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.
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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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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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DOI: https://doi.org/10.1007/s13369-013-0581-6