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Thermal Analysis of Natural Convection in Porous Fins with Homotopy Perturbation Method (HPM)

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Abstract

In this paper, porous fin has been studied and its nonlinear ordinary differential equation has been solved through homotopy perturbation method. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants, which can be determined by imposing the boundary and initial conditions. To study the thermal performance, one type case is considered: finite-length fin with insulated tip.

Abbreviations

k:

Thermal conductivity

Da:

Darcy number, K/t2

Kr:

Thermal conductivity ratio, (k eff /k f )

K:

Permeability of porous fin

L:

Length

m:

convection parameter

q:

Heat transfer rateα

Ra:

Rayleigh number, Gr × Pr

Sh:

Porous parameter

T(x):

Temperature at any point

Tb:

Temperature at fin base

t:

Thickness of the fin

ν W(x) :

Velocity of fluid passing through the fin anypoint

W:

Width of the fin

x:

Axial coordinate

X:

Dimensionless axial coordinate, (x/L)

θ :

Dimensionless temperature

θb:

Base temperature difference, (Tb–T∞)

s:

Solid properties

f:

Fluid properties

eff:

Porous properties

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Correspondence to Majid Shahbabaei.

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Saedodin, S., Shahbabaei, M. Thermal Analysis of Natural Convection in Porous Fins with Homotopy Perturbation Method (HPM). Arab J Sci Eng 38, 2227–2231 (2013). https://doi.org/10.1007/s13369-013-0581-6

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Keywords

  • Porous fin
  • Homotopy perturbation method (HPM)
  • Nonlinear ordinary differential equation
  • Finite-length fin with insulated tip