Ary Conditions Research Articles

A novel semi-coupled solid desiccant heat pump system Part 2: Experimental investigation

A novel semi-coupled solid desiccant heat pump (SCSDHP) system, in which a desiccant coated evaporator (DCE) and a conventional evaporator (CE) operate in series, is proposed to realize high COP and improve thermal comfort. In order to determine the parameters of the heat exchanger and verify the superiority of this system, the simulation model of the system has been established. In this part of study, an experimental setup is built and tested to evaluate performance of SCSDHP system. The results show that the SCSDHP system can supply satisfactory air under the typical ARI conditions. Compared with SDHP system, the supply air temperature is reduced by about 7–8 °C, and the corresponding cooling power is increased by more than 50%. It is noteworthy that the COP of this novel SCSDHP system is still more than 4 which is higher than the traditional vapor compression system. The results also show that this novel system can be applied in a wide range of temperature and humidity, the COP will be higher when applied in higher temperature and humidity ratio.

A stabilized RBF collocation scheme for Neumann type boundary value problems

The numerical solutionof partial dif- ferential equations (PDEs) with Neumann bound- ary conditions (BCs) resulted from strong form collocation scheme are typically much poorer in accuracy compared to those with pure Dirichlet BCs. In this paper, we show numerically that the reason of the reduced accuracy is that Neu- mann BC requires the approximation of the spa- tial derivatives at Neumann boundaries which are significantly less accurate than approximation of main function. Therefore, we utilize boundary treatment schemes that based upon increasing the accuracy of spatial derivatives at boundaries. In- creased accuracy of the spatial derivative approx- imation can be achieved by h-refinement reduc- ing the spacing between discretization points or byincreasingthemultiquadricshape parameter, c. Increasing the MQ shape parameter is very com- putationally cost effective, but leads to increased ill-conditioning. We have implemented an im- proved version of the truncated singular value de- composition (IT-SVD) originated by Volokh and Vilnay (2000) that projects very small singular values into the null space, producing a well con- ditioned system of equations. To assess the pro- posed refinement scheme, elliptic PDEs with dif- ferent boundary conditions are analyzed. Com- parisons that made with analytical solution reveal superior accuracy and computationalefficiency of the IT-SVD solutions.

Thermodynamic Performance Analysis of Eco friendly Refrigerant Mixtures to Replace R22 Used in Air Conditioning Applications

Abstract In the present study theoretical thermodynamic performance of a 0.8 TR window air conditioner with ten binary refrigerant mixtures consists of propylene (R1270) and propane (R290) was investigated based on actual vapour compression refrigeration cycle. All the investigated refrigerant mixtures consist of zero ozone depletion potential. Global warming potential of R22 is 1760 whereas GWP of all the studied refrigerant mixtures were below three and also these mixtures are closer to azeotropic containing the temperature glide below 0.4 o C. Thermodynamic performance of all the refrigerant mixtures are computed at the evaporating and condensing temperatures of 7.2 o C and 54.4 o C (ARI conditions) respectively. The results revealed that the coefficient of performance for the mixture R1270/R290 (75/25 by mass %) was closer to R22. The percentage variation in cop for the mixture R1270/R290 (75/25 by mass %) was least by 0.97% among the ten investigated refrigerant mixtures when compared to R22. Refrigeration capacity of all the considered refrigerant mixtures was similar to that of capacity of refrigerant R22. The compressor discharge temperature for all the studied refrigerants were reduced in the range of 5.6-8.4 o C when compared to the reference refrigerant R22. The power required per ton of refrigeration for the refrigerant mixture R1270/R290 (75/25 by mass %) was least among the ten investigated refrigerant mixtures. Since refrigerant mixtures consist of hydrocarbons, therefore they had better miscibility with the mineral lubricant oil. Overall the thermodynamic performance of a refrigerant mixture R1270/R290 (75/25 by mass %) was nearest to R22 and hence it is a suitable environmentally alternative refrigerant to substitute R22 used in residential air conditioning applications.

