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Search results for: THERMAL BOUNDARY CONDITIONS
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Positive solutions to boundary value problems for impulsive second-order differential equations
PublicationIn this paper, we discuss four-point boundary value problems for impulsive second-order differential equations. We apply the Krasnoselskii's fixed point theorem to obtain sufficient conditions under which the impulsive second-order differential equations have positive solutions. An example is added to illustrate theoretical results.
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On analytical solution of stationary two dimensional boundary problem of natural convection
PublicationApproximate analytical solution of two dimensional problem for sta- tionary Navier-Stokes, continuity and Fourier-Kirchho equations describ- ing free convective heat transfer from isothermal surface of half innite vertical plate is presented. The problem formulation is based on the typ- ical for natural convection assumptions: the uid noncompressibility and Boussinesq approximation. We also assume that orthogonal to the plate component...
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AN OVERVIEW OF HEAT TRANSFER ENHANCEMENT BASED UPON NANOPARTICLES INFLUENCED BY INDUCED MAGNETIC FIELD WITH SLIP CONDITION VIA FINITE ELEMENT STRATEGY
PublicationThe mathematical model of heat generation and dissipation during thermal energy transmission employing nanoparticles in a Newtonian medium is investigated. Dimensionless boundary layer equations with correlations for titanium dioxide, copper oxide, and aluminium oxide are solved by the finite element method. Parameters are varied to analyze their impact on the flow fields. Various numerical experiments are performed consecutively...
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Minimal number of periodic points of smooth boundary-preserving self-maps of simply-connected manifolds
PublicationLet M be a smooth compact and simply-connected manifold with simply-connected boundary ∂M, r be a fixed odd natural number. We consider f, a C1 self-map of M, preserving ∂M . Under the assumption that the dimension of M is at least 4, we define an invariant Dr(f;M,∂M) that is equal to the minimal number of r-periodic points for all maps preserving ∂M and C1-homotopic to f. As an application, we give necessary and sufficient...
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A finite element analysis of thermal energy inclination based on ternary hybrid nanoparticles influenced by induced magnetic field
PublicationThe use of hybrid nanoparticles to improve thermal processes is a key method that has implications for a variety of interventions utilized in many sectors. This paper aimed to look into the impacts of ternary nanoparticles on hyperbolic tangent materials to establish their thermal characteristics. Flow describing equations have been explored in the presence of heat production, non-Fourier heat flux, and an induced magnetic field....
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Positive solutions for second order impulsive differential equations involving Stieltjes integral conditions
PublicationIn this paper we investigate integral boundary value problems for fourth order differentialequations with deviating arguments.Wediscuss our problem both for advanced or delayedarguments. We establish sufficient conditions under which such problems have positivesolutions. To obtain the existence of multiple (at least three) positive solutions, we use afixed point theorem due to Avery and Peterson. An example is also included to...
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Modeling of the Two-Dimensional Flow Caused by Sea Conditions and Wind Stresses on the Example of Dead Vistula
PublicationThe article presents the results of two-dimensional modeling of flows caused by the sea conditions and wind stresses on the example of Dead Vistula. Based on the available bathymetric data, a numerical model of the river section was created, which was supplemented with data on the position of the water table depending on hydrometeorological conditions. To describe the flow field in steady conditions, a simplified model of two-dimensional...
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New hybrid quadrature schemes for weakly singular kernels applied to isogeometric boundary elements for 3D Stokes flow
PublicationThis work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for several partial differential equations including the Stokes equation for viscous flow and the Helmholtz equation for acoustics. The proposed quadrature schemes apply a Duffy transform-based quadrature...
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Turbulence models impact on the flow and thermal analyses of jet impingement
PublicationAccurate numerical reconstruction of heat and mass transfer processes in particular applications, such a jet impingement, is difficult to obtain even with the use of modern computational methods. In the proposed paper, the flow and thermal phenomena occurring during single minijet impingement on the flat, concave and convex, heated surfaces were considered. Problem of impingement on non-flat surface, still not common and purely...
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Positive solutions to fractional differential equations involving Stieltjes integral conditions
PublicationIn this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument b can change the character on [0, 1], so in some subinterval I of...
