Search

This paper uses the Galerkin method to find approximate solutions of some boundary value problems. The solving process requires to solve a system of algebraic equations, which are large and difficult to be solved. According to the Groebner bases theory, an improved Buchberger's algorithm is proposed to solve the algebraic system. The results show that the Galerkin approach is simple and efficient. [ABSTRACT FROM AUTHOR]

This study aims to perform a numerical simulation of the boundary flow with the characteristic Sakiadis flow of the MHD Jeffrey fluid under the Cattaneo-Christov heat flux model over the horizontal plate. The similarity transformation for the local similarity solution was used to reduce the set of governing equations to non-linear ODE. The equations were solved by using 'dsolve' command with the numeric option for the boundary value problem in MAPLE. Simulations have been carried out for different values of the relaxation retardation times, the Deborah number, the magnetic field parameter, the heat flux relaxation time, the Prandtl number, and the Schmidt parameter. A comparative study of the numerical results from the previously published paper with the present result for the dimensionless velocity gradient over the horizontal plate shows excellent agreement. It has been found that the growth of the Deborah number leads to the dimensionless velocity gradient enhancement, while the increment of the relaxation retardation times parameter and the magnetic field parameter indicates the opposite trend. The heat transfer rate noticeably decreased with an increment in the Prandtl number and thermal relaxation time at the fluid regime. Also, fluid concentration decreases with larger values of the Schmidt parameter. [ABSTRACT FROM AUTHOR]

In this paper, the fractional heat equation in a sphere with hybrid fractional derivative operator is investigated. The heat conduction is considered in the case of central symmetry with heat absorption. The closed form solution in the form of three parameter Mittag-Leffler function is obtained for two Dirichlet boundary value problems. The joint finite sine Fourier-Laplace transform is used for solving these two problems. The dynamics of the heat transfer in the sphere is illustrated through some numerical examples and figures. [ABSTRACT FROM AUTHOR]

In this paper, the initial boundary value problem of the dissipative symmetric regularized long wave equation with a damping term is studied numerically, and a decoupled linearized difference scheme with a theoretical accuracy of O(τ²+h4) is proposed. Because the scheme removes the coupling between the variables in the original equation, the linearized difference scheme and the explicit difference scheme can be used to solve the two variables in parallel, which greatly improves the efficiency of numerical solutions. To obtain the maximum norm estimation of numerical solutions, the mathematical induction and the discrete functional analysis methods are introduced directly to prove the convergence and the stability of the scheme. Numerical experiments have also verified the reliability of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper describes reconstruction of the heat transfer coefficient occurring in the boundary condition of the third kind for the time fractional heat conduction equation. Fractional derivative with respect to time, occurring in considered equation, is defined as the Caputo derivative. Additional information for the considered inverse problem is given by the temperature measurements at selected points of the domain. The direct problem is solved by using the implicit finite difference method. To minimize functional defining the error of approximate solution the Nelder-Mead algorithm is used. The paper presents results of computational examples to illustrate the accuracy and stability of the presented algorithm. [ABSTRACT FROM AUTHOR]

Boundary value problems arising in fluid mechanics and thermal science can be transformed uniformly to a set of linear equations, whose coefficient matrix is circulant. This paper adopts a matrix iteration LSQR to solve the inverse of coefficient matrix. The solution process is elucidated step by step, and the numerical results reveal the effectiveness and feasibility of the presented method. [ABSTRACT FROM AUTHOR]

