Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik最新文献

{"title":"Turbulent heat and mass lines in finite difference regime","authors":"Suresha S P, G. Janardhana Reddy, Hussain Basha","doi":"10.1002/zamm.202300093","DOIUrl":"https://doi.org/10.1002/zamm.202300093","url":null,"abstract":"Abstract Finite difference modelling of turbulent heat and mass flow visualization finds numerous applications in atmospheric flows/oceanic currents, wind turbines, thermal transfer in nuclear reactors, drag in oil pipelines, cooling of industrial machineries, and to investigate the complexity, dynamic and chaotic nature of the physical system. A turbulent phenomenon is effectively implemented in engineering, physics, earth sciences, bio‐engineering and medicine. Hence, motivated by the advantages of turbulence in various engineering fields, in the current article, a finite difference analysis is performed to demonstrate the k‐ε turbulence model‐based heat and mass lines visualization in boundary layer regime under turbulent buoyancy‐driven convective conditions along a cylinder. Turbulent flow characteristics are accurately explored by deploying the classical Newtonian flow model. Further, to accomplish a more sophisticated finite difference simulation, the effects of extra kinetic energy and its dissipation rate equations are considered. The produced Navier‐Stokes equations for time‐dependent turbulent heat and mass transmission are rendered to non‐dimensional by deploying suitable dimensionless numbers. The advanced coupled nonlinear turbulent unsteady buoyancy‐motivated vertical convection problem is then solved with a well‐sophisticated finite difference scheme such as Crank‐Nicolson technique using computational software. Authentication of current results with former solutions over a range of buoyancy number, Schmidt, and Prandtl parameters are presented. An extensive tabular and graphical discussion along with contours, heat and masslines visualization is included to enumerate the hydro‐dynamic, thermal and mass diffusion behaviour for the impact of emerged regulating numbers in the Prandtl regime. It is confirmed that, the accelerating turbulent buoyancy‐ratio number, maximizes the velocity, kinetic energy and dissipation rate at . Further, the numerical values of laminar thermal and mass diffusion rates are monotonically enhanced when compared to the turbulent values. Also, to verify the current findings, the authors compared the LRN k‐ε model turbulent results with the existing solutions and found good agreement. Further, the uniqueness and novelty of the current investigation is the exploration of heat and masslines in unsteady buoyancy‐driven convection regime under the influence of k‐ε turbulence model which extends the former studies and offers a more precise appraisal of the thermal and mass diffusion lines via the Crank‐Nicolson analysis.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"125 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135766165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A continuum active structure model for the interaction of cilia with a viscous fluid","authors":"Astrid Decoene, Sébastien Martin, Fabien Vergnet","doi":"10.1002/zamm.202100534","DOIUrl":"https://doi.org/10.1002/zamm.202100534","url":null,"abstract":"Abstract This paper presents a model for a thin active structure interacting with a viscous fluid, as well as a discretization and numerical simulations of the arising fluid‐structure interaction problem. The developed model allows to reproduce the behavior of cilia or flagella immersed in a viscous flow. In the context of linear or nonlinear elasticity, the model is based upon the definition of a suitable internal Piola‐Kirchoff tensor mimicking the action of the internal dyneins that induce the motility of the structure. In the subsequent fluid‐structure interaction problem, two difficulties arise and are discussed: on the one hand the internal activity of the structure leads to more restrictive well‐posedness conditions and, on the other hand, the coupling conditions between the fluid and the structure require a specific numerical treatment. A weak formulation of the time‐discretized problem is derived in functional spaces that include the coupling conditions, but for numerical purposes, an equivalent formulation using Lagrange multipliers is introduced in order to get rid of the constraints in the functional spaces. This new formulation allows for the use of standard (fluid and structure) solvers, up to an iterative procedure. Numerical simulations are presented, including the beating of one or two cilia in 2d, discussing the competition between the magnitude of the internal activity and the viscosity of the surrounding fluid.