Utilization of symmetrical or anti‐symmetrical condition could improve the calculation efficiency. In this paper, a mathematical formulation is proposed to deal with the symmetrical or anti‐symmetrical condition in an integral nonlocal stress gradient model (INSGM), which is transformed equivalently into differential form with constitutive boundary condition as well as constitutive symmetrical or anti‐symmetrical condition. Unlike general constitutive boundary conditions, an integral item is introduced to constitutive symmetrical and anti‐symmetrical conditions, and they are opposite to each other. Based on INSGM with symmetrical or anti‐symmetrical conditions, static bending of simply‐supported (SS) and clamped‐clamped (CC) functionally graded porous Timoshenko nanobeams is investigated for symmetrical loads, including uniformly distributed load (UDL) and middle point force, as well as anti‐symmetrical loads, including anti‐symmetrical UDL and middle point moment. The exact solutions are deduced and expressed in explicit form for different boundary and loading conditions. Calculation shows that, under UDL, bending deflections of half Timoshenko nanobeams based on current model agree well with those for whole Timoshenko nanobeams based on general INSGM for both SS and CC boundary conditions. Numerical study is performed to show the effectiveness of current model.
{"title":"Integral nonlocal stress gradient elasticity of functionally graded porous Timoshenko nanobeam with symmetrical or anti‐symmetrical condition","authors":"Chang Li, Hai Qing","doi":"10.1002/zamm.202300282","DOIUrl":"https://doi.org/10.1002/zamm.202300282","url":null,"abstract":"Utilization of symmetrical or anti‐symmetrical condition could improve the calculation efficiency. In this paper, a mathematical formulation is proposed to deal with the symmetrical or anti‐symmetrical condition in an integral nonlocal stress gradient model (INSGM), which is transformed equivalently into differential form with constitutive boundary condition as well as constitutive symmetrical or anti‐symmetrical condition. Unlike general constitutive boundary conditions, an integral item is introduced to constitutive symmetrical and anti‐symmetrical conditions, and they are opposite to each other. Based on INSGM with symmetrical or anti‐symmetrical conditions, static bending of simply‐supported (SS) and clamped‐clamped (CC) functionally graded porous Timoshenko nanobeams is investigated for symmetrical loads, including uniformly distributed load (UDL) and middle point force, as well as anti‐symmetrical loads, including anti‐symmetrical UDL and middle point moment. The exact solutions are deduced and expressed in explicit form for different boundary and loading conditions. Calculation shows that, under UDL, bending deflections of half Timoshenko nanobeams based on current model agree well with those for whole Timoshenko nanobeams based on general INSGM for both SS and CC boundary conditions. Numerical study is performed to show the effectiveness of current model.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"87 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90933117","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}
Sameh A. Hussein, Sameh E. Ahmed, A. Arafa, A. A. Elshekhipy
Mathematical simulation of biological fluids is of upmost significance due to its numerous medical uses. Interpreting various biological flows necessitates a thorough knowledge of the peristaltic mechanism. This paper presents a computational study for the peristaltic pumping within vertical asymmetric channels filled with BN‐EG nanofluid under the influence of temperature‐dependent electrical conductivity and thermal radiation. Experimental study showed that the nanofluid created by suspending Boron Nitride particles in a combination of Ethylene Glycol exhibited non‐Newtonian characteristics. Further, the Carreau's fluid model provides accurate predictions about the rheological properties of BN‐EG nanofluid. Various configurations of the outer boundaries are considered, namely, square wave, multi‐sinusoidal wave, trapezoidal wave, and triangular wave. A uniform magnetic field together with nanoparticles and mass concentrations, joule heating, first‐order chemical reaction as well as viscous dissipation are considered. Influences of the Dufour and Soret numbers are examined, and the cases of biological scientific assumptions which is known as low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND‐Solve), and the obtained results are presented in terms of the axial velocity u, heat transfer rate Z, concentration profile Ω, temperature profile θ, extra stress tensor , pressure gradient , pressure rise and stream function ψ. The major outcomes revealed that the maximizing in electrical conductivity coefficient, variable viscosity coefficient and magnetic field parameter is better to obtain a higher rate of the heat transfer while the increase in thermo‐diffusion effects as well as linear thermal radiation coefficient causes a reduction in the rate of heat transfer.