In this paper, a triple-medium flow model for carbonate geothermal reservoirs with an exponential external boundary flux is established. The pressure solution under constant production conditions in Laplace space is solved. The geothermal wellbore pressure change considering wellbore storage and skin factor is obtained by Stehfest numerical inversion. The well test interpretation charts and Fetkovich production decline chart for carbonate geothermal reservoirs are proposed for the first time. The proposed Fetkovich production decline curves are applied to analyze the production decline behavior. The results indicate that in carbonate geothermal reservoirs with exponential external boundary flux, the pressure derivative curve contains a triple dip, which represents the interporosity flow between the vugs or matrix and fracture system and the invading flow of the external boundary flux. The interporosity flow of carbonate geothermal reservoirs and changing external boundary flux can both slow down the extent of production decline and the same variation tendency is observed in the Fetkovich production decline curve. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new non-linear partial differential equation to describe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method. [ABSTRACT FROM AUTHOR]

In this paper, we study and analyze a three-level linear finite difference scheme for the initial boundary value problem of the symmetric regularized long wave equation with damping. The proposed scheme has the second accuracy both for the spatial and temporal discretization. The convergence and stability of the numerical solutions are proved by the mathematical induction and the discrete functional analysis. Numerical results are given to verify the accuracy and the efficiency of proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a local fractional homotopy perturbation method is presented to solve the boundary and initial value problems of the local fractional Korteweg-de Vries equations with non-homogeneous term. In order to demonstrate the validity and reliability of the method, two types of the Korteweg-de Vries equations with non-homogeneous term are proposed. [ABSTRACT FROM AUTHOR]

The paper deals with a parameter identification problem for creep and fracture model. The system of ordinary differential equations of kinetic creep theory is applied for describing this model. As for solving the parameter identification problem, we proposed to use the technique of neural network modeling, as well as the multilayer approach. The procedures of neural network modeling and multilayer approximation constructing application is demonstrated by the example of finding parameters for uniaxial tension model for isotropic steel 45 specimens at creep conditions. The solution corresponding to the obtained parameters agrees well with theoretical strain-damage characteristics, experimental data, and results of other authors. [ABSTRACT FROM AUTHOR]

This paper presents the solution of the initial boundary-value problem for the system of 1-D thermoelasticity using a new modified decomposition method that takes into accounts both initial and boundary conditions. The obtained solution is based on the generalized form of the inverse operator and is given in the form of a finite series. Also, some numerical experiments were presented to the both the effectiveness and the accuracy of the presented method. [ABSTRACT FROM AUTHOR]

The MHD flow of three immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied electric and inclined magnetic field has been investigated in the paper. All three fluids are electrically conducting, while the channel plates are electrically insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ODE and closed-form solutions are obtained in three fluid regions of the channel. Separate solutions with appropriate boundary and interface conditions for each fluid have been determined. The analytical results for various values of the Hartmann number, magnetic field inclination angle, ratio of fluid viscosities, and electrical conductivities have been presented graphically to show their effect on the flow and heat transfer characteristics. [ABSTRACT FROM AUTHOR]

This paper, dealing with the problems of mathematical description of the tunnel fire development process with the use of experimental data, outlines the procedure of correction of the existing and obtaining of an improved CFD model package. The improved CFD model was developed on the basis of detailed analysis and comparison of experimental and numerical results, through consideration of the physical structure of all processes affecting combustion. During the analysis it was noticed that the existing CFD model in the part covering combustion based on the so-called steady laminar flamelet model, treats the combustion process almost as a direct correlation between the processes of mixing gasses and heat release rate. This potential deficiency has been overcome by correction of the model in the section defining boundary condition for the burning surface and by establishing a direct correlation between the measured value of the fuel mass change rate and the amount of heat released from burning surface. In this way a modification of complex stoichiometric combustion processes was avoided, while providing the model that better describes and predicts the course of events in this type of complex, anisotropic and turbulent flow of gases in the tunnel. [ABSTRACT FROM AUTHOR]