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134946890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Moore‐Gibson‐Thompson heat conduction equation for non centrosymmetric rigid solids","authors":"Noelia Bazarra, José R. Fernández, Ramón Quintanilla","doi":"10.1002/zamm.202300531","DOIUrl":"https://doi.org/10.1002/zamm.202300531","url":null,"abstract":"Abstract In this paper, we propose a new thermal model based on the so‐called Moore‐Gibson‐Thompson equation for heat conduction, assuming that the material is not centrosymmetric. The existence of a unique solution is proved, although only the main steps of its proof are provided for the sake of simplicity in the presentation. A sufficient condition is proposed to guarantee the stability of the solutions. Then, a fully discrete scheme is introduced by using the classical finite element scheme and the implicit Euler scheme. A discrete stability property and an a priori error analysis are shown, from which the linear convergence of the approximations is deduced. Finally, some numerical simulations in one‐dimensional examples are performed to show the behavior of the discrete energy decay.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"303 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135590795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al₂O₃ + TiO₂/DW based ternary hybrid nanofluid","authors":"Saqib Murtaza, Poom Kumam, Thana Sutthibutpong, Panawan Suttiarporn, Thanarak Srisurat, Zubair Ahmad","doi":"10.1002/zamm.202300459","DOIUrl":"https://doi.org/10.1002/zamm.202300459","url":null,"abstract":"Abstract Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel. The tri‐hybridized nanoparticles of zinc oxide ZnO, Aluminum oxide Al 2 O 3 , and titanium oxide TiO 2 is dissolved in base fluid distilled water (DW) to form a homogenous suspension. The impact of thermal radiation, joule heating, and viscous dissipation are also assumed. The classical Newtonian ternary nanofluid model has been generalized by using fractal‐fractional derivative (FFD) operator. The generalized model has been discretized by using the Crank–Nicolson scheme and then solved by using computational software. To analyze the behavior of fluid flow and heat distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is noted from the figure that when the volume fraction ϕ reaches to 0.04 (4% of the base fluid), the ternary nanofluid flow shows a significant amount of enhancement in heat transfer rate as compared to binary and unary nanofluid flows. This enhancement in the rate of heat transfer leads to improve the thermophysical characteristics such as viscosity, thermal expansion, and heat capacity etc. of the base fluid. It is also worth mentioning here that the thermal field is also enhance with the higher values of Eckert number , radiation parameter , and joule heating parameter .","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136341314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of constant proportional Caputo operator on the unsteady Oldroyd‐B fluid flow with Newtonian heating and non‐uniform temperature","authors":"Muhammad Arif, Poom Kumam, Wiboonsak Watthayu","doi":"10.1002/zamm.202300048","DOIUrl":"https://doi.org/10.1002/zamm.202300048","url":null,"abstract":"Abstract The Caputo operator has recently gained popularity as a widely used operator in fractional calculus. The purpose of this current research is to develop a new operator by combining the Caputo and proportional derivatives, resulting in the constant proportional Caputo (CPC) fractional operator. To demonstrate the dynamic behavior of this newly defined operator, it was applied to the unsteady Oldroyd‐B fluid model. Additionally, the research considered an Oldroyd‐B fluid in a generalized Darcy medium, considering non‐uniform temperature, radiation, and heat generation. Analytical solutions for the proposed model were obtained and presented in graphical form using the computational software MATHCAD. The impact of various physical parameters was also examined through graphical analysis of velocity and temperature profiles, as well as a comparison between isothermal and non‐uniform temperature. In conclusion, this research found that the CPC fractional operator effectively explains the dynamics of the Oldroyd‐B fluid model with stable and strong memory effects, compared to the classical model.