• Journal of Advanced Marine Engineering and Technology
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• v.40 no.5
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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.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.1
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• pp.42-51
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• 1995

In order to establish a theoretical basis for the analyses of transient behaviors in stratified thermal storage tanks, analytical approaches to an improved one-dimensional model are made. In the present model the storage tank is treated as a finite region with an adiabatic tank exit, whereas it has been considered as a simple semi-infinite region previously. Application of the Laplace transformation and the Inversion theorem to the governing equations makes it possible to obtain an exact infinite-series solution, which is convergent only at sufficiently large time. Accordingly a complementary solution which is available for short times, i.e., the time range of this study is sought by an approximate method. The approximate solution which is rigorously validated through the examination of neglected terms in the solution procedure agrees quite well with the exact one. Moreover, it is simpler to use and more convenient to interpret the physical meaning of the solution. Comparison of the present solution with the previous ones shows relatively large difference near the tank bottom, which results from the more realistic boundary condition adopted in the present model. Some representative results by the approximate solution including effects of the Peclet number on temperature distrbutions are illustrated to show the utility of this study. In consequence, it is expected that the present results based on the improved model replace the foregoing ones as a new theoretical reference for studies of thermal stratification fields.

• Steel and Composite Structures
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• v.25 no.2
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• pp.127-139
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• 2017

In this paper, an exact analytical solution for simply supported sandwich plate which considers the permeation effect of adhesives is presented. The permeation layer is described as functionally graded material (FGM), the elastic modulus of which is assumed to be graded along the thickness following the exponential law. Based on the exact three-dimensional (3-D) elasticity theory, the solution of stresses and displacements for each layer is derived. By means of the recursive matrix method, the solution can be efficiently obtained for plates with many layers. The present solution obtained can be used as a benchmark to access other simplified solutions. The comparison study indicates that the finite element (FE) solution is close to the present one when the FGM layer in the FE model is divided into a series of homogeneous layers. However, the present method is more efficient than the FE method, with which the mesh division and computation are time-consuming. Moreover, the solution based on Kirchhoff-Love plate theory is greatly different from the present solution for thick plates. The influence of the thickness of the permeation layer on the stress and displacement fields of the sandwich plate is discussed in detail. It is indicated that the permeation layer can effectively relieve the discontinuity stress at the interface.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.1
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• pp.231-239
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• 1995

This paper describes a computer simulation of the triple effect, water-lithium bromide absorption cooling cycles. The performance of the absorption systems is investigated through cycle simulation to obtain the system characteristics with the cooling water inlet temperature, the working solution concentrations, the ratio of the amount of the weak solution to the high, middle and low temperature generators, and the temperature difference of each solution heat exchanger. The efficiency of different cycles has been studied and the simulation results show that higher coefficient of performance could be obtained for the parallel cycle of constant solution distribution rate. As a result of this analysis, the optimum designs and operating conditions were determined based on the operating conditions and coefficient of performance.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.36D no.1
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• pp.22-28
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• 1999

An exact asymptotic solution for a perfect conducting wedge with H-polarized plane wave incidence is analytically derived by substituting the exact boundary fields of the perfeet conducting wedge, the well known series solution, into the dual integral exquation in the spectral domain. The validity of the derivation is assured by showing that the analytic integration gives the null fields in the complementary region. The merits taking the dual integral equation for derivation of an asymptotic solution for a perfect conduction wedge is discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.949-956
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• 2006

The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

• Steel and Composite Structures
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• v.20 no.5
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• pp.1043-1066
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• 2016

A new analytical solution based on a third order shear deformation theory for the problem of static analysis of cross-ply doubly-curved shells is presented. The boundary-discontinuous generalized double Fourier series method is used to solve highly coupled linear partial differential equations with the mixed type simply supported boundary conditions prescribed on the edges. The complementary boundary constraints are introduced through boundary discontinuities generated by the selected boundary conditions for the derivation of the complementary solution. The numerical accuracy of the solution is compared by studying the comparisons of deflections, stresses and moments of symmetric and anti-symmetric laminated shells with finite element results using commercially available software under uniformly distributed load. Results are in good agreement with finite element counterparts. Additional results of the symmetric and anti-symmetric laminated and sandwich shells under single point load at the center and pressure load, are presented to provide data for the unsolved boundary conditions, benchmark comparisons and verifications.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.11 no.3
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• pp.422-430
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• 1999

This paper concerns the study of a two-stage absorption heat pump cycle to utilize treated sewage. This two-stage cycle consists of coupling double-effect with parallel or series flow type and single effect cycle so that the first stage absorber and condenser produces hot water to evaporate refrigerant in the evaporator of the second stage. The effects of operating variables such as absorber temperature on the coefficient of performance have been studied for two-stage absorption heat pump cycle. The working fluid is lithium bromide and water solution. The efficiency of the two-stage absorption heat pump cycle has been studied and simulation results show that higher coefficient of performance could be obtained for the first stage with parallel flow type. The optimum ratio of solution distribution can be shown by considering the COP, the crystallization of solution and the generator temperature.

• Steel and Composite Structures
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• v.24 no.6
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• pp.659-670
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• 2017

In the present work, an analytical solution for the static analysis of laminated composites, functionally graded and sandwich singly and doubly curved panels on the rectangular plan-form, subjected to uniformly distributed transverse loading is presented. Mathematical formulation is based on the higher order shear deformation theory and principle of virtual work is applied to derive the equations of equilibrium subjected to small deformation. A solution methodology based on the fast converging finite double Chebyshev series is used to solve the linear partial differential equations along with the simply supported boundary condition. The effect of span to thickness ratio, radius of curvature to span ratio, stacking sequence, power index are investigated. The accuracy of the solution is checked by the convergence study of non-dimensional central deflection and moments. Present results are compared with those available in the literature.

• Bulletin of the Korean Chemical Society
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• v.16 no.10
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• pp.938-945
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• 1995

Hydrolysis of p-nitrophenyl acetate (PNPA) and p-nitrophenyldiphenyl phosphate (PNPDPP) by N-chloro compounds in micellar solution were studied. N,N'-dichloroisocyanuric acid sodium salt (DCI) in cetyltrimethylammonium chloride (CTACl) micellar solution gave pseudo first-order kinetics. But, DCI in cetyltrimethylammonium bromide (CTABr) micellar solution showed typical series first-order kinetics - fast hydrolysis of the esters and concomitant slow decay of the hydrolyzed product, p-nitrophenolate. The hydrolysis rate was decreased as the hydrophobicity of N-chloro compounds was increased, which is the opposite trend to the usual bimolecular micellar reaction. This curious behavior of the N-chloro compounds in the catalytic hydrolysis of PNPA and PNPDPP in a cationic micellar system can be best explained by participation of counter ions of the surfactants during hydrolysis.