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Numerical simulation of hardening of concrete plate
PublicationThe paper presents a theoretical formulation of concrete curing in order to predict temperature evolution and strength development. The model of heat flow is based on a well-known Fourier equation. The numerical solution is implemented by means of the Finite Difference Method. In order to verify the model, the in situ temperature measurements at the top plate of a road bridge were carried out. A high agreement between numerical...
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Strongly anisotropic surface elasticity and antiplane surface waves
PublicationWithin the new model of surface elasticity, the propagation of anti-plane surface waves is discussed. For the proposed model, the surface strain energy depends on surface stretching and on changing of curvature along a preferred direction. From the continuum mechanics point of view, the model describes finite deformations of an elastic solid with an elastic membrane attached on its boundary reinforced by a family of aligned elastic...
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Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory
PublicationThis paper studies the electro-mechanical shear buckling analysis of piezoelectric nanoplate using modified couple stress theory with various boundary conditions.In order to be taken electric effects into account, an external electric voltage is applied on the piezoelectric nanoplate. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using...
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Stability analysis of nanobeams in hygrothermal environment based on a nonlocal strain gradient Timoshenko beam model under nonlinear thermal field
PublicationThis article is dedicated to analyzing the buckling behavior of nanobeam subjected to hygrothermal environments based on the principle of the Timoshenko beam theory. The hygroscopic environment has been considered as a linear stress field model, while the thermal environment is assumed to be a nonlinear stress field based on the Murnaghan model. The size-dependent effect of the nanobeam is captured by the nonlocal strain gradient...
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The Dynamical Projectors Method Hydro and Electrodynamics
PublicationThe dynamical projectors method proves to reduce a multicomponent problem to the simplest one-component problem with its solution determined by specific initial or boundary conditions. Its universality and application in many different physical problems make it particularly useful in hydrodynamics, electrodynamics, plasma physics, and boundary layer problems. A great variety of underlying mechanisms are included making this book...
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Adam Dąbrowski dr inż.
PeopleAdam Dabrowski has obtained a PhD in mechanical engineering from Gdańsk University of Technology and MSc. degree in mechatronics from Technische Universität Hamburg. He has an industry experience in Institute of Aviation Engineering Design Center (Warsaw, Poland) and SICK AG (Hamburg, Germany). Additionally, as an assistant at Gdansk University of Technology he teaught courses on mechanics, space mechanisms and dynamics of space...
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DISTRIBUTION OF FLOWS IN A CHANNEL NETWORK UNDER STEADY FLOW CONDITIONS
PublicationThe article presents an algorithm for calculating the distribution of flow in a junction of open channel network under steady flow conditions. The article presents a simplified calculation algorithm used to estimate the distribution of flow in a network of channels under steady flow conditions. The presented algorithm is based on the continuity equation and a simplified energy equation. To describe the relationship between the...
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Solving Boundary Value Problems for Second Order Singularly Perturbed Delay Differential Equations by ε-Approximate Fixed-Point Method
PublicationIn this paper, the boundary value problem for second order singularly perturbed delay differential equation is reduced to a fixed-point problem v = Av with a properly chosen (generally nonlinear) operator A. The unknown fixed-point v is approximated by cubic spline vh defined by its values vi = vh(ti) at grid points ti, i = 0, 1, ... ,N. The necessary for construction the cubic spline and missing the first derivatives at the boundary...
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Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method
PublicationIn this paper, bending analysis of rectangular functionally graded (FG) nanoplates under a uniform transverse load has been considered based on the modified couple stress theory. Using Hamilton’s principle, governing equations are derived based on a higher-order shear deformation theory (HSDT). The set of coupled equations are solved using the dynamic relaxation (DR) method combined with finite difference (FD) discretization technique...
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Rothe’s method for physiologically structured models with diffusion
PublicationWe consider structured population models with diffusion and dynamic boundary conditions. The respective approximation, called Rothe’s method, produces positive and exponentially bounded solutions. Its solutions converge to the exact solution of the original PDE.