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135579909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spectral simulation of hydromagnetic flow with dissipative and radiative heat transfer over an inclined rotating disk within a non‐Darcy porous medium","authors":"Premful Kumar, Raj Nandkeolyar","doi":"10.1002/zamm.202200395","DOIUrl":"https://doi.org/10.1002/zamm.202200395","url":null,"abstract":"Abstract The goal of the research presented in this paper is to examine how a magnetic field affects the unsteady flow of an incompressible nanofluid over a spinning disc that is inclined and stretched while the flow is embedded in a non‐Darcy porous medium. Furthermore, the heat transmission mechanism takes into account Joule heating and viscous dissipation. By imposing thermal radiation to enhance the heat transmission system under the effects of convection, the current article becomes more realistic. A set of nonlinear partial differential equations and associated boundary conditions defines the mathematical problem. Using an appropriate similarity transformation, the mathematical model is converted into a set of nonlinear ordinary differential equations with boundary conditions, which are then solved numerically by the Spectral Quasi Linearization Method (SQLM). Graphs and tables for various flow parameters illustrate the complete results for the exploration of dimensionless velocity and temperature. Regression analysis is used to statistically estimate the local Nusselt number and the skin friction coefficients. From the numerical results, it is found that when the magnetic parameter is increased, the flow velocity in the radial and tangential directions decreases due to the Lorentz force. With the variation of the Forchheimer number, the fluid flow in both directions decreases with increasing inertia coefficient. By increasing the magnetic parameter and Eckart number, the temperature of the fluid increases. The performed quadratic regression analysis reveals that the permeability of the medium and the generated Lorentz force are significant for the skin friction coefficient in the radial direction, whereas the stretching parameter and Forchheimer number are significant for the skin friction coefficient in the tangential direction. Thermal radiation and convective heating are found to significantly affect the heat transfer coefficient.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135961632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nanofluid turbulent flow inside a duct equipped with disturber with new shape","authors":"Bandar Almohsen","doi":"10.1002/zamm.202200201","DOIUrl":"https://doi.org/10.1002/zamm.202200201","url":null,"abstract":"Abstract To intensify the productivity of solar systems, researchers utilized a perforated tape with obstacles in a circular tube filled with nanomaterial. ANSYS FLUENT was used to simulate the results, combining K‐ε approach and a homogeneous approach for the nanomaterial. Grid size was optimized to reduce computation costs, and the accuracy of the simulation was verified using previously published data. The simulations considered the height of the disturber and the revolution as parameters. The insertion of the disturber increases the impingement with the wall, resulting in a colder outer wall. Although the use of the tape increases convection, resistance with the wall also increases. Therefore, a perforated tape shape was used with obstacles to intensify rotational velocity. Increasing the height and number of revolutions can enhance velocity by 4.58% and 7.04%, respectively. Meanwhile, as the values of N and Re increase, the temperature decreases by 2.1% and 0.11%, respectively.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136014910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Hermitian <i>Cⁿ</i> finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages","authors":"Chih‐Ping Wu, Hao‐Ting Hsu","doi":"10.1002/zamm.202300472","DOIUrl":"https://doi.org/10.1002/zamm.202300472","url":null,"abstract":"Abstract Within the framework of the consistent couple stress theory (CCST), we develop a Hermitian C n ( n = 1, 2) finite cylindrical layer method (FCLM) for carrying out the three‐dimensional (3D) analysis of the size‐dependent buckling and free vibration behaviors of simply supported, functionally graded (FG) piezoelectric cylindrical sandwich microshells. The microshells of interest are placed under closed‐circuit surface conditions and subjected to axial compression and electric voltages. We derive a 3D weak formulation based on Hamilton's principle for this study. In the resulting formulation, the microshell is artificially divided into n l microlayers, with the elastic displacement components and the electric potential selected as the primary variables. By incorporating a layer‐wise kinematic model into our weak formulation, we develop a Hermitian C n FCLM, which can be used for analyzing FG piezoelectric cylindrical sandwich microshells. Each primary variable is expanded as a double Fourier series in the in‐surface domain and is interpolated in the thickness direction using Hermitian C n polynomials. The accuracy and the convergence rate of our Hermitian C n FCLMs are validated by comparing the solutions they produce for FG piezoelectric cylindrical macroshells and FG elastic cylindrical microshells with the relevant exact and approximate 3D solutions which have been reported in the literature. The material length scale parameter of our FCLMs is set at zero in the comparison made with the FG piezoelectric macroshells. In contrast, the piezoelectric and flexoelectric effects are ignored in the comparison made with the FG elastic microshells. The impact of some essential factors on the critical load, critical voltage, and natural frequency of simply supported FG piezoelectric cylindrical sandwich microshells is assessed. The important factors are identified as piezoelectricity, flexoelectricity, the material length scale parameter, the inhomogeneity index, the radius‐to‐thickness ratio, the length‐to‐radius ratio, and the magnitude of the applied voltage and the applied load.