Simulation of potential standalone liquid desiccant cooling cycles

LDCS (Liquid desiccant cooling systems), capable of achieving dehumidification and cooling with low-grade heat input, can be effectively used for treating fresh air in hot and humid regions. These can also be operated using non-concentrating solar collectors. The present study is concerned with the evaluation of various potential liquid desiccant cycles for tropical climatic conditions. Six potential standalone liquid desiccant cycles are identified and analyzed to select the best configuration for achieving thermal comfort. A computer simulation model is developed in EES (Equation Solver) software platform to evaluate the performance of all the cycles at various operating conditions. Aqueous solution of LiCl (lithium chloride) is used as desiccant. Mass and energy balance equations of all the components along with their effectiveness and LiCl property correlation equations are solved simultaneously for given ambient conditions. As the desiccant circuit is a closed loop, no assumptions are made about its concentration and temperature in the algorithm. Supply air conditions, cooling capacity, COP (capacity and coefficient of performance) and CR (circulation rate) per unit cooling capacity and hot water temperature requirement are used as a measure for analyzing the performance of the different cycles. The effect of hot water temperature on the performance of the cycles is evaluated at ARI conditions. The performances of the cycles are also evaluated for cities selected from each of the climatic zone of India that represent typical tropical climates. Although all the cycles are feasible at ARI and hot and dry conditions, only two cycles can achieve the selected indoor conditions in the peak humid conditions. The results would be useful for selecting suitable liquid desiccant cycle for a given climate.

Systems of functional-differential equations with maxima, of mixed type

In this paper we study some properties of the solutions of a second order system of functional differential equations with maxima, of mixed type, with bound- ary conditions. We use Perov's fixed point theorem and the weakly Picard operator technique.

Propagation of low-frequency electromagnetic waves across a multilayer cylindrical shell

In the paper the results of the analysis of propaga tion of the low-frequency electromagnetic waves across the multilayer cylindrical shell are presented. The mathematical model of non-local bilateral boundary cond itions of multilayer cylindrical shells was created. These non-local bilateral bound ary conditions describe the penetration of low-frequency electromagnetic waves acr oss layers of the shell. The method of transformation of the boundary problem to the integral Fredholm equations of the second kind was developed. Furthermore, the value of efficiency coefficient of the shell was calculated. Analytical tra nsformations are based on the Bessel functions.

Effect of Prandtl Number on Natural Convection Heat Transfer from a Heated Semi-Circular Cylinder

Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upw ard) has been investigated for the following ranges of conditions ; Grashof number, and Prandtl number. The governing partial different ial equations (continuity, Navier-Stokes and energy equations) ha ve been solved numerically using a finite volume formulation. In a ddition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. Natural convection heat tr ansfer from a heated horizontal semi-circular cylinder (flat surf ace upward) has been investigated for the following ranges of condi tions; Grashof number, and Prandtl number, . The governing part ial differential equations (continuity, Navier-Stokes and energy equ ations) have been solved numerically using a finite volume formu lation. In addition, the role of the type of the thermal bound ary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. The resulting flow and temperature fields are visualized in terms of t he streamline and isotherm patterns in the proximity of the cylinder. The flow remains attached to the cylinder surface over the range of conditions spanned here except that for and ; at these conditions, a separated flow region is observed when the condition of the consta nt wall temperature is prescribed on the surface of the cyl inder. The heat transfer characteristics are analyzed in terms of t he local and average Nusselt numbers. The maximum value of the local Nusselt number always occurs at the corner points whereas it is fo und to be minimum at the rear stagnation point on the flat surface. O verall, the average Nusselt number increases with Grashof number and/ or Prandtl number in accordance with the scaling consideration s. The numerical results are used to develop simple correlations as functions of Grashof and Prandtl number thereby enabling the int erpolation of the present numerical results for the intermediate valu es of the Prandtl or Grashof numbers for both thermal boundary conditions. Keywords—Constant heat flux, Constant surface temperature, Grashof number, natural convection, Prandtl number, Semi-circular cylinder