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Application of the Boundary Element Method for the Simulation of Two-dimensional Viscous Incompressible Flow
PublicationThe paper presents the application of an indirect variant of the boundary element method (BEM) to solve the two-dimensional steady flow of a Stokes liquid. In the BEM, a system of differential equations is transformed into integral equations. Thi smakes it possible to limit discretization to the border of the solution. Numerical discretization of the computational domain was performed with linear boundary elements, for which a...
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Linear Pantographic Sheets: Existence and Uniqueness of Weak Solutions
Publicationwe address the well-posedness of the planar linearized equilibrium problem for homogenized pantographic lattices. To do so: (i) we introduce a class of subsets of anisotropic Sobolev’s space as the most suitable energy space E relative to assigned boundary conditions; (ii) we prove that the considered strain energy density is coercive and positive definite in E ; (iii) we prove that the set of placements for which the strain...
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Buckling Analysis of a Micro Composite Plate with Nano Coating Based on the Modified Couple Stress Theory
PublicationThe present study investigates the buckling of a thick sandwich plate under the biaxial non-uniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (S-FSDT) is employed and the governing differential...
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On weak solutions of boundary value problems within the surface elasticity of Nth order
PublicationA study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining...
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Nonlocalized thermal behavior of rotating micromachined beams under dynamic and thermodynamic loads
PublicationRotating micromachined beams are one of the most practical devices with several applications from power generation to aerospace industries. Moreover, recent advances in micromachining technology have led to huge interests in fabricating miniature turbines, gyroscopes and microsensors thanks to their high quality/reliability performances. To this end, this article is organized to examine the axial dynamic reaction of a rotating...
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Significant Production of Thermal Energy in Partially Ionized Hyperbolic Tangent Material Based on Ternary Hybrid Nanomaterials
PublicationNanoparticles are frequently used to enhance the thermal performance of numerous materials. This study has many practical applications for activities that have to minimize losses of energy due to several impacts. This study investigates the inclusion of ternary hybrid nanoparticles in a partially ionized hyperbolic tangent liquid passed over a stretched melting surface. The fluid motion equation is presented by considering the...
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On instabilities and post-buckling of piezomagnetic and flexomagnetic nanostructures
PublicationWe focus on the mechanical strength of piezomagnetic beam-like nanosize sensors during post-buckling. An effective flexomagnetic property is also taken into account. The modelled sensor is selected to be a Euler-Bernoulli type beam. Long-range interactions between atoms result in a mathematical model based on the nonlocal strain gradient elasticity approach (NSGT). Due to possible large deformations within a post-buckling phenomenon,...
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Fractional Problems with Right-Handed Riemann-Liouville Fractional Derivatives
PublicationIn this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T ]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems...
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Bernstein-type theorem for ϕ-Laplacian
PublicationIn this paper we obtain a solution to the second-order boundary value problem of the form \frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u}), t\in [0,1], u\colon \mathbb {R}\to \mathbb {R} with Sturm–Liouville boundary conditions, where \varPhi\colon \mathbb {R}\to \mathbb {R} is a strictly convex, differentiable function and f\colon[0,1]\times \mathbb {R}\times \mathbb {R}\to \mathbb {R} is continuous and satisfies a suitable growth...
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Experimental study on single phase operation of microjet augmented heat exchanger with enhanced heat transfer surface
PublicationThe article presents experimental investigations on a prototype heat exchanger. Presented research is focused on combined active and passive enhancement techniques of surface modification and microjet impingement. The results were compared to reference plate heat exchanger without microjet impingement. The Wilson plot method was applied to determine the heat transfer coefficients in the single phase operation. The heat exchanger...
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Estimation of Stresses in a Dry Sand Layer Tested on Shaking Table
PublicationTheoretical analysis of shaking table experiments, simulating earthquake response of a dry sand layer, is presented. The aim of such experiments is to study seismic-induced compaction of soil and resulting settlements. In order to determine the soil compaction, the cyclic stresses and strains should be calculated first. These stresses are caused by the cyclic horizontal acceleration at the base of soil layer, so it is important...
