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Thermal analysis of porous fins enclosure with the comparison of analytical and numerical methods

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Abstract

In this study, heat transfer though a porous fin with rectangular cross section is investigated. The Darcy model is utilized to simulate heat transfer in this porous media. It is assumed that the fin is one-dimensional, homogenous, the flow is laminar, and the generated heat is a linear function of temperature. In this research, three different analytical methods are used to obtain the temperature distribution after deriving the heat transfer equation. In order to validate the obtained solution the collocation method (CM) is compared with the results by a numerical method, in order to validate the solutions, homotopy perturbation method (HPM) and homotopy analysis method (HAM) are employed. This problem is solved for the general case, and the output is obtained as a relationship for one iteration. The effects of various parameters including convection (Nc), porosity (Sh), Rayleigh number (Ra) are examined in this research.

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Abbreviations

Ra:

Rayleigh number

Sh:

Porosity parameter

Nc:

Convection parameter

Kr :

Ratio of conduction heat transfer

Nr:

Radiation parameter

G :

Dimensionless number of generated heat

ε :

Parameter of internal heat generation

θ :

Parameter of surface temperature

Q :

Heat transfer rate

α :

Thickness ratio

Bi :

Biot number

Θ :

Dimensionless temperature of convection medium

θs:

Dimensionless temperature of sink for radiation

H :

Homotopy method

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Authors and Affiliations

  1. Young Researchers and Elite Club, West Tehran Branch, Islamic Azad University, Tehran, Iran

    S. Hoseinzadeh

  2. Centre for Asset Integrity Management, Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa

    P. S. Heyns

  3. Mechanical Engineering Department, Prince Sultan Endowment for Energy and Environment, Prince Mohammad Bin Fahd University, Al-Khobar, 31952, Saudi Arabia

    A. J. Chamkha

  4. RAK Research and Innovation Center, American University of Ras Al Khaimah, Ras Al Khaimah, United Arab Emirates

    A. J. Chamkha

  5. School of Chemical, Petroleum and Gas Engineering, Iran University of Science and Technology, Tehran, Iran

    A. Shirkhani

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  1. S. Hoseinzadeh
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  3. A. J. Chamkha
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  4. A. Shirkhani
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Correspondence to S. Hoseinzadeh.

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Hoseinzadeh, S., Heyns, P.S., Chamkha, A.J. et al. Thermal analysis of porous fins enclosure with the comparison of analytical and numerical methods. J Therm Anal Calorim 138, 727–735 (2019). https://doi.org/10.1007/s10973-019-08203-x

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