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136061927","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermal characteristics for the flow of Williamson hybrid nanofluid with distinct shape factors","authors":"S. Kavya, V. Nagendramma","doi":"10.1002/zamm.202200311","DOIUrl":"https://doi.org/10.1002/zamm.202200311","url":null,"abstract":"Abstract The main purpose of the present article is to investigate the flow of 2‐D, incompressible, steady, hydro magnetic Williamson hybrid nanofluid with three distinct shape factors namely spherical, cylindrical, and platelet shapes under the influence of thermal radiation and viscous dissipation effects on the flow. The aim of the current work is to investigate the thermal conduction capacity of three different shaped nanoparticles by comparison. We have modelled copper and molybdenum disulfide nanoparticles suspension in Williamson fluid blood as a conventional real fluid passing through a horizontal stretching cylinder in this case. A set of non‐linear PDEs are used to conceivably formulate the problem's physical model. The transformation from these modelled PDEs to ODEs is accomplished through the use of appropriate similarity variables. To address the problem, the RK method of order four is used in conjunction with shooting system in order to get first order ordinary equations from non‐linear higher order ordinary differential equations. To run the code for numerical results, computational Matlab bvp4c solver is used and graphs are depicted to explain the impact of various embedded physical quantities on the momentum and energy profiles accompanying the rates of shear stress and heat transfer for the considered Williamson hybrid nanofluid. The use of spherical shaped nanoparticles is thought to improve the thermal conductivity rate of the flowing fluid more than cylinder and platelet shaped nanoparticles. The skin friction coefficient is enhancing for larger values of magnetic parameter and curvature parameter but Weissenberg number has a negative trend. The rate of cooling is high for greater values of magnetic parameter, Williamson fluid parameter, heat generation parameter, thermal conduction parameter, viscous dissipation parameter and thermal radiation parameter.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"2674 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136373958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Electrokinetic peristaltic transport of Bingham‐Papanastasiou fluid via porous media","authors":"Farida Aslam, Saima Noreen","doi":"10.1002/zamm.202300070","DOIUrl":"https://doi.org/10.1002/zamm.202300070","url":null,"abstract":"Abstract An important rheological mathematical model is created to investigate the rheological impacts of slip velocity and varied zeta potentials in an inclined asymmetric channel. The flow is taken in an isotropic porous medium and is governed by Bingham‐Papanastasiou model. The membrane based pumping analysis is done in a wave frame of reference moving with the speed of the wave. Flow model is simplified by considering small wave number δ, small Reynolds number and small Peclet number . The emerging linearized non‐dimensional system of equations is evaluated for analytical and numerical methods. The effects of sundry parameters on pumping, temperature θ, axial velocity u and trapping have been studied graphically. The viscous model is retrieved for Bingham number or stress growth parameter . Finally, the effects of relevant parameters on heat transfer rate and shear stress at walls are discussed numerically. The results show that more pressure is required to flow same amount of fluid in an inclined channel. The temperature field θ is boosted by both the Bingham number and the continuation parameter M . It is also observed that different zeta potentials and velocity slip conditions are significant phenomena to influence channel flow. A pumping‐based device can be built using the existing model to combine and filter physiological samples and chemicals as well as to visualize the transit of physiological fluids.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135063113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}