Boundary waves at the water-sea bottom interface

991 The theory of wave processes in layered media developed in classical works [1–3] is based on the solution of the key boundary problem of hydroacous tics formulated and solved by Pekeris in [1] for a sys tem homogeneous fluid layer–homogeneous fluid half space. A characteristic peculiarity of the model formulation suggested in [1–3] is the fact that bound ary conditions at the interface waveguide–half space are formulated as conditions of local continuity by pressure and the normal component of oscillation velocity (continuity conditions (p, vz)), while the model formulation appears self conjugated. As a con sequence of the assumed model formulation, the power flux through the impedance interface boundary is zero at all incidence angles including subcritical angles, and the wave motion at the impedance bound ary degenerates at small glancing angles due to a mild screen effect. We suggested in [4] a non self conjugated model formulation of boundary problems for layered media and a generalized theory built on its basis. In this model formulation, continuity conditions (p, vz) are satisfied only on average, but the power flux through the impedance boundary is nonzero. It is positively specified at subcritical incidence angles with an alter nating sign, while at supercritical incidence angles, the flux becomes alternating with zero mean value. A bot tom wave of the boundary type is formed at the imped ance boundary as a sequence of the assumed model formulation, which is absent in the classical solution. In the simplest case of spherical wave reflection at the boundary between two half spaces, the level of sound wave inflow into the lower half space z ≥ 0 is determined by the condition of mild screen compen sation by an outflowing nonuniform wave, whose amplitude increases exponentially to the boundary of Boundary Waves at the Water–Sea Bottom Interface

The differentiation of hypoelliptic diffusion semigroups

Basic derivative formulas are presented for hypoelliptic heat semi- groups and harmonic functions extending earlier work in the elliptic case. Fol- lowing the approach of (22), emphasis is placed on developing integration by parts formulas at the level of local martingales. Combined with the optional sampling theorem, this turns out to be an efficient way of dealing with bound- ary conditions, as well as with finite lifetime of the underlying diffusion. Our formulas require hypoellipticity of the diffusion in the sense of Malliavin cal- culus (integrability of the inverse Malliavin covariance) and are formulated in terms of the derivative flow, the Malliavin covariance and its inverse. Finally some extensions to the nonlinear setting of harmonic mappings are discussed.

Multiple positive solutions for second order impulsive boundary value problems in Banach spaces

By means of the fixed point index theory of strict set contraction operators, we establish new existence theorems on multiple positive solutions to a boundary value problem for second-order impulsive integro-differential equations with integral bound- ary conditions in a Banach space. Moreover, an application is given to illustrate the

Scattering from a Metamaterial Hemispherical Boss on an Infinite Plane

An exact solution is presented to the problem of scattering of a plane electromagnetic wave from a metamate- rial hemispherical boss located on an infinite conducting plane, using the method separation of variables. The formulation is based on an image technique, where the original problem is replaced by that of scattering of two plane waves by the corresponding sphere in the absence of the infinite plane. The solution is obtained by expressing all the electromagnetic fields associated with the problem in terms of vector spherical wave functions, and then imposing the appropriate bound- ary conditions. Numerical results are presented as normalized backscattering cross sections for hemispherical bosses of different sizes and types, for both transverse electric and transverse magnetic polarizations of the incident wave.

Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method

A meshless method based on the local Petrov-Galerkin approach is proposed for the solution of steady-state and transient heat conduction problems in a continuously non- homogeneous anisotropic medium. The Laplace transform is used to treat the time dependence of the variables for transient problems. The an- alyzed domain is covered by small subdomains with a simple geometry. A weak formulation for the set of governing equations is transformed into local integral equations on local subdomains by using a unit test function. Nodal points are ran- domly distributed in the 3D analyzed domain and each node is surrounded by a spherical subdo- main to which a local integral equation is applied. The meshless approximation based on the Mov- ing Least-Squares (MLS) method is employed for the implementation. Several example problems with Dirichlet, mixed, and/or convection bound- ary conditions, are presented to demonstrate the veracity and effectiveness of the numerical ap-

A Highly Accurate MCTM for Direct and Inverse Problems of Biharmonic Equation in Arbitrary Plane Domains

Trefftz method (TM) is one of widely used meshless numerical methods in el- liptic type boundary value problems, of which the approximate solution is expressed as a lin- ear combination of T-complete bases, and the un- known coefficients are determined from bound- ary conditions by solving a linear equations sys- tem. However, the accuracy of TM is severely limitedbyitsill-conditioning. Thispaperisacon- tinuation of the work of Liu (2007a). The col- location TM is modified and applied to the di- rect and inverse problems of biharmonic equation in a simply connected plane domain. Due to its well-conditioningoftheresultinglinearequations system, the present modified collocation Trefftz method (MCTM) can effectively solve the inverse problems without needing of overspecified data, iteration, and regularization. So that, the compu- tational cost of MCTM is saving. Numerical ex- amples show the effectiveness of the new method in providing highly accurate numerical solutions even subjectingto large noise of the given bound- ary data.

FDMFS for Diffusion Equation with Unsteady Forcing Function

In this paper, a novel numerical scheme called (FDMFS), which combines the fi- nite difference method (FDM) and the method of fundamental solutions (MFS), is proposed to simulate the nonhomogeneous diffusion problem with an unsteady forcing function. Most mesh- less methods are confined to the investigations of nonhomogeneous diffusion equations with steady forcing functions due to the difficulty to find an unsteady particular solution. Therefore, we pro- posed a FDM with Cartesian grid to handle the unsteady nonhomogeneous term of the equations. The numerical solution in FDMFS is decomposed into a particular solution and a homogeneous so- lution. The particular solution is constructed us- ing the FDM in an artificial regular domain which contains the real irregular domain without bound- ary conditions, and the homogeneous solution can be obtained by the time-space unification MFS in the irregular domain with boundary conditions. Besides, the Cartesian grid for particular solution is very simple to generate automatically. Our pa- per is the first time to propose an algorithm to solve nonhomogeneous diffusion equations with unsteady forcing functions using MFS to solve homogeneous solutions and FDM to calculate the particular solutions. Numerical experiments are presented for 2D problems in regular and irregu- lar domains to show the high performance of this proposed scheme. Moreover, the stabilities of ex- plicit and implicit FDM for particular solution are analyzed. Numerical studies suggest that the pro- posed FDMFS can speed up the simulation and save the CPU time and memory storage substan- tially.

A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain's Characteristic Length

A newly modified Trefftz method is developed to solve the exterior and interior Dirichlet problems for two-dimensional Laplace equation, which takes the characteristic length of problem domain into account. After introducing a circular artificial boundary which is uniquely determined by the physical problem domain, we can derive a Dirichlet to Dirichlet mapping equa- tion, which is an exact boundary condition. By truncating the Fourier series expansion one can match the physical boundary condition as accu- rate as one desired. Then, we use the colloca- tion method and the Galerkin method to derive linear equations system to determine the Fourier coefficients. Here, the factor of characteristic length ensures that the modified Trefftz method is stable. We use a numerical example to ex- plore why the conventional Trefftz method is fail- ure and the modified onestill survives. Numerical examples with smooth boundaries reveal that the present method can offer very accurate numeri- cal results with absoluteerrors about in the orders from 10 −10 to 10 −16 . The new method is pow- erful even for problems with complex boundary shapes, with discontinuous boundary conditions or with corners on boundary. Keyword: Laplace equation, Artificial bound- ary condition, Modified Trefftz method, Char- acteristic length, Collocation method, Galerkin method, DtD mapping

Parameter estimates for linear partial differential equations with fractional boundary noise

Parameter-dependent linear evolution equations with a fractional noise in the bound- ary conditions are studied. Ergodic-type theorems for stationary and non-stationary solutions are verified and used to prove the strong consistency of a suitably defined family of estimators.

