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A numerical study of the thermal performance of fins with time-dependent boundary conditions, including initial transient effects

Numerische Untersuchung des thermischen Verhalten von Rippen mit zeitabhängigen Randbedingungen, einschließlich der anfänglich auftretenden transienten Effekte

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Abstract

A finite-volume numerical model is constructed and applied to evaluate the time-dependent heat-transfer characteristics of longitudinal fins with a rectangular profile. To facilitate comparisons with analytical solutions, the problem is taken to be one-dimensional with constant thermal properties. Two base boundary conditions are considered: (1) a step change and (2) a periodic change in temperature. Parametric studies are carried out to investigate the effects of grid size, time step, fin parameter, Fourier number, amplitude and frequency of base-temperature oscillation on the fin temperature distribution, heat-transfer rate and efficiency. The study shows an excellent agreement between the numerical and analytical results and investigates the importance of the initial transient effects.

Zusammenfassung

Ein numerisches Finit-Volumen-Modell wird aufgestellt und zur Ermittlung des zeitabhängigen Wärmeübergangsverhaltens langer Rechteckrippen herangezogen. Um den Vergleich mit analytischen Lösungen zu erleichtern, soll das Problem eindimensional mit konstanten Stoffwerten vorausgesetzt sein. Als Randbedingungen werden aufgeprägt: (1) ein Temperatursprung und (2) eine periodische Temperaturänderung. Parameterstudien zeigen den Einfluß der Maschenweite, des Zeitschrittes, des Rippenparameters, der Fourierzahl, der Amplitude und Frequenz der Fußtemperaturschwingung auf die Verteilung der Rippentemperatur, des übergehenden Wärmestroms und den Wirkungsgrad. Die Studie ergab ausgezeichnete Übereinstimmung zwischen den numerischen und analytischen Ergebnissen. Ferner wird der Einfluß der anfänglichen transienten Effekte untersucht.

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Abbreviations

A :

dimensionless amplitude of base temperature oscillation

B :

dimensionless frequency,ω L 2/α

c :

specific heat

DT :

a finite increment of time

Fo :

Fourier number,αt/L 2

h :

heat-transfer coefficient

k :

thermal conductivity

L :

fin length

N :

dimensionless fin parameter, (2hL 2/kδ)1/2

NJ :

number of finite-difference grid nodes along the fin

q*:

normalized rate of fin base heat flow,q b /q norm

q :

heat-transfer rate

q norm :

normalizing factor,kδ(T m −T ∞)/L

t :

time

T :

temperature

y :

axial distance along the fin

Y :

dimensionless distance,y/L

α :

thermal diffusivity,k/ϱc

δ :

fin thickness

δt, Δt :

a finite increment of time

δy :

relates to axial dimension of a node, Fig. 1

η :

instantaneous fin efficiency,q b /2hL(T b −T ∞)

ϑ :

=(T−T ∞)/(T b −T ∞), for a sudden change inT b =(T−T ∞)/(T m −T ∞), for a periodic change inT b

ϱ :

density

ω :

frequency of base temperature oscillation

b :

base

i :

initial

m :

mean

∞:

ambient

old:

relates to previous time step

-:

average

References

  1. Yang, J. W.: Periodic heat transfer in straight fins. J. Heat Transfer 94 (1972) 310–314

    Google Scholar 

  2. Suryanarayana, N. V.: Transient response of straight fins. J. Heat Transfer 97 (1975) 417–423

    Google Scholar 

  3. Mujahid, A.: Analysis of performance of a straight fin with oscillating base heat flux and environment temperature. J. Eng. Sci., King Saud University 13(1) (1987) 25–37

    Google Scholar 

  4. Aziz, A.; Na, T. Y.: Steady periodic heat transfer in fins of arbitrary profile. Num. Heat Transfer 3 (1980) 331–344

    Google Scholar 

  5. Mujahid, A.; Abu-Abdou, K.: Thermal performance of annular fins of arbitrary profile subjected to periodic base and environment temperatures. J. King Saud Univ. 5, Eng. Sci. (1) (1993) 105–122

  6. Abu-Abdou, K.; Mujahid, A.: Heat transfer in straight fins of arbitrary profile subjected to periodic base and environment temperatures. Wärme-Stoffübertrag. 24 (1989) 353–361

    Google Scholar 

  7. Myers, G. E.: Analytical methods in conduction heat transfer. New York: McGraw-Hill 1971

    Google Scholar 

  8. Gosman, A. D.; Launder, B. E.; Reece, G. L.: Computer aided engineering heat transfer and fluid flow. Chichester: Ellis Horwood 1985

    Google Scholar 

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Authors and Affiliations

  1. Mechanical Engineering Department College of Engineering, King Saud University, P.O. Box 800, 11421, Riyadh, Saudi Arabia

    S. A. Al-Sanea & A. A. Mujahid

Authors
  1. S. A. Al-Sanea
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  2. A. A. Mujahid
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Al-Sanea, S.A., Mujahid, A.A. A numerical study of the thermal performance of fins with time-dependent boundary conditions, including initial transient effects. Wärme - und Stoffübertragung 28, 417–424 (1993). https://doi.org/10.1007/BF01577883

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  • DOI: https://doi.org/10.1007/BF01577883

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