This paper deals with fluid flow, heat transfer, and entropy generation in an internally ribbed micro-channel. Mass, momentum, and energy equations for constant heat flux boundary condition are solved using the finite volume method. Average Nusselt number and Fanning friction factor are reported as a function of rib height at different Reynolds numbers. The effects of non-dimensional rib height, wall heat flux, and the Reynolds number on the entropy generation attributed to friction, heat transfer, and total entropy generation are explored. The first law indicates that rib height has the great effect on the flow filed and heat transfer. The second law analysis reveals that for any values of Reynolds number and wall heat flux, as rib height grows, the frictional irreversibility increases while, there is a rib height which provides the minimum heat transfer irreversibility. It is found that the optimum rib height with the minimum total entropy generation rate depends on Reynolds number and wall heat flux. [ABSTRACT FROM AUTHOR]

The main role in air/fuel mixture formation at the IC Diesel engines has the energy in-troduced by fuel into the IC engine that is the characteristics of spraying fuel into the combustion chamber. The characteristic can be defined by the spray length, the spray cone angle, and the physical and chemical structure of fuel spray by different sections. Having in mind very complex experimental setups for researching in this field, the mentioned characteristics are mostly analyzed by calculations. There are two methods in the literature. The first based on use of the semiempirical expressions (correlations) and the second, the calculations of spray characteristics by use of very complex mathematical methods. The second method is dominant in the modern literature. The main disadvantage of the calculation methods is a correct definition of real state at the end of the nozzle orifice (real boundary conditions). The majority of the researchers in this field use most frequently the coefficient of total losses inside the injector. This coefficient depends on injector design, as well as depends on the level of fuel energy and fuel energy transformation along the injector. Having in mind the importance of the real boundary conditions, the complex methods for calculation of the fuel spray characteris-tics should have the calculation of fuel flows inside the injector and the calculation of spray characteristics together. This approach is a very complex numerical problem and there are no existing computer programs with satisfactory calculation results. Analysis of spray characteristics by use of the semi-empirical expressions (correlations) is presented in this paper. The special attention is dedicated to the analysis of the constant in the semi-empirical expressions and influence parameters on this constant. Also, the method for definition of realistic boundary condition at the end of the nozzle orifice is presented in the paper. By use of this method completely avoid a use of the coefficient of total losses inside the injector. At the same time, semi-empirical expressions have the universal constant that does not depend on the injector design. [ABSTRACT FROM AUTHOR]

This paper studies the effect of micro-structural interaction on bioheat transfer in skin, which was stratified into epidermis, dermis, and subcutaneous. A modified non-Fourier equation of bio-heat transfer was developed based on the second-order Taylor expansion of dual-phase-lag model and can be simplified as the bio-heat transfer equations derived from Pennes' model, thermal wave model, and the linearized form of dual-phase-lag model. It is a fourth order partial differential equation, and the boundary conditions at the interface between two adjacent layers become complicated. There are mathematical difficulties in dealing with such a problem. A hybrid numerical scheme is extended to solve the present problem. The numerical results are in a good agreement with the contents of open literature. It evidences the rationality and reliability of the present results. [ABSTRACT FROM AUTHOR]

In the current paper, the peristaltic transport of a non-Newtonian fluid obeying a Casson model with heat and mass transfer inside a vertical circular cylinder is studied. The considered system is affected by a strong horizontal uniform magnetic field together with the heat radiation and the Hall current. The problem is modulated mathematically by a system of PDE that describe the basic behavior of the fluid motion. The boundary value problem is analytically solved with the appropriate boundary conditions in accordance with the special case, in the absence of the Eckert number. The solutions are obtained in terms of the modified Bessel function of the first kind. Again, in the general case, the system is solved by means of the homotopy perturbation and then numerically through the Runge- Kutta Merson with a shooting technique. A comparison is done between these two methods. Therefore, the velocity, temperature and concentration distributions are obtained. A set of diagrams are plotted to illustrate the influence of the various physical parameters in the forgoing distributions. Finally, the trapping phenomenon is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method is proposed for 1-D fractional heat equations subject to non-local boundary conditions. The reproducing kernel satisfying nonlocal conditions is constructed and reproducing kernel theory is applied to solve the considered problem. A numerical example is given to show the effectiveness of the method. [ABSTRACT FROM AUTHOR]

