• Journal of Advanced Marine Engineering and Technology
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• 제40권5호
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• pp.389-396
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• 2016

The theory of Fourier heat conduction predicts accurately the temperature profiles of a system in a non-equilibrium steady state. However, in the case of transient states at the nanoscale, its applicability is significantly limited. The limitation of the classical Fourier's theory was overcome by C. Cattaneo and P. Vernotte who developed the theory of non-Fourier heat conduction in 1958. Although this new theory has been used in various thermal science areas, it requires considerable mathematical skills for calculating analytical solutions. The aim of this study was the identification of a newer and a simpler type of solution for the hyperbolic partial differential equations of the non-Fourier heat conduction. This constitutes the first trial in a series of planned studies. By inspecting each term included in the proposed solution, the theoretical feasibility of the solution was achieved. The new analytical solution for the non-Fourier heat conduction is a simple exponential function that is compared to the existing data for justification. Although the proposed solution partially satisfies the Cattaneo-Vernotte equation, it cannot simulate a thermal wave behavior. However, the results of this study indicate that it is possible to obtain the theoretical solution of the Cattaneo-Vernotte equation by improving the form of the proposed solution.

• Journal of Advanced Marine Engineering and Technology
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• 제32권5호
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• pp.684-690
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• 2008

In most engineering applications related with the heat conduction phenomena, a conventional Fourier heat conduction equation has been successfully applied and it has supplied quite reasonable results. However, it is well known that the Fourier heat conduction equation is failed in the application to the extremely small space and short time, in other words, a nano-scale system and a pico-second time. In this study, non-Fourier effect was evaluated in the heat conduction by considering the concept of a phase lag model. The results show the existence of a heat wave, which means that the heat is transferred with a finite speed while an infinite speed of heat transfer is assumed in the conventional Fourier heat conduction. In addition, the copper and the gold are tested to evaluate the phase lag time between the heat flux and the temperature gradient. The results show that the gold has the heat wave speed faster than that of the copper consistent with the prediction based on an actual experiment.

• 한국마린엔지니어링학회:학술대회논문집
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• 한국마린엔지니어링학회 2005년도 후기학술대회논문집
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• pp.37-38
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• 2005

Although the law of classical fourier heat conduction predicts the heat conduction phenomena occurred in most engineering fields with a good accuracy, it is also well-known that the conventional fourier law of a heat conduction has an application limit when the heating and cooling are periodic for a short duration or when the heat conduction is analyzed in the extremely low temperature region. This application limit of classical fourier law results from the fact that it assumed the infinite speed of a heat wave. In this study, we investigated the feasibility of whether the molecular dynamics could be used to calculate the speed of a heat wave through a solid. The calculated sound velocity showed a good agrement with the theoretical prediction qualitatively. From the calculated results, we confirmed that the same methodology can be applied the evaluation of the speed of a heat wave.

• 한국자동차공학회논문집
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• 제5권4호
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• pp.219-224
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• 1997

A transient short-hot-wire technique has been presented for simultaneous measurements of the thermal conductivity and diffusivity of fluids under the microgravity condition. Two-dimensional heat conduction equations for concentric cylinders with various radius ration and length-diameter ratio have been solved numerically by taking account of the heat capacity of the inner cylinder. A unique relation between the non-dimensional temperature of inner cylinder and Fourier number is obtained for a wide range of thermal properties of the fluids, because the relation if found to be almost independent of these properties. Then the characteristic could be utilized as a masterplot to evaluate both the thermal conductivity and diffusivity. In principle, this method is proved to have an error within 1% for both of these properties.

• Structural Engineering and Mechanics
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• 제56권1호
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• pp.137-156
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• 2015

In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.