Effect of ambient conditions on the first and second law performance of an open desiccant cooling process

An open desiccant cooling process is presented and applied to ventilation and recirculation modes of the system operation. The cooling system consists of a desiccant wheel, a rotary regenerator, two evaporative coolers, and a heating unit. Certain ideal operating characteristics based primarily on the first law of thermodynamics are assumed for each component. The system with indoor and outdoor ARI conditions has a thermal coefficient of performance (COP) of 1.17 in ventilation mode and 1.28 in recirculation mode. A second law analysis is also performed and at ARI conditions, the reversible COP of the system is determined to be 2.63 in ventilation mode and 3.04 in recirculation mode. Variation of the first and second law based COP terms and cooling load with respect to ambient temperature and relative humidity are investigated in both modes of the system operation. The results of the analysis provide an upper limit for the system performance at various ambient conditions and may serve as a model to which actual desiccant cooling systems may be compared. As an additional study, a non-ideal system operation is considered and it is determined that both the COP and cooling load decrease with increasing ambient temperature and relative humidity, and they approach zero at high values of ambient temperature and humidity.

Index in K-Theory for Families of Fibred Cusp Operators

A families index theorem in K-theory is given for the setting of Atiyah, Patodi and Singer of a family of Dirac operators with spectral bound- ary condition. This result is deduced from such a K-theory index theorem for the calculus of cusp, or more generally fibred cusp, pseudodierential opera- tors on the fibres (with boundary) of a fibration; a version of Poincare duality is also shown in this setting.

On the asymptotics of solutions to the Neumann problem for hyperbolic systems in domains with conical points

Hyperbolic systems of second-order differential equations are considered in a domain with conical points at the boundary; in particular, the equations of elastodynamics are discussed. The asymptotics of solutions near conical points is studied. The character of the asymptotics shows itself in the properties of the coefficients (stress intensity factors) depending on time. Some formulas for the coefficients are presented and sharp estimates in Soboloev's norms are proved. Let G be a domain in R n with boundary ∂G containing conical points. We consider a class of hyperbolic systems of second-order differential equations with Neumann's bound- ary conditions in the cylinder G × R = {(x, t ): x ∈ G, t ∈ R} (and in the semicylinder G × R+). In particular, this class includes the dynamical equations of elasticity the- ory. Our main purpose is to study the asymptotics of solutions near the conical points. We investigate the solvability of the problem mentioned above in a scale of weighted spaces. This enables us to obtain and justify asymptotic formulas. For the coefficients in the asymptotics (depending on time), we give explicit formulas and sharp estimates in Sobolev's norms. The principal part of the asymptotics near a conical point is a linear combination � cj(t)uj(x) of functions uj satisfying a homogeneous elliptic problem in the tangent cone; the latter problem is the elliptic part of the initial problem. The hyperbolic char- acter of the asymptotics shows itself in the coefficients cj. They admit representations of the form

Optimality Conditions and Duality for Multiobjective Control Problems

Fritz John and Kuhn-Tucker type necessary optimality con- ditions for a Pareto optimal (ecient) solution of a multiobjective con- trol problem are obtained by rst reducing the multiobjective control problem to a system of single objective control problems, and then using already established optimality conditions. As an application of Kuhn-Tucker type optimality conditions, Wolfe and Mond-Weir type dual multiobjective control problems are formulated and usual dual- ity results are established under invexity/generalized invexity, relating properly ecient solutions of the primal and dual problems. Wolfe and Mond-Weir type dual multiobjective control problems with free bound- ary conditions are also presented.