Inverse Determination of Thermal Conductivity in Functionally Graded Material Plates with a Prescribed Temperature Distribution

Excess fin length results in material waste and additional weight leading to increased cost with no benefit in return. Moreover, extra fin length affects the overall performance of the fin as fluid motion is suppressed, resulting in reduced convective heat transfer coefficient. To achieve a miniaturised system with effective cooling, the determination of appropriate length of extended surfaces becomes a key performance and fabrication process factor. Therefore, the present work aims at determining the proper or effective length of a convective-radiative moving fin of functionally graded material under the influence of a magnetic field. The developed governing equation of the analysis is solved analytically with the aid of Kummer’s function. The analytical solutions are used to investigate the effects of non-homogeneity, convective, radiative and magnetic parameter on the thermal performance and the proper fin length. The present study is hoped to assist in making cost-effective decisions on designing cooling approaches for different consumer electronics and high-power systems under various operating conditions.

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Study on the thermal conductivity of diamond-like carbon functionally graded material on copper substrate

Acta Physica Sinica ◽

10.7498/aps.61.058102 ◽

2012 ◽

Vol 61 (5) ◽

pp. 058102

Author(s):

Wang Jing ◽

Liu Gui-Chang ◽

Li Hong-Ling ◽

Hou Bao-Rong

Keyword(s):

Thermal Conductivity ◽

Functionally Graded Material ◽

Copper Substrate ◽

Functionally Graded ◽

Diamond Like Carbon ◽

Graded Material

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Free vibration behavior of tapered functionally graded material beam in thermal environment considering geometric non-linearity, shear deformability and temperature-dependent thermal conductivity

Proceedings of the Institution of Mechanical Engineers Part L Journal of Materials Design and Applications ◽

10.1177/1464420718759376 ◽

2018 ◽

Vol 233 (7) ◽

pp. 1429-1448

Author(s):

Amlan Paul ◽

Debabrata Das

Keyword(s):

Thermal Conductivity ◽

Free Vibration ◽

Functionally Graded Material ◽

Functionally Graded ◽

Temperature Dependent ◽

Graded Material ◽

Post Buckling ◽

Clamped Beams ◽

Steady State Heat ◽

Temperature Dependent Thermal Conductivity

An improved mathematical model is presented to investigate the free vibration behavior of post-buckled tapered functionally graded material beam, subjected to uniform temperature rise and steady-state heat conduction. The material properties including the thermal conductivity are considered to be temperature-dependent and an iterative algorithm for solving temperature-dependent steady-state heat conduction equation is presented to get the correct temperature profile. The initial static post-buckling problem is formulated using minimum potential energy principle and the subsequent free vibration problem is formulated using Hamilton’s principle by employing the tangent stiffness of the post-buckled configuration. The solution of the governing equations is obtained using Ritz method. Following Timoshenko beam theory, a geometrically non-linear mathematical model is developed by employing the non-linear strain–displacement relationships for both normal and shear strains. The study is carried out for both hinged–hinged and clamped–clamped beams. Non-dimensional load–frequency behaviors are presented for different gradation indices, taperness parameters, and length–thickness ratios. Static post-buckling equilibrium path for clamped–clamped beams is also presented. The significant effects of shear non-linearity and temperature-dependent thermal conductivity on dynamics of tapered functionally graded material beam are shown in the paper.

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