The novelty and innovativeness of this paper are the combination of reproducing kernel theory and spline, this leads to a new simple but effective numerical method for solving variable-order anomalous sub-diffusion equation successfully. This combination overcomes the weaknesses of piecewise polynomials that can not be used to solve differential equations directly because of lack of the smoothness. Moreover, new bases of reproducing kernel spaces are constructed. On the other hand, the existence of any ε-approximate solution is proved and an effective method for obtaining the ε-approximate solution is established. A numerical example is given to show the accuracy and effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

In the present paper we investigate the fractal boundary value problems for the Fredholm and Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator is described by the local fractional operators. The four illustrative examples are given to elaborate the accuracy and reliability of the obtained results. [ABSTRACT FROM AUTHOR]

A class of boundary value problems can be transformed uniformly to a least square problem with Toeplitz constraint. Conjugate gradient least square, a matrix iteration method, is adopted to solve this problem, and the solution process is elucidated step by step so that the example can be used as a paradigm for other applications. [ABSTRACT FROM AUTHOR]

Investigation of the nature of dual solutions of the water-based micropolar nanofluid- flow with thermal transmission due to a contracting surface has been done in the work. The flow is characterized by its shrinking velocity and imposed magnetic field. Also, this work is one of the contributions that illustrate the microrotation and microinertia descriptions of nanofluids. The effects of metallic nanoparticles Cu and CuO have been discussed throughout this study. A uniform magnetic field has been applied in the normal direction of the flow. A set of basic equations that supports the present problem are derived from the principle of conservation laws and have been modernized into a set of solvable forms by employing suitable similarity variables. The MATLAB built-in bvp4c solver scheme is engineered to solve this problem. In order to tackle boundary value problems that are highly non-linear, this numerical method largely relies on collocation and finite difference techniques. From this study, we have perceived that the speed of the motion of CuO-water nanofluid in both cases (the first and second solutions) is less than CuO-water nanofluid. The material parameter plays an important role by enhancing the heat transfer rate of the fluid at the surface of the sheet in both time-dependent and time-independent cases. From the stability analysis, the first solution has been found as the stable and physically attainable solution. Additionally, the material parameter aids in reducing the effects of couple stress and shear stress on the fluid in both situations near the surface. [ABSTRACT FROM AUTHOR]

A considerable slide exists between the flanks of worm and gear during the work, which results in flank wear and considerable loss of energy. The energy is, thereby, converted into heat, which leads to the warming-up of gear drive, compromising its correct operation, and to scuffing in critical cases. Oil temperature has an important role in thermal stability. Viscosity depends on temperature. Viscosity significantly affects the processes in the contact zone, i. e. the energy losses, and hence the temperature. Optimal lubrication can be provided only in the relevant field of temperatures. The paper presents experimental and theoretical research on the effect of temperatures and thermal stability of a worm and gear set with a gear made of sintered steel Fe1.5Cr0.2Mo on their ability and appearance of boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, the fully-developed temperature profile and corresponding Nusselt value is determined analytically for a gaseous flow in a microtube with a thermal boundary condition of constant wall heat flux. The flow assumed to be laminar, and hydrodynamically and thermally fully developed. The fluid is assumed to be constant property and incompressible. The effect of rarefaction, viscous dissipation and axial conduction, which are important at the microscale, are included in the analysis. Second-order slip model is used for the slip-flow and temperature jump boundary conditions for the implementation of the rarefaction effect. Closed form solutions for the temperature field and the fully-developed Nusselt number is derived as a function of Knudsen number, Brinkman number and Peclet number. [ABSTRACT FROM AUTHOR]

In this article we consider the boundary value problems for differential equations in fractal heat transfer. The exact solutions of non-differentiable type are obtained by using the local fractional differential transform method. [ABSTRACT FROM AUTHOR]

