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One-dimensional finite element heat transfer solution of a fin with triangular perforations of bases parallel and towered its base

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Abstract

Heat transfer dissipation from a horizontal rectangular fin embedded with equilateral triangular perforations is computed numerically using one-dimensional finite element technique. The bases of the triangles are parallel and toward the fin base. The body of the fin is discretized into a number of subdivisions (finite elements). The number of these elements can be altered as required according to the automatic mesh generation. The heat dissipation of the perforated fin is computed and compared with that of the solid one of the same dimensions and same thermal properties. The comparison refers to acceptable results and heat dissipation enhancement due to certain perforation.

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Abbreviations

A:

cross sectional area of the solid fin (m2)

A c :

cross sectional area of the triangle perforation (m2)

A e :

cross sectional area of the finite element (m2)

A pc :

area of the inner surface of the perforation (m2)

A ps :

area of the perforated surface of the fin (m2)

b :

triangle perforation dimension (m)

h :

heat transfer coefficient (W/m2°C)

h pc :

heat transfer coefficient of the inner surface of the perforation (W/m2°C)

h ps :

heat transfer coefficient of the perforated surface of the fin (W/m2 °C)

h s :

heat transfer coefficient of surface of the two sides of the fin (W/m2 °C)

h t :

heat transfer coefficient of the fin tip (W/m2 °C)

k :

thermal conductivity of fin material (W/m °C)

L :

fin length (m)

l :

vector unit (m)

Le:

finite element length (m)

N :

number of perforations

P :

fin perimeter (m)

Pe:

finite element perimeter (m)

Q :

fin heat dissipation rate (W)

RQF:

ratio of heat dissipation rate of perforated fin to that of non-perforated (solid) one

S :

perforation spacing (m)

t :

fin thickness (m)

Ve:

finite element volume (m 3)

W :

fin width (m)

b:

fin base

e:

finite element

max:

maximum

pf:

perforated fin

pc:

inner surface of the perforation (lining surface of the perforation)

ps:

perforated surface which is the remaining solid portion of the perforated fin

s:

solid surfaces of the fin sides

sf:

solid (non-perforated) fin

t:

fin tip

x :

in or along the direction of x-axis

y :

in or along the direction of y-axis

z :

in or along the direction of z-axis

∞:

ambient

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Authors and Affiliations

  1. Mechanical Engineering Department, Al-Huson University College, Al-Balqa Applied University, Al-Huson-Irbid, P. O. Box 50, Salt, Jordan

    Abdullah H. M. AlEssa

Authors
  1. Abdullah H. M. AlEssa
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Correspondence to Abdullah H. M. AlEssa.

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AlEssa, A.H.M. One-dimensional finite element heat transfer solution of a fin with triangular perforations of bases parallel and towered its base. Arch Appl Mech 79, 741–751 (2009). https://doi.org/10.1007/s00419-008-0250-5

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  • DOI: https://doi.org/10.1007/s00419-008-0250-5

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