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Abstract
This paper analyses heat transfer across straight convecting fins with temperature dependent thermal conductivity and internal heat generation using the Adomian decomposition method (ADM). The ADM is the preferred analytical scheme adopted to provide approximate solutions to nonlinear equations arising from the dependence of thermal conductivity and heat transfer coefficient on temperature distribution. The effect of parameters such as internal heat generation, thermo geometric and thermal conductivity on the temperature profile and heat flux is studied. Where results reveal that thermo geometric parameter and thermal conductivity causes a significant increase in heat transfer across fin base. This study provides useful insight to fins operational performance in applications such as radiators, boilers, refrigeration devices, oil pipelines amongst others. Comparison of solutions with existing works in literature forms good agreement.
Highlights
Overtime fins have found useful applications in heat transfer equipments due to its relatively large area which enhances heat transfer
In efforts to study fins Atay and Coskun [1] presented a comparative analysis of fin efficiency using analytical and numerical techniques to better ascertain the accuracy of the analytical solutions while Chowdhury et al [2] compared analytical solutions for non-linear fin problems applying the homotopy analysis method (HAM) and homotopy pertubation method (HPM) where they showed that the HAM proves to be more accurate
The efficiency of fully wet semi-spherical porous fins was studied by Hatami et al [5] where the effect of porosity is investigated on fins efficiency shortly after numerical and experimental investigation of heat exchangers was presented by Hatami et al [6,7,8] where they optimised the operating condition and were able to recover waste heat from the heat exchangers
Summary
Overtime fins have found useful applications in heat transfer equipments due to its relatively large area which enhances heat transfer. Temperature equation governing the heat transfer problem becomes nonlinear due to its dependence on coefficient of heat transfer and thermal conductivity which makes the exact solutions difficult to obtain. The method of solutions of decomposing nonlinear coupled equations into linear and nonlinear terms makes the Adomian Decomposition Method (ADM) a powerful,yet relatively simplistic method which is not limited by any artificial parameter or initial guess term These makes ADM an interesting scheme in providing analytical solutions to nonlinear problems in science and engineering as often employed by researchers. Adomian decomposition method is adopted in analyzing the coupled nonlinear equation which is used to investigate temperature distribution, heat flux at fins base and effiency. APPLICATION OF ADM The adomian decomposition method (ADM) is adopted in generating solutions to the coupled ordinary nonlinear second order differential equation which may be expressed as: Lxx ( ). Fins efficiency can be obtained upon simplifying the equation 38 which can be shown as,
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