Phase change materials have found many industrial applications such as cooling of electronic devices and thermal energy storage. This paper investigates numerically the melting process of a phase change material in a 2-D horizontal annulus with different arrangements of two discrete heat sources. The sources are positioned on the inner cylinder of the annulus and assumed as constant-temperature boundary conditions. The remaining portion of the inner cylinder wall as well as the outer cylinder wall is considered to be insulated. The emphasis is mainly on the effects of the arrangement of the heat source pair on the fluid flow and heat transfer features. The governing equations are solved on a non-uniform O type mesh using a pressure-based finite volume method with an enthalpy porosity technique to trace the solid and liquid interface. The results are obtained at Ra = 104 and presented in terms of streamlines, isotherms, melting phase front, liquid fraction, and dimensionless heat flux. It is observed that, depending on the arrangement of heat sources, the liquid fraction increases both linearly and non-linearly with time but will slow down at the end of the melting process. It can also be concluded that proper arrangement of discrete heat sources has the great potential in improving the energy storage system. For instance, the arrangement C.3 where the heat sources are located on the bottom part of the inner cylinder wall can expedite the melting process as compared to the other arrangements. [ABSTRACT FROM AUTHOR]

An extended variational iteration method within the local fractional derivative is introduced for the first time, where two Lagrange multipliers are adopted. Moreover, the sufficient conditions for convergence of the new variational iteration method are also established. [ABSTRACT FROM AUTHOR]

In the present paper, the stress distribution is studied in an infinite elastic body, reinforced by an arbitrary number of non-intersecting co-phase locally spatially curved filler layers under bi-axial compression is studied. It is assumed that this system is loaded at infinity with uniformly distributed normal forces with intensity p1(p3) acting in the direction which is parallel to the layers' location planes. It is required to determine the self-equilibrated stresses within, caused by the spatially local curving of the layers. The corresponding boundary and contact value problem is formulated within the scope of geometrically non-linear exact 3-D equations of the theory of elasticity by utilizing of the piece-wise homogeneous body model. The solution the formulated problem is represented with the series form of the small parameter which characterizes the degree of the aforementioned local curving. The boundary-value problems for the zeroth and the first approximations of these series are determined with the use of the exponential double Fourier transform. The original of the sought values is determined numerically. Consequently, in the present investigation, the effect of the local curving on the considered interface stress distribution is taken into account within the framework of the geometrical non-linear statement. The numerical results related to the considered interface stress distribution and to the influence of the problem parameters on this distribution are given and discussed. [ABSTRACT FROM AUTHOR]

This research aims to propose a numerical scheme for solving boundary value problems. It is a two-stage, third-order accurate scheme known as a predictorcorrector scheme. The two main results are finding the region of the scheme where it is stable and determining the stability criterion for a set of linearized first-order differential equations. In addition, a mathematical model for heat and mass transfer of Darcy-Forchheimer flow of non-Newtonian nanofluid over the sheet is presented. The similarity transformations reduce PDE into a system of ODE for easier manipulation. The results are compared with the past research and those obtained by MATLAB SOLVER BVP4C. The results show that the velocity profile slightly decays by enhancing the Weisenberg number. [ABSTRACT FROM AUTHOR]

We consider a model of lithospheric structures contacting along rectilinear geological faults as a system of composite plates on an elastic foundation. A simplification of the block element method for different-sized blocks is proposed. We also describe an approach that is a modification of the block element method using the method of eigenfunctions. The method is considered on the example of a static interaction problem of extended plates on the surface of an elastic layer for a given surface load. As a result we obtain the representations of solutions describing the surface displacements. The application of the proposed approach will allow us to draw conclusions about the effect of the physical and mechanical properties of lithospheric structures and the type of fault on the nature of displacements in the geological environment which are applicable for studying the structure of faults in the upper part of the earth's crust. [ABSTRACT FROM AUTHOR]

