Noelia Bazarra, José R. Fernández, Ramón Quintanilla
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.
{"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":null,"pages":null},"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}
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 .
{"title":"Fractal‐fractional analysis and numerical simulation for the heat transfer of ZnO + Al<sub>2</sub>O<sub>3</sub> + TiO<sub>2</sub>/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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
Ramzy M. Abumandour, Islam M. Eldesoky, Essam T. Abdelwahab, Muhammad M. Ahmed
Abstract This article analyzes the impact of conjugated dissipative radiative heat transfer with heat source/sink, thermal slip, and the transverse magnetic field on the behavior of the magnetohydrodynamic (MHD) peristaltic thrust containing ferromagnetic gold nanoparticles (AuNPs) with different shape factors through the non‐Newtionian blood flow within compliant walls tube. Entropy generation (EG) plays a prominent role in all aspects connected to thermodynamics and heat transfer aiding in the identification and reduction of system irreversibilities. The sources of irreversibility stem from dissipative friction inherent in fluid flow, the presence of a magnetic field, and the heat transfer process. The ferromagnetic gold nanoparticles (AuNPs) exhibit diverse shapes (bricks, cylinders, and platelets) and possess both magnetic and thermal attributes thereby enhancing the efficiency of heat transfer process. The peristaltic thrust drives the dynamic behavior of the gold blood nanofluid through a compliant tube. The tube walls are flexible and exhibit a curvature effects that can alter the dynamics of fluid flow. The effective Hamilton‐Crosser model is selected to express the thermal conductivity of the nanofluid. Gold blood nanofluids can be treated as incompressible, non‐Newtonian, and MHD fluid flow. The governing equations of the system are solved using the perturbation approach under the assumptions of low Reynolds numbers and long wavelength. Hybrid interactions of magnetic field, radiative heating, thermal slip, elastic wall properties, and gold nanoparticles shapes and concentrations are investigated within the gold blood nanofluid flow. The resulting graphs include the profiles of velocity, temperature distributions, EG, and irreversibility parameters under the influence of the above parameters. The findings reveal that the overall EG rises with increasing values of heat source intensity, Brinkman number, temperature difference factor, compliant wall curvature coefficient, and gold nanoparticles concentrations. Additionally, it is observed that an increase in magnetic flux strength results in the emergence of reversal flow patterns near the walls. This arises due to the augmented magnetic flux obstructing the peristaltic nanofluid flow leading to reduce streamwise velocity. Moreover, heightened magnetic flux strength causes temperature reduction for both thermal slip and non‐slip conditions. Generally, the presence of a thermal slipping parameter further enhances the distribution of temperature. In essence, the rationale and significance of this study primarily revolve around comprehending the interplay of these diverse factors with MHD peristaltic motion of gold blood nanofluid and EG. This not only furthers our theoretical understanding of complex systems but also has practical implications that can improve new technologies, processes, and medical applications. For example, in medical treatments like photothermal therapy (PPT), insights
{"title":"Conjugate dissipative radiative heating with thermal slipping and the entropy production on the thrust of MHD gold blood nanofluid with curvature effects","authors":"Ramzy M. Abumandour, Islam M. Eldesoky, Essam T. Abdelwahab, Muhammad M. Ahmed","doi":"10.1002/zamm.202300260","DOIUrl":"https://doi.org/10.1002/zamm.202300260","url":null,"abstract":"Abstract This article analyzes the impact of conjugated dissipative radiative heat transfer with heat source/sink, thermal slip, and the transverse magnetic field on the behavior of the magnetohydrodynamic (MHD) peristaltic thrust containing ferromagnetic gold nanoparticles (AuNPs) with different shape factors through the non‐Newtionian blood flow within compliant walls tube. Entropy generation (EG) plays a prominent role in all aspects connected to thermodynamics and heat transfer aiding in the identification and reduction of system irreversibilities. The sources of irreversibility stem from dissipative friction inherent in fluid flow, the presence of a magnetic field, and the heat transfer process. The ferromagnetic gold nanoparticles (AuNPs) exhibit diverse shapes (bricks, cylinders, and platelets) and possess both magnetic and thermal attributes thereby enhancing the efficiency of heat transfer process. The peristaltic thrust drives the dynamic behavior of the gold blood nanofluid through a compliant tube. The tube walls are flexible and exhibit a curvature effects that can alter the dynamics of fluid flow. The effective Hamilton‐Crosser model is selected to express the thermal conductivity of the nanofluid. Gold blood nanofluids can be treated as incompressible, non‐Newtonian, and MHD fluid flow. The governing equations of the system are solved using the perturbation approach under the assumptions of low Reynolds numbers and long wavelength. Hybrid interactions of magnetic field, radiative heating, thermal slip, elastic wall properties, and gold