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Heat transfer from convecting-radiating fins of different profile shapes

Wärmeübertragung durch Konvektion und Strahlung bei Rippen mit verschiedenen Profilformen

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Abstract

A finite difference method is used to predict the performance of convecting-radiating fins of rectangular, trapezoidal, triangular, and concave parabolic shapes. The analysis assumes one-dimensional, steady conduction in the fin and neglects radiative exchange between adjacent fins and between the fin and its primary surface. For the range of thermal and geometrical parameters investigated, the variation of heat transfer rate and the fin efficiency with other profile shapes was found to be within 11 percent of the rectangular shape. The effect of profile shape is most pronounced when the Biot number,Bi, and radiation number,N r, are small compared to unity. Because of several limiting assumptions, the results would be used only for preliminary analysis and design particularly when a fin assembly is involved rather than an individual fin.

Zusammenfassung

Ein Finite-Differenzen-Verfahren findet Anwendung zur Berchnung der Wärmeübertragungsleistung mittels Konvektion und Strahlung an Rippen, die rechteckige, trapezförmige, dreieckige und konkav-parabolische Formen besitzen. Die Berechnungen setzen eine eindimensionale, stetige Wärmeleitung in den Rippen voraus und vernachlässigen den Strahlungsaustausch zwischen aneinandergrenzenden Rippen und zwischen den Rippen und ihrer Oberfläche. Für den betrachteten Bereich der thermischen und geometrischen Parameter wurde herausgefunden, daß die Veränderung der Wärmeübertragungsrate und des Rippenwirkungsgrades der anderen Profilformen im Bereich von 11 Prozent im Vergleich zur Rechteckform liegen. Der Einfluß der Profilform ist am stärksten, wenn die Biot-ZahlBi und die StrahlungszahlN r im Vergleich zu 1 klein sind. Aufgrund einiger einschränkender Annahmen sollten die Ergebnisse nur für die Voruntersuchungen und den Vorentwurf benutzt werden, insbesondere wenn es sich um eine Rippenanordnung und nicht um eine Einzelrippe handelt.

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Abbreviations

A (x):

fin cross sectional are atx

Bi :

Biot number based on one half base thickness =h w b/2k

F :

vector representing the finite difference equation

h :

convective heat transfer coefficient

i :

subscript denoting the grid point

J :

Jacobian

k :

thermal conductivity of fin material

L :

fin length

n :

superscript denoting the iteration number

N r :

radiation-conduction number =ε σ w b T 3 b /2k

N R :

alternate radiation-conduction number =2L 2 ε σ T 3 b k w b =α 2 N r

N CV :

alternate convection-conduction number = 2h L 2/k w b =α 2 Bi

q :

heat transfer rate

Q :

dimensionless heat transfer rateQ=q/kT b

T :

temperature

T b :

fin base temperature

T s :

effective sink temperature for radiation

T ∞ :

environment temperature for convection

w b :

fin thickness at the base

w t :

fin thickness at the tip

w(x):

fin thickness at distancex

W(ξ):

dimensionless thickness =w(x)/w b

α :

ratio of length to one-half base thickness = 2L/w b

β :

ratio of tip to base thickness =w t /w b

ε :

surface emissivity

Θ :

dimensionless temperature =T/T b

Θ ∞ :

dimensionless convective environment temperature =T ∞/T b

Θ s :

dimensionless sink temperature for radiation =T s /T b

σ :

Stefan-Boltzmann constant

η :

fin efficiency

ξ :

dimensionless distance =x/L

References

  1. Kraus, A. D.: Sixty-five years of extended surface technology (1922–1987). Appl. Mech. Rev. 41 (1988) 321–364

    Google Scholar 

  2. Cobble, M. H.: Nonlinear fin heat transfer. J. Franklin Inst. 277 (1964) 206–216

    Google Scholar 

  3. Okamoto, Y.: Temperature distribution and efficiency of a single sheet of radiative fin accompanied by an internal heat source. Bull JSME 9 (1964) 143–149

    Google Scholar 

  4. Aziz, A.; Na, T. Y.: Numerical solution of nonlinear fin problems via initial value methods. Letters in Heat and Mass Transfer. 7 (1980) 15–24

    Google Scholar 

  5. Shouman, A. R.: An exact solution for the temperature distribution and radiant heat transfer along a constant cross sectional area fin with finite equivalent surrounding sink temperature. Proc. Ninth Midwestern Mechanics Conf., Madison WI (1965) 175–183

  6. Shouman, A. R.: An exact solution for the temperature distribution and the composite radiation and convection heat exchange along a constant cross sectional area fin. Quart. Appl. Math. 25 (1968) 458–469

    Google Scholar 

  7. Eno, B. E.: Combined convection and radiation from rectilinear fins. Trans. ASHRAE 73 (1967) paper 2022

    Google Scholar 

  8. Sparrow, E. M.; Niewerth, E. R.: Radiating, conducting, and convecting fins. Int. J. Heat Mass Transfer. 11 (1968) 377–379

    Google Scholar 

  9. Bilenas, J. A.; Jiji, L. M.: A perturbation solution for fins with conduction, convection and radiation interaction. AIAA J. 8 (1970) 168–169

    Google Scholar 

  10. Aziz, A.; Benzies, J. Y.: Application of perturbation techniques to heat transfer problems with variable thermal properties. Int. J. Heat Mass Transfer 19 (1976) 271–276

    Google Scholar 

  11. Campo, A.: Variational techniques applied to radiative-convective fins with steady and unsteady conditions. Wärme- und Stoffübertragung 9 (1976) 139–144

    Google Scholar 

  12. Kern, D. Q.; Kraus, A. D.: Extended surface heat transfer. New York: McGraw Hill 1972

    Google Scholar 

  13. Okamoto, Y.: Thermal performance of radiative and convective plate fins with mutual irradiation. Bull JSME 9 (1966) 150–155

    Google Scholar 

  14. Frost, W.; Eraslan, A. H.: Solution of heat transfer in a fin with combined convection and radiative interaction between the fin and the surrounding surfaces. Proc. Heat Transfer and Fluid Mech. Inst. Seattle, WA (1968) 206–216

  15. Manzoor, M.; Ingham, D. B.; Heggs, P. J.: Improved formulations for the analysis of convecting and radiating finned surfaces. AIAA J. 21 (1983) 120–126

    Google Scholar 

  16. Love, T. J.; Francis, J.: A linearized analysis for longitudinal fins with radiative and convective exchange. Second AIAA/ASME Thermophysics and Heat Transfer Conf. Palo Alto, CA (1978) paper 856

  17. Wilkins, Jr., J. E.: Optimum shapes for fins rejecting heat by convection and radiation. J. Franklin Inst. 297 (1974) 1–6

    Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Gonzaga University, 99258-0001, Spokane, WA

    H. Nguyen & A. Aziz

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  1. H. Nguyen
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  2. A. Aziz
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Nguyen, H., Aziz, A. Heat transfer from convecting-radiating fins of different profile shapes. Wärme- und Stoffübertragung 27, 67–72 (1992). https://doi.org/10.1007/BF01590120

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  • DOI: https://doi.org/10.1007/BF01590120

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