In this study, a mathematical model of far-infrared vacuum drying of shrinkage body is presented. The system of two coupled PDE for heat and mass transfer with appropriate initial and boundary conditions are solved numerically with used of the finite difference method. On the basis of the numerical solutions a computer program for calculation of temperature profiles, transient moisture content, mid-plane temperature, and the volume averaged moisture content changes for different drying regime was developed. For verification of a mathematical model a series of numerical calculations were carried out with experimental conditions similar to those in the realized experiments of far-infrared vacuum drying of apple slices. Very good agreement between the experimental and numerical temperature and moisture content changes during the drying was obtained. [ABSTRACT FROM AUTHOR]

In this paper He's variational iteration method is used to solve some examples of linear and non-linear forth-order boundary value problems. The first problem compared with homotopy analysis method solution and the other ones with the exact solution. The results show the high accuracy and speed of convergence of this method. It is found that the variational iteration method is a powerful method for solving of the non-linear equations. [ABSTRACT FROM AUTHOR]

Mach number of 4 can be taken as a boundary value for transition from conditions for supersonic, into the area of hypersonic flow, distinguishing two areas: area of supersonic in which the effects of the aerodynamic heating can be neglected and the area of hypersonic, in which the thermal effects become dominant. This paper presents the effects in static and dynamic areas, as well as presentation of G.R.O.M. software for determination of the values of aerodynamic derivatives, which was developed on the basis of linearized theory of supersonic flow. Validation of developed software was carried out through different types of testing, proving its usefulness for engineering practice in the area of supersonic wing aerodynamic loading calculations, even at high Mach numbers, with dominant thermal effects. [ABSTRACT FROM AUTHOR]

In the present work, the influence of the amplitude ratio, phase deviation, and undulation number on natural convection in a wavy-walled enclosures differentially heated and filled with a water based nanofluid is studied. The upper and bottom walls are wavy with several undulations. The sinusoidal distribution of temperature is imposed at the vertical walls. The flow, heat, and mass transfer are calculated by solving governing equations for embody the conservation of total mass, momentum, thermal energy, and nanoparticles, taking into account the Darcy-Boussinesq-Buongiorno approximation with second order finite difference method in "stream function-temperature-concentration" formulation. Results are presented in the form of streamlines, isotherm, and isoconcentration contours, and distributions of the average Nusselt number for the different values of the amplitude ratio of the sinusoidal temperature on the right side wall to that on the left side wall (γ = 0-1), phase deviation (φ = 0-л), and undulation number (κ = 1-4). It has been found that variations of the undulation number allow to control the heat and mass transfer rates. Moreover, an increase in the undulation number leads to an extension of the non-homogeneous zones. [ABSTRACT FROM AUTHOR]

Heat conduction in solids subjected to non-homogenous boundary conditions leads to singularities in terms of heat flux density. That kind of issues can be also encountered in various scientists' fields as electromagnetism, electrostatic, electrochemistry, and mechanics. These problems are difficult to solve by using the classical methods such as integral transforms or separation of variables. These methods lead to solving of dual integral equations or Fredholm integral equations, which are not easy to use. The present work addresses the calculation of thermal resistance of a finite medium submitted to conjugate surface Neumann and Dirichlet conditions, which are defined by a band-shape heat source and a uniform temperature. The opposite surface is subjected to a homogeneous boundary condition such uniform temperature or insulation. The proposed solving process is based on simple and accurate correlations that provide the thermal resistance as a function of the ratio of the size of heat source and the depth of the medium. A judicious scale analysis is performed in order to fix the asymptotic behaviour at the limits of the value of the geometric parameter. The developed correlations are very simple to use and are valid regardless of the values of the defined geometrical parameter. The performed validations by comparison with numerical modelling demonstrate the relevant agreement of the solutions to address singularity calculation issues. [ABSTRACT FROM AUTHOR]

