Variation of parameters method for optimizing annular fins with variable thermal properties

Arslantürk, Cihat

doi:10.5505/pajes.2017.78736

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…However, this method also provides the opportunity to be used to solve nonlinear differential equations as mentioned in the literature. [33][34][35][36][37][38][39] Consider the following general nonlinear differential equation to demonstrate the key ideas of this method…”

Section: Variation Of Parameters Methods For Nonlinear Problemsmentioning

confidence: 99%

Performance analysis and optimization of a radiating fin array

Solak

Arslantürk

2022

Proceedings of the Institution of Mechanical Engineers, Part G:

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Space radiators are used to reject waste heat from power units, electronic devices, and various equipment in space vehicles. It is important that radiators can achieve the heat desired to be dissipated into space with the least mass. With a view to ensuring this aim, the heat transfer calculations that must be performed must be highly accurate. Therefore, the variation of conductivity with temperature should also be taken into account in the mathematical model. This paper presents heat transfer performance and optimization of a fin array consisting of straight fins put axially on a tube and radiating heat into deep space. The mathematical model yields the governing equation as a highly nonlinear integro-differential equation which is solved by the variation of parameters method (VPM). By applying an appropriate optimization procedure, the conduction–radiation parameter, Nc, providing maximum heat transfer is obtained for a given fixed fin profile emissivity, ε, opening angle among the fins, γ, and thermal conductivity parameter describing the variation of thermal conductivity, β. For the range of suitable problem parameters, optimum values of the dimensionless conduction–radiation parameter Nc, which is a combination of thermal and geometric quantities, are expressed in ε and γ for a given β. The correlation equations are expected to provide remarkable benefits to the designer.

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Section: Variation Of Parameters Methods For Nonlinear Problemsmentioning

confidence: 99%

Performance analysis and optimization of a radiating fin array

Solak

Arslantürk

2022

Proceedings of the Institution of Mechanical Engineers, Part G:

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“…Moreover, this method is a simple and relatively easy to implement technique for solving nonlinear equations of the complicated problems such as absorbing and emitting non-gray planar media [22]. Arslantürk [23][24][25] investigated the validity of this method to estimate temperature distribution in the solid fins with various geometries and to establish optimal dimensions of a space radiator. Güngör and Arslantürk [26] solved the three--dimensional problem of condensation film on an obliqued rotating disk under the steady-state condition using this method.…”

Section: And Kundumentioning

confidence: 99%

Thermal analysis of longitudinal a porous fin with temperature-dependent internal heat generation using the variation of parameters method

Gungor¹,

Arslantürk²

2020

J. Appl. Math. Comput. Mech.

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The present study investigates the thermal performance of longitudinal a porous fin with temperature-dependent internal heat generation. The Darcy model is utilized to obtain the differential form of the governing equation that solves the nonlinear temperature distribution equation using the method of variation of parameters. Although this method is applied to solve both linear and nonlinear differential equations, there exist rare applications of this method to solve nonlinear heat transfer problems. In the present study, we applied the method to estimate the thermal analysis of the porous fin exposed to convection. The heat generation is assumed as a function of temperature. The effects of the convection parameter , internal heat generation , porosity and generation number parameter on the dimensionless temperature distribution are discussed in detail. The accuracy of the variation of parameters method is verified through comparison with homotopy perturbation method and the Matlab bvp4c solver (NUM). The results have disclosed that the variation of parameters method can be used as a very effective and practical approach for further studies of the porous medium.

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