• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.23 no.12
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• pp.821-827
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• 2011

A simple analytical model has been developed from the approximate solution of the governing equations for desiccant wheels. The model has been compared with a numerical twodimensional transient model and found capable of making realistic prediction. The analytical model will be further developed to provide simple effectiveness correlations which can be useful for the rough design or long-term simulation of the desiccant wheels in DEC systems.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.12
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• pp.1726-1734
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• 1998

This paper focuses on the unsteady close-contact melting phenomenon occurring between a phase change material kept at its melting temperature and a flat surface on which constant heat flux is imposed. Based on the same simplifications and framework of analysis as the case of constant surface temperature, an approximate analytical solution which depends only on the liquid-to-solid density ratio is successfully derived. In order to keep consistency with the known solution procedure, both the dimensionless wall heat flux and the Stefan number are properly redefined. The obtained solution proves to agree quite well with the published numerical data and to be capable of resolving the fundamental features of unsteady close-contact melting, especially in the presence of the solid-liquid density difference. The density ratio directly affects the film growth rate and the initial value of solid descending velocity, thereby controlling the duration of unsteady process. The effects of other parameters can be evaluated readily from the steady solution which is implied in the normalized result. Since the dimensionless surface temperature for the present boundary condition increases from zero to unity along the evolution path of the liquid film thickness, the unsteady process lasts longer than that for the case of isothermal heating.

• Steel and Composite Structures
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• v.26 no.4
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• pp.453-461
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• 2018

In this paper, nonlinear vibrations of the unsymmetrical laminated composite beam (LCB) on a nonlinear elastic foundation are studied. The governing equation of the problem is derived by using Galerkin method. Two different end conditions are considered: the simple-simple and the clamped-clamped one. The Hamiltonian Approach (HA) method is adopted and applied for solving of the equation of motion. The advantage of the suggested method is that it does not need any linearization of the problem and the obtained approximate solution has a high accuracy. The method is used for frequency calculation. The frequency of the nonlinear system is compared with the frequency of the linear system. The influence of the parameters of the foundation nonlinearity on the frequency of vibration is considered. The differential equation of vibration is solved also numerically. The analytical and numerical results are compared and is concluded that the difference is negligible. In the paper the new method for error estimation of the analytical solution in comparison to the exact one is developed. The method is based on comparison of the calculation energy and the exact energy of the system. For certain numerical data the accuracy of the approximate frequency of vibration is determined by applying of the suggested method of error estimation. Finally, it has been indicated that the proposed Hamiltonian Approach gives enough accurate result.

• Steel and Composite Structures
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• v.44 no.4
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• pp.531-543
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• 2022

An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.9 no.1
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• pp.43-54
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• 1997

This paper presents an approximate analytical solution to a two-region one-dimensional model for the charging process of stratified thermal storage tanks with variable inlet temperature in the presence of momentum-induced mixing. Based on the superposition principle, an arbitrary-varying inlet temperature is decomposed into inherent discontinuous steps and continuous intervals approximated as a finite number of piecewise linear functions. This approximation allows the temperature of the upper perfectly-mixed layer to be expressed in terms of constant, linear and exponential functions with respect to time. Applying the Laplace transform technique to the model equation for the lower thermocline layer subject to each of three representative interfacial conditions yields compact-form solutions, a linear combination of which constitutes the final temperature profile. A systematic method for deriving solutions to the plug-flow problem having polynomial-type boundary conditions is also established. The effect of adiabatic exit boundary on solution behaviors proves to be negligible under the actual working conditions, which justifies the assumption of semi-infinite domain introduced in the solution procedure. Finally, the approximate solution is validated by comparing it with an exact solution obtained for a specific variation of inlet temperature. Excellent agreements between them suffice to show the necessity and utility of this work.

• Geomechanics and Engineering
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• v.3 no.1
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• pp.17-28
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• 2011

This paper presents an analytical solution for steady state flow into a close-ended cylindrical permeameter. The soil medium is considered to be uniform, isotropic, and of infinite thickness. Laplace equation is solved by considering rotational symmetry and by using curvilinear coordinates obtained from conformal mapping. The deduced shape factors, which are compared to approximate relationships obtained from both numerical and physical modelling, and idealizations involving ellipsoidal cavities, are proposed for use in field measurements. It is shown that some of the shape factors obtained are significantly different from published values and show a much higher dependence of the rate of flow on the aspect ratio, than deduced from approximate solutions.

• Geomechanics and Engineering
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• v.3 no.2
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• pp.109-116
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• 2011

This note presents an analytical solution for the determination of the shape factor of a flush bottom piezometer in a uniform, isotropic, and incompressible deep soil deposit. The deduced shape factor is compared to published values obtained by approximate methods. Depending on the selected value, the difference may reach 11%.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.853-862
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• 2014

In this paper, two approximate analytical methods have been applied to forced nonlinear vibration problems to assess a high accurate analytical solution. Variational Iteration Method (VIM) and Perturbation Method (PM) are proposed and their applications are presented. The main objective of this paper is to introduce an alternative method, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Some patterns are illustrated and compared with numerical solutions to show their accuracy. The results show the proposed methods are very efficient and simple and also very accurate for solving nonlinear vibration equations.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.11
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• pp.3655-3665
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• 1996

An analytical solution is presented for the conduction-dominated solidification of a binary mixture in a semi-infinite medium. The present approach differs from that of other solution by these four characteristics. (1) Solid fraction is determined from the phase diagram, (2) thermophysical properties in mushy zone are weighted according to the local solid fraction, (3) non-equilibrium solidification can be simulated and (4) the cooling condition of under-eutectic temperature can be simulated. Up to now, almost all analyses are based on the assumption of constant properties in mushy zone and solid fraction linearly with temperature or length. The validation for these assumptions, however, shows that serious error is found except some special cases. The influence of microscopic model on the macroscopic temperature profile is very small and can be ignored. But the solid fraction and average solid concentration which directly influence the quality of materials are drastically changed by the microscopic models. An approximate solution using the method of weighted residuals is also introduced and shows good agreement with the analytical solution. All calculations are performed for NH$_{4}$Cl-H$_{2}$O and Al-Cu system.