This article presents the fractal heat transfer problems from the local fractional calculus point of view. At low and high excess temperatures, the linear and non-linear heat transfer equations are presented. The non-homogeneous linear and non-linear oscillator equations in fractal heat transfer are discussed. The results are adopted to present the behaviors of the heat transfer in fractal media. [ABSTRACT FROM AUTHOR]

The solutions for a dimensional system with radial symmetry and governed by a fractional diffusion equation have been investigated. More specifically, a spherical system was considered, being defined in the semi-infinity interval [R, ∞) and subjected to surface effects described in terms of integro-differential boundary conditions which has many practical applications. The analytical solutions were obtained by using the Green function approach, showing a broad range of different behaviors which can be related to anomalous diffusion. The analyses also considered the influence of the parameters of the analytical solution in order to describe a more realistic scenario. [ABSTRACT FROM AUTHOR]

The non-differentiable analytical solution of the 3-D diffusion equation in fractal heat transfer is investigated in this article. The Adomian decomposition method is considered in the local fractional operator sense. The obtained result is given to show the sample and efficient features of the presented technique to implement fractal heat transfer problems. [ABSTRACT FROM AUTHOR]

Gas flow sequentially moving through three zones (input z < 0, internal heat release 0 ≤ z ≤ l, and output z > 1) of a cylindrical channel was considered. Analytical solutions taking into account the influence of heat source limitation in the axial direction and intensity of air flow in this direction on thermal balance were obtained. [ABSTRACT FROM AUTHOR]

The level of pollution concentration to the archeological site Viminacium caused by the stack of Kostolac B power plant is analysed using CFD software. The wind is directed from the stack toward Viminacium-Archeological Site, Therma and Viminacium-Museum. Three different meteorological conditions resulting in fanning, fumigating, and looping plume are modelled. The temperature gradient as the most important factor defining the conditions of the atmosphere is included through the appropriate boundary conditions. It is shown that concentrations of the pollutants on the objects of Viminacium are very low. It can be attributed to the stack height and high temperature of the smoke at its exit. It also indicates that other sources of pollution such as open ash dumps and acid rain should be checked. [ABSTRACT FROM AUTHOR]

A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed. [ABSTRACT FROM AUTHOR]

Integral approach by using approximate profile is successfully applied to heat conduction equation with fading memory expressed by a Jeffrey's kernel. The solution is straightforward and the final form of the approximate temperature profile clearly delineates the "viscous effects" corresponding to the classical Fourier law and the relaxation (fading memory). The optimal exponent of the approximate solution is discussed in case of Dirichlet boundary condition. [ABSTRACT FROM AUTHOR]

An analytical model for deep bed filtration of suspension in porous media and straining under size exclusion capture mechanism is developed and validated by laboratory tests on suspension flow in engineered media. The fraction of swept particles is introduced in the inlet boundary condition. The model is successfully matched with the results from column experiments, predicting the suspended particle concentrations at the outlet. [ABSTRACT FROM AUTHOR]

The current study extends the applications of the variational iteration method for the analytical solution of fractional contact problems. The problem involves Caputo sense while calculating the derivative of fractional order, we apply the Penalty function technique to transform it into a system of fractional boundary value problems coupled with a known obstacle. The variational iteration method is employed to find the series solution of fractional boundary value problem. For different values of fractional parameters, residual errors of solutions are plotted to make sure the convergence and accuracy of the solution. The reasonably accurate results show that one of the highly effective and stable methods for the solution of fractional boundary value problem is the method of variational iteration. [ABSTRACT FROM AUTHOR]

