferred by the fin, which subsequently improves the fin efficiency. In addition, there is significant increase in heat transfer at the base of the fin whenever the thermal conductivity of the fin decreases. The result of DJM is validated by an established result of Adomian decomposition method, and compared with the results of numerical method using first-order Runge–Kutta with shooting method and homotopy analysis method. The comparison shows that Daftardar-Gejiji and Jafari’s method exhibits higher accuracy than the established two results.

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Abbreviations

\( A \) :

Cross-sectional area

\( x \) :

Axial distance of fin

\( w \) :

Width of fin

\( X \) :

Dimensionless length of the fin

\( P \) :

Perimeter of fin

L :

Fin length

U :

Velocity of fin

\( t \) :

Fin thickness

\( Da \) :

Darcy constant

\( g \) :

Gravitational constant

\( P_{e} \) :

Peclet constant

\( R_{a} \) :

Modified Rayleigh number

\( R_{d} \) :

Radiation–condition number

M :

Convective dimensionless parameter

N :

Dimensionless radiation number

\( N_{c} \) :

Dimensionless convective parameter

\( N_{r} \) :

Dimensionless radiative parameter

\( S_{h} \) :

Porosity parameter

J :

Total current density

\( J_{c} \) :

Conduction current density

\( T \) :

Fin temperature

\( T_{b} \) :

Fin base temperature

\( q \) :

Rate of heat transfer

\( q_{c} \) :

Rate of heat transfer by convection

\( q_{r} \) :

Rate of heat transfer by radiation

\( k \) :

Thermal conductivity of fin material

\( k_{a} \) :

Thermal conductivity of fin material at ambient temperature

\( Q \) :

Dimensionless heat transfer rate per unit area

\( h \) :

Coefficient of heat transfer over the fin surface

\( H \) :

Coefficient of dimensionless heat transfer at the fin base

\( \rho \) :

Density of saturates single-phase fluid

\( \dot{m} \) :

Mass flowage of saturated single-phase fluid

\( v_{w} \) :

Velocity of saturated single-phase fluid at any point

K :

Permeability

\( \alpha \) :

Thermal diffusivity of the fin

\( \sigma \) :

Stefan–Boltzmann constant

\( \sigma_{e} \) :

Electric conductivity

\( \lambda \) :

Variable thermal conductivity with temperature

\( \beta \) :

Thermal conductivity parameter or nonlinear parameter

\( q \) :

Heat transfer per unit area

\( \eta \) :

Fin efficiency

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Acknowledgements

This work is supported in part by the European Union’s Horizon 2020 research and innovation programme under Grant Agreement H2020-MSCA-ITN-2016 SECRET-722424. In addition, the authors wish to thank the reviewers for their constructive comments.

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Authors and Affiliations

  1. School of Electrical Engineering, Faculty of Engineering and Informatics, University of Bradford, Bradford, West Yorkshire, UK

    George Oguntala, Raed Abd-Alhameed & Stephen Jones

  2. Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria

    Gbeminiyi Sobamowo

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  1. George Oguntala
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Correspondence to George Oguntala.

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Oguntala, G., Sobamowo, G., Abd-Alhameed, R. et al. Efficient Iterative Method for Investigation of Convective–Radiative Porous Fin with Internal Heat Generation Under a Uniform Magnetic Field. Int. J. Appl. Comput. Math 5, 13 (2019). https://doi.org/10.1007/s40819-018-0592-9

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