Radiation from an Array of Gray Circular Fins of Trapezoidal Profile

Schnurr, N.M.; Cothran, C. A.

doi:10.2514/3.49532

Cited by 19 publications

(5 citation statements)

References 7 publications

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“…It can be seen from Table 2 that there is a slight discrepancy between the present results and those of Ref. 2. Because of the high accuracy and rapid convergence of the present finite element, we believe that the results obtained by the present element are more accurate.…”

Section: Radiation From An Array Of Longitudinalcontrasting

confidence: 51%

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Radiation from an Array of Longitudinal Fins of Triangular Profile

Schnurr

1975

AIAA Journal

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TECHNICAL NOTES 691 be one of the nodal parameters and then can be easily satisfied in the usual manner. Numerical Examples and DiscussionUsing the present Galerkin finite element method, the critical loads for three cases of stability of uniform cantilever column subjected to tangential loads, namely: 1) a sub tangential concentrated load P at the free end; 2) a uniformly distributed tangential load of intensity q 0 per unit length; and 3) a triangularly varying distributed tangential load of intensity q, where q = q 0 (\ -x) are obtained. Table 1 gives the critical load parameter A cr for case (1), for various values of y. For the sake of comparison, the results of Ref. 4 and Beck's 6 values for y = 1 are included in this Table. The results indicate that the present results are very accurate even with a two element idealization of the column.

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Section: Radiation From An Array Of Longitudinalcontrasting

confidence: 51%

“…Fins of Triangular Profile Table 2 gives the critical load parameter /, cr for cases (2) and (3) for one and two element idealizations. The results of Ref.…”

Section: Radiation From An Array Of Longitudinalmentioning

confidence: 99%

Radiation from an Array of Longitudinal Fins of Triangular Profile

Schnurr

1975

AIAA Journal

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“…With the advent of space age, space radiators equipped with annular fins of triangular profiles became popular. For example, Schnurr and Cothran [1] used a finite difference approach to study fin-and-tube radiator fitted with annular fins of triangular and trapezoidal profiles and included these effects in their analysis for the fin-to-fin and fin-to-base radiative exchange. http://ppr.buaa.edu.cn/ www.sciencedirect.com Design charts were produced to allow the calculation of heat dissipation for various values of the radiation parameter and the fin radii ratio.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, six new papers that are relevant to the present discussion have appeared in the literature. The problem considered by Schnurr and Cothran [1] has been solved by Hryshchak and Pohrebyts'ka [26] using a double asympto tic expansion. The method, which combines the Poincare small parameter and the method of phase integrals, reduced the mathematical model of the problem to a nonlinear differential equation of second order with variable coeffi cients.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation for a hyperbolic annular fin with temperature dependent thermal conductivity

Darvishi

Khani

Aziz

2016

Propulsion and Power Research

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An annular fin of hyperbolic profile with temperature dependent thermal conductivity is studied by pseudospectral method. Graphs illustrating the effect of fin dimensions, surface convection characteristics and the thermal conductivity parameter on the thermal performance of the fin are presented and discussed. A comparison of the obtained numerical results is made with the closed form analytical solution available in the literature for the case of constant thermal conductivity. This comparison confirms the high accuracy of numerical results. When the thermal conductivity increases with temperature, the effect is to elevate both the temperature distribution in the fin and the fin efficiency. The converse is true when the thermal conductivity decreases with temperature.

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“…In most of the investigations, a finite-difference formulation was employed and the radiosity method 3 was used to solve the problem of multiple reflections within a gray, nonisothermal enclosure. Schnurr and Cothran, 4 and Sparrow and coauthors 5 ' 7 have investigated radiating fin problems of a steady-state nature successfully.…”

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confidence: 98%

Periodic Heat Transfer in Radiating and Convecting Fins or Fin Arrays

Eslinger

Chung

1979

AIAA Journal

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A finite-element solution is presented for the heat transfer from radiating and converting fins or fin arrays. Consideration is given to thin, straight fins attached to a base surface for which the temperature varies periodically. Fin-to-fin, fin-to-base, and fin-to-environment radiative interactions are considered. It is assumed that the radiating surfaces are gray, the environment is black, and the surrounding fluid is transparent. An absorption factor technique is employed for the computation of energy exchange within the nonisothermal enclosure of the fin array.(ff\e (h] I Ie [K\e [K\ k L L' Nomenclature = dimensionless amplitude parameter = surface area fin = dimensionless frequency parameter, uL 2 k/pc p = absorption factor = fin thickness = elemental capacitance matrix = global thermal capacitance matrix = specific heat = displacement matrix, 0 0 1 -/th row [D] e = 0 1 j throw 0 0 = base length between adjacent fins = differential absorption factor = functional to be minimized = elemental form of functional to be minimized = elemental internal heat generation column vector = internal heat generation column vector = elemental global convection matrix = convection column vector = variational statement = elemental form of variational statement = elemental global conduction matrix = global conduction matrix = thermal conductivity = length of fin = length of the fin immediately adjacent to the fin under consideration Received Feb. 2, 1978; presented as Paper 78-893 at the 2nd AIAA/ASME Thermophysics and Heat Transfer Conference, Palo We [R] (r} e [t} e K) u X x ij a e 6 Se P CO Q! X V -number of fin elementŝ convection number, hL 2 Ibk = radiation number, eat s b L 2 /2bk -numerical step size parameter -U x] --total heat transfer from the fin = elemental radiation matrix = global radiation matrix = elemental radiation column vector = radiation column vector = temperature = elemental temperature vector = column vector of nodal temperatures = column vector of temperature time derivatives = an environment temperature = temperature at location x, on the fin = temperature at location Xj on the fin = mean temperature of base surface = first derivative of temperature with respect to location = first derivative of temperature with respect to time = internal heat generation = space coordinates of fin = designates AJ•.-x f = Stef an-Boltzmann constant = surface emissivity = time = Kronecker delta = fin density = circular frequency of base temperature oscillation = thermal dif fusivity = convergence interval = time step designation = radiation fin efficiency = combined mode fin efficiency [ ] = £ [D] e [ } e [D]l global matrix = elemental matrix m = ]C \P\e\ )e» column vector e=7 = elemental column vector = transpose of a matrix = inverse of a matrix Downloaded by PRINCETON UNIV. LIBRARY on August 26, 2014 | http://arc.aiaa.org |

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Radiation from an Array of Gray Circular Fins of Trapezoidal Profile

Cited by 19 publications

References 7 publications

Radiation from an Array of Longitudinal Fins of Triangular Profile

Radiation from an Array of Longitudinal Fins of Triangular Profile

Numerical investigation for a hyperbolic annular fin with temperature dependent thermal conductivity

Periodic Heat Transfer in Radiating and Convecting Fins or Fin Arrays

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