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AN ATTEMPT AT IDENTIFYING THE INFLUENCE OF TEST HEAD ASSEMBLY STIFFNESS ON THE RESULTS OF A TRIBOLOGICAL EXPERIMENT CONDUCTED UNDER MICRO-OSCILLATION CONDITIONS
PublicationThe outcome of experimental research on a group of dry bearing materials carried out under small oscillation conditi ons and using a test rig designed and made at Gdansk University of Technology inspired the decision to find out if the stiffness of test head elements in fluenced the generated results. Therefore, a computer model utilising finite elements was devised and used to simulate the workings of the test head. The mode l...
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Transient response of oscillated carbon nanotubes with an internal and external damping
PublicationThe present works aims at modeling a viscoelastic nanobeam with simple boundary conditions at the two ends with the introduction of the Kelvin-Voigt viscoelasticity in a nonlocal strain gradient theory. The nanobeam lies on the visco-Pasternak matrix in which three characteristic parameters have a prominent role. A refined Timoshenko beam theory is here applied, which is only based on one unknown variable, in accordance with the...
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Analytical predictions for the buckling of a nanoplate subjected to non-uniform compression based on the four-variable plate theory
PublicationIn the present study, the buckling analysis of the rectangular nanoplate under biaxial non-uniform compression using the modified couple stress continuum theory with various boundary conditions has been considered. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using the Hamilton’s principle. An analytical approach has been applied to obtain...
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Method of identification of the slide tribological system top layer condition by assessment of the t-02 four-ball tester friction node operation
Publicationa method is proposed of the assessment of t-02 four-ball tester friction node operation during extreme unit loads on the tribological system for identification of the top layer condition in that system lubricated with the tested lubricating oil. by identification of the friction node with a thermodynamic system, that operation is treated as an energy generating process of the created servo-layer structure. the friction node operation...
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Explicit and implicit difefrence methods for quasilinear first order partial functional differential equations.
PublicationInitial boundary value problems of the Dirichlet type for quasilinear functional differential equations are considered. Explicit difference schemes of the Euler type and implicit difference methods are investigated. Suffcient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both classes...
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CLASSIFICATION OF RESTRAINTS IN THE OPTIMIZATION PROBLEM OF A COLD-FORMED PROFILE
PublicationThis work describes the restraints in the optimization problem. This is an important and complicated issue because it requires taking into account a vast range of information related to the design and production. In order to describe the relations of a specific optimization problem, it is essential to adopt appropriate criteria and to collect information on all kinds of restraints, i.e. boundary conditions. The following paper...
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NUMERICAL SIMULATION OF CRATER CREATING PROCESS IN DYNAMIC REPLACEMENT METHOD BY SMOOTH PARTICLE HYDRODYNAMICS
PublicationA theoretical base of SPH method, including the governing equations, discussion of importance of the smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocode simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into the soil caused by falling mass in Dynamic Replacement Method is discussed. An influence of particles spacing on method...
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Novel Analytic-Numerical Model of Free Convection: with Leading Edge Considered
PublicationA novel solution of the free convection boundary problem is represented in analytical form for velocity and temperature for an isothermal vertical plate, as an example. These fields are built as a Taylor Series in the x coordinate with coefficients as functions of the vertical coordinate (y). We restrict ourselves by cubic approximation for both functions. The basic Navier-Stokes and Fourier-Kirchhoff equations and boundary conditions...
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Resonant Frequencies in the Open Microstrip Structures Placed on Curved Surfaces
PublicationThe paper presents the research on open microstrip structures placed on curved surfaces such as cylindrical, elliptical or spherical. The numerical analysis of investigated structures is based on expansion of electric and magnetic fields into suitable function series. Utilizing the continuity conditions the boundary problem is formulated which is solved with the use of method of moments. The investigated structures find application...
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A graphical approach to yield and boundary surfaces of selected hypoplastic constitutive equations
PublicationThe article describes how to identify the boundary and yield surface for hypoplastic constitutive equations proposed by Wu, Gudehus and Bauer. It is shown how to identify and plot the surfaces for any equation in this class. Calculation errors are analyzed characteristic for appleid set of numerical formulas. In the paper there are computer links to the source code prepared in the MATLAB system, based on istructions in the article....