nanoparticles shapes and concentrations are investigated within the gold blood nanofluid flow. The resulting graphs include the profiles of velocity, temperature distributions, EG, and irreversibility parameters under the influence of the above parameters. The findings reveal that the overall EG rises with increasing values of heat source intensity, Brinkman number, temperature difference factor, compliant wall curvature coefficient, and gold nanoparticles concentrations. Additionally, it is observed that an increase in magnetic flux strength results in the emergence of reversal flow patterns near the walls. This arises due to the augmented magnetic flux obstructing the peristaltic nanofluid flow leading to reduce streamwise velocity. Moreover, heightened magnetic flux strength causes temperature reduction for both thermal slip and non‐slip conditions. Generally, the presence of a thermal slipping parameter further enhances the distribution of temperature. In essence, the rationale and significance of this study primarily revolve around comprehending the interplay of these diverse factors with MHD peristaltic motion of gold blood nanofluid and EG. This not only furthers our theoretical understanding of complex systems but also has practical implications that can improve new technologies, processes, and medical applications. For example, in medical treatments like photothermal therapy (PPT), insights ","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135718952","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}
Yusuf O. Tijani, Mojeed T. Akolade, Olumuyiwa Otegbeye, Abdulhakeem Yusuf
Abstract Stretching and shrinking application ranges from aerodynamic extrusion of plastic sheets, biological implants, condensation of metallic plates to the design of musical instruments. To emphasize the need for proper fluid flow in the mammalian system, the phenomenon of stretching or shrinking suppresses muscle strains and cramps, and also prevents stroke and heart disease. For further insight into the dynamics of blood with Prandtl number of 21.0 in a rotating system, the present study theoretically investigates the flow of a Jeffrey fluid induced with gold nanoparticles over a rotating sheet. The homogenization of the gold nanoparticle with the base fluid is due to the Tiwari‐Das approach. To investigate the flow profiles and dynamics of the sheet, the spectral local linearization method (SLLM) is used to obtain approximate solutions to the resulting system of nonlinear differential equations. The results obtained using the SLLM are validated by taking the limiting case and comparing against published literature results. The obtained results suggest that the velocity of the nanofluid and the heat transfer rate on the stretching and shrinking sheets exhibit an opposing behaviour. A blood sample with gold nanoparticles is advised for a reduced skin friction effect in the stretching sheet but a more significant drag force in the shrinking sheet than in the base fluid. For a unit value of the rotating parameter, the skin drag force reduces by 36% for the primary skin drag force and 57% for the secondary skin drag force.
{"title":"Surface dynamics on Jeffrey nanofluid flow with Coriolis effect and variable Darcy regime","authors":"Yusuf O. Tijani, Mojeed T. Akolade, Olumuyiwa Otegbeye, Abdulhakeem Yusuf","doi":"10.1002/zamm.202300217","DOIUrl":"https://doi.org/10.1002/zamm.202300217","url":null,"abstract":"Abstract Stretching and shrinking application ranges from aerodynamic extrusion of plastic sheets, biological implants, condensation of metallic plates to the design of musical instruments. To emphasize the need for proper fluid flow in the mammalian system, the phenomenon of stretching or shrinking suppresses muscle strains and cramps, and also prevents stroke and heart disease. For further insight into the dynamics of blood with Prandtl number of 21.0 in a rotating system, the present study theoretically investigates the flow of a Jeffrey fluid induced with gold nanoparticles over a rotating sheet. The homogenization of the gold nanoparticle with the base fluid is due to the Tiwari‐Das approach. To investigate the flow profiles and dynamics of the sheet, the spectral local linearization method (SLLM) is used to obtain approximate solutions to the resulting system of nonlinear differential equations. The results obtained using the SLLM are validated by taking the limiting case and comparing against published literature results. The obtained results suggest that the velocity of the nanofluid and the heat transfer rate on the stretching and shrinking sheets exhibit an opposing behaviour. A blood sample with gold nanoparticles is advised for a reduced skin friction effect in the stretching sheet but a more significant drag force in the shrinking sheet than in the base fluid. For a unit value of the rotating parameter, the skin drag force reduces by 36% for the primary skin drag force and 57% for the secondary skin drag force.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135719101","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}
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.
{"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":null,"pages":null},"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}
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.
{"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":null,"pages":null},"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}
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.