Exact general solutions for hydromagnetic flows of an incompressible viscous fluid between two horizontal infinite parallel plates are established when the upper plate is fixed and the inferior one applies a time-dependent shear stress to the fluid. Porous effects are taken into consideration and the problem in discussion is completely solved for moderate values of the Hartman number. It is found that the fluid velocity and the non-trivial shear stress satisfy PDE of the same form and the motion characteristics do not depend of magnetic and porous parameters independently but only by a combination of them that is called the effective permeability. For illustration, as well as to bring to light some physical insight of results that have been obtained, three special cases are considered and the influence of Reynolds number as well as combined porous and magnetic effects on the fluid motion are graphically underlined and discussed for motions due to constant or ramped-type shear stresses on the boundary. The starting solutions corresponding to motions induced by the lower plate that applies constant or oscillatory shear stresses to the fluid are presented as sum of steady-state and transient solutions and the required time to reach the steady-state is graphically determined. This time is greater for motions due to sine as compared to cosine oscillating shear stresses on the boundary. The steady-state is rather obtained in the presence of a magnetic field or porous medium. [ABSTRACT FROM AUTHOR]

Bio-inspired pumping systems exploit a variety of mechanisms including peristalsis to achieve more efficient propulsion. Non-conducting, uniformly dispersed, spherical nanosized solid particles suspended in viscoelastic medium forms a complex working matrix. Electromagnetic pumping systems often employ complex working fluids. A simulation of combined electromagnetic bio-inspired propulsion is observed in the present article. Currents formation has increasingly more applications in mechanical and medical industry. A mathematical study is conducted for MHD pumping of a bi-phase nanofluid coupled with heat transfer in a planar channel. Two-phase model is employed to separately identity the effects of solid nanoparticles. Base fluid employs Jeffery's model to address viscoelastic characteristics. The model is simplified using long wavelength and creeping flow approximations. The formulation is taken to wave frame and non-dimensionalise the equations. The resulting boundary value problem is solved analytically, and exact expressions are derived for the fluid velocity, particulate velocity, fluid-particle temperature, fluid and particulate volumetric flow rates, axial pressure gradient and pressure rise. The influence of volume fraction density, Prandtl number, Hartmann number, Eckert number, and relaxation time on flow and thermal characteristics is evaluated in detail. The axial flow is accelerated with increasing relaxation time and greater volume fraction whereas it is decelerated with greater Hartmann number. Both fluid and particulate temperature are increased with increment in Eckert and Prandtl numbers, whereas it is reduced when the volume fraction density increases. With increasing Hartmann number pressure rise is reduced. [ABSTRACT FROM AUTHOR]

In study, we show the existence and integral representation of solution for energy- dependent fractional Sturm-Liouville impulsive problem of order with a (1,2] impulsive and boundary conditions. An existence theorem is proved for energy-dependent fractional Sturm-Liouville impulsive problem by using Schaefer fixed point theorem. Furthermore, in the last part of the article, an application is given for the problem and visual results are shown by figures. [ABSTRACT FROM AUTHOR]

To develop a reliable method for modeling fire case scenarios within the road tunnels and observing the effects of the skewed velocity, experimental and numerical approach is used. Experimental results obtained from a laboratory tunnel model installation, are used to define geometry and boundary conditions. The result for the overall ventilation performance is compared to the available cases, for empty tunnel and stationary bi-directional vehicle traffic. For a unidirectional traffic road tunnel, in traffic loaded conditions, with a ventilation system based on axial ducted fans, the numerical simulation is used to determine the flow and temperature fields, the ventilation efficiency (efficiency of momentum transfer), and to assess the shape of the velocity distribution. The effect that a skewed velocity distribution can have on the resulting thermal and pollutant fields (CO2), smoke backlayering and stratification, is evaluated using numerical simulations, for the model-scale tunnel fire conditions. The effect of two possible limiting shapes of the velocity distribution, dependent only on the location of the fire with respect to the nearest upstream operating fans, is analyzed. The numerical results for a fire are scenario are a starting point in assessing the feasibility of a laboratory model fire-scenario experiment, what is planned as the next step in this research. [ABSTRACT FROM AUTHOR]