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Resonant Frequencies in Microstrip Structure with Omega Medium Substrate
PublicationThe paper presents the research on a rectangular microstrip structure with multilayer substrate containing dielectric and omega medium layers. The effect of pseudochiral medium layer location in the substrate and its thickness on the resonant frequency of the rectangular microstrip structure is investigated. The numerical analysis of investigated structures is based on expansion of electric and magnetic fields. Utilizing the continuity...
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Numerical tests of time-stepping schemes in the context of FEM for 6-field shell dynamics
PublicationThe paper deals with integration of dynamic equations of irregular shells performed with relatively long time steps. Numerical instability appearing often in this kind of analysis motivated the authors to present some studies based on numerical tests referring to convergence problems of finite element analysis as well the applied stability conditions. The analysis is carried out on simulations of shell dynamics with the where the...
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Numerical methods in heat and fluid flow, PG_00057408
e-Learning CoursesReiteration of information on thermodynamic cycles and extension of information on their modelling using commercial software tools. Presentation of balances, constitutive equations, how to set up conditions in CFD type codes. Equipment regulation and control in the context of heat exchangers.Presentation of the computational capabilities of the CFD calculation code ANSYS Fluent. Mass, momentum and energy balances in 0D and 3D terms.Analysis...
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Ocena przekształceń piętrowego, ceglanego domu z dachem półpłaskim z przełomu XIX–XX wieku pod wpływem termomodernizacji na przykładzie gminy Puck, woj. pomorskie.
PublicationCeglane budynki mieszkalne z przełomu XIX i XX wieku, które stanowiły charakterystyczny element krajobrazu wsi pomorskiej, obecnie powszechnie poddawane są modernizacji w celu poprawy warunków cieplnych. Przedmiotem badania jest stan zachowania najmłodszego, historycznego typu domuw zagrodzie chłopskiej na Kaszubach – piętrowego, ceglanego domu z dachem półpłaskim. Badanie przeprowadzono na obszarze gminy Puck. Zidentyfikowano...
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Numerical analysis of crack propagation in silicone nitride
PublicationThe properties of ceramics, specifically low density, high hardness, high temperature capability and low coefficient of thermal expansion are of most interest to rolling element manufacturers. The influence of ring crack size on rolling contact fatigue failure has been studied using numerical fracture analysis. Such cracks are very often found on ceramic bearing balls and decrease fatigue life rapidly. The numerical calculation...
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Under the Fire of Disinformation. Attitudes Towards Fake News in the Ukrainian Frozen War
PublicationIn this article, we examine individual attitudes towards fake news in the extreme conditions of a propaganda war, taking into account the complex regional social and historical conditions. For this purpose, within the mobile boundary zone during frozen war in Ukraine, we conducted qualitative research among representatives of generations X and Z (high school teachers and students). Being accustomed to fake news turned out to be...
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How much a geometrical model of a honeycomb seal can be simpli ed in the CFD calculation
PublicationThis paper presents the inuence of geometry simplication on the results obtained in the computational fluid dynamics simulation. The subject of simulation was part of the honeycomb seal located at the inlet to high pressure part of a steam turbine. There were three different geometrical models assumed in the calculations. First one was two-dimensional case and two others were three dimensional, one with the radius of curvature...
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Analiza i ocena smarności olejów w ujęciu energetycznym i działania układu tribologicznego = Analysis and evaluation of oil lubricity from the viewpoint of energy apects and of the tribological system action
PublicationBased on measurement results, an interpretation is presented of the tribological system boundary layer action in the form of a four-ball tester friction node. The evaluation was performed of the boundary layer action understood as transfer of energy Ep resulting from loading the tribological system in a determined time t with work Lp, which may lead to breaking the boundary layer. That energy and time are the values unequivocally...
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Simulation of unsteady flow over floodplain using the diffusive wave equation and the modified finite element method
PublicationWe consider solution of 2D nonlinear diffusive wave equation in a domain temporarily covered by a layer of water. A modified finite element method with triangular elements and linear shape functions is used for spatial discretization. The proposed modification refers to the procedure of spatial integration and leads to a more general algorithm involving a weighting parameter. The standard finite element method and the finite difference...