摘要在一致耦合应力理论(CCST)的框架下，我们建立了一种hermite C n (n = 1,2)有限圆柱层法(FCLM)，用于对简支功能梯度(FG)压电圆柱夹层微壳的尺寸相关屈曲和自由振动行为进行三维(3D)分析。我们感兴趣的微壳被置于闭环表面条件下，并经受轴向压缩和电压。我们推导了一个基于Hamilton原理的三维弱公式。在所得到的公式中，微壳被人为地划分为n个微层，并选择弹性位移分量和电势作为主要变量。通过将分层运动模型纳入弱公式，我们开发了一个厄米C n FCLM，可用于分析FG压电圆柱形夹层微壳。每个主变量在曲面域中展开为二重傅立叶级数，并使用厄米多项式在厚度方向上进行插值。通过与文献中报道的精确和近似三维解进行比较，验证了我们的hermite C n FCLMs的精度和收敛速度。在与FG压电大壳的对比中，我们的fclm材料长度尺度参数设为零。相比之下，在与FG弹性微壳的比较中忽略了压电效应和柔电效应。分析了一些关键因素对简支FG压电圆柱夹层微壳临界载荷、临界电压和固有频率的影响。重要的影响因素包括压电性、挠性、材料长度尺度参数、非均匀性指数、半径与厚度比、长度与半径比、外加电压和外加载荷的大小。
{"title":"A Hermitian <i>C<sup>n</sup></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":null,"pages":null},"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}
Abstract A numerical study of the thermally stratified flow of H 2 O based Cu − Al 2 O 3 hybrid nanofluid over a linearly stretching cylinder placed vertically in a porous media has been performed. The influences of viscous dissipation, thermal source/sink, and an inclined magnetic field were also considered. Using appropriate similarity transformations, the non‐linear mathematical equations of the flow model are translated into a dimensionless form. The in‐build finite difference Matlab code Bvp4c is used to attain the numerical solution of the transformed non‐linear ordinary differential equations (ODEs). Influences of nanoparticles when added to the water and also the flow parameters’ impacts on the flow rate and thermal transport rate are shown in graphs and tables. The results showed that the absolute value of the shear stress of the hybrid nanofluids was enhanced by up to 33% compared to the considered nanofluid. The study also revealed that the heat transport rate in the convective flow region was much higher in hybrid nanofluid as compared to nanofluid. For Cu − Al 2 O 3 /water hybrid nanofluid, the temperature went negative for high thermal stratification. The present study has important implications for the design and optimization of heat transfer devices that use thermally stratified hybrid nanofluids. The results also provide novel insights into the flow behavior of these fluids, that can be used to improve our understanding of their physical properties.
摘要采用数值方法研究了基于h2o的Cu - Al - 2o3杂化纳米流体在垂直放置于多孔介质中的线性拉伸圆柱体上的热分层流动。同时考虑了粘性耗散、热源/汇和倾斜磁场的影响。利用适当的相似变换，将流动模型的非线性数学方程转化为无因次形式。利用内置的有限差分Matlab代码Bvp4c对变换后的非线性常微分方程(ode)进行数值求解。以图形和表格的形式显示了纳米颗粒加入水中的影响以及流动参数对流速和热输运率的影响。结果表明，混合纳米流体的剪切应力绝对值比考虑的纳米流体提高了33%。研究还发现，与纳米流体相比，混合纳米流体对流区的传热速率要高得多。对于Cu−al2o3 /水混合纳米流体，温度为负，热分层高。本研究对采用热分层混合纳米流体的传热装置的设计和优化具有重要意义。该结果还为这些流体的流动行为提供了新的见解，可用于提高我们对其物理性质的理解。
{"title":"Thermally stratified Cu–Al<sub>2</sub>O<sub>3</sub>/water hybrid nanofluid flow with the impact of an inclined magnetic field, viscous dissipation and heat source/sink across a vertically stretching cylinder","authors":"Ashish Paul, Jintu Mani Nath, Tusar Kanti Das","doi":"10.1002/zamm.202300084","DOIUrl":"https://doi.org/10.1002/zamm.202300084","url":null,"abstract":"Abstract A numerical study of the thermally stratified flow of H 2 O based Cu − Al 2 O 3 hybrid nanofluid over a linearly stretching cylinder placed vertically in a porous media has been performed. The influences of viscous dissipation, thermal source/sink, and an inclined magnetic field were also considered. Using appropriate similarity transformations, the non‐linear mathematical equations of the flow model are translated into a dimensionless form. The in‐build finite difference Matlab code Bvp4c is used to attain the numerical solution of the transformed non‐linear ordinary differential equations (ODEs). Influences of nanoparticles when added to the water and also the flow parameters’ impacts on the flow rate and thermal transport rate are shown in graphs and tables. The results showed that the absolute value of the shear stress of the hybrid nanofluids was enhanced by up to 33% compared to the considered nanofluid. The study also revealed that the heat transport rate in the convective flow region was much higher in hybrid nanofluid as compared to nanofluid. For Cu − Al 2 O 3 /water hybrid nanofluid, the temperature went negative for high thermal stratification. The present study has important implications for the design and optimization of heat transfer devices that use thermally stratified hybrid nanofluids. The results also provide novel insights into the flow behavior of these fluids, that can be used to improve our understanding of their physical properties.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136061476","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}
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.
{"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":null,"pages":null},"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}
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