{"title":"Temperature‐dependent electrical conductivity impact on radiative and dissipative peristaltic transport of boron nitride‐ethylene glycol nanofluid through asymmetric channels","authors":"Sameh A. Hussein, Sameh E. Ahmed, A. Arafa, A. A. Elshekhipy","doi":"10.1002/zamm.202300136","DOIUrl":"https://doi.org/10.1002/zamm.202300136","url":null,"abstract":"Mathematical simulation of biological fluids is of upmost significance due to its numerous medical uses. Interpreting various biological flows necessitates a thorough knowledge of the peristaltic mechanism. This paper presents a computational study for the peristaltic pumping within vertical asymmetric channels filled with BN‐EG nanofluid under the influence of temperature‐dependent electrical conductivity and thermal radiation. Experimental study showed that the nanofluid created by suspending Boron Nitride particles in a combination of Ethylene Glycol exhibited non‐Newtonian characteristics. Further, the Carreau's fluid model provides accurate predictions about the rheological properties of BN‐EG nanofluid. Various configurations of the outer boundaries are considered, namely, square wave, multi‐sinusoidal wave, trapezoidal wave, and triangular wave. A uniform magnetic field together with nanoparticles and mass concentrations, joule heating, first‐order chemical reaction as well as viscous dissipation are considered. Influences of the Dufour and Soret numbers are examined, and the cases of biological scientific assumptions which is known as low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND‐Solve), and the obtained results are presented in terms of the axial velocity u, heat transfer rate Z, concentration profile Ω, temperature profile θ, extra stress tensor , pressure gradient , pressure rise and stream function ψ. The major outcomes revealed that the maximizing in electrical conductivity coefficient, variable viscosity coefficient and magnetic field parameter is better to obtain a higher rate of the heat transfer while the increase in thermo‐diffusion effects as well as linear thermal radiation coefficient causes a reduction in the rate of heat transfer.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"24 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82032427","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}
This nonsimilar convection study is about the flow of Carreau–Yasuda (CY) nanofluid model above a vertically extendible surface. Convection in a fluid‐filled permeable medium has given due consideration because of its relevance in a variety of applications, including insulation, relocation of water from geothermal reservoirs, storage of nuclear waste, renewable energy, mechanical engineering, and enhanced oil reservoir recovery. By virtue of linear stretching and buoyancy effects, flow in a stationary fluid is induced along a vertical porous surface. In x‐momentum equation, linear buoyancy in the context of temperature and concentration is taken into consideration. Modeling of energy expression is done in the presence of Dufour and Soret influences. Governing differential system describing convection equations is changed into nonlinear partial differential system (PDE) by implementing applicable nonsimilar transformations. By making use of analytical local nonsimilarity (LNS) technique and bvp4c (numerical finite difference‐based algorithm), the transformed dimensionless nonsimilar structure is simulated numerically. At the end, the alteration of important nondimensional numbers is studied on transport quantities such as temperature, concentration and velocity field. The repercussions of relevant parameters on drag coefficient, Nusselt number and Sherwood number have been tabulated. Numerical simulations of nonsimilar model suggests that the velocity profile reduces due to rise in the values of Weissenberg number, porosity and suction parameter. The temperature profile is increased in comparison with the higher estimates, Eckert, and Dufour numbers. Because of larger values of Soret and Prandtl number, an increase in concentration profile is seen. Friction coefficient and Nusselt number increases with respect to higher estimations of porosity parameter, Weissenberg number and Prandtl number respectively, whereas they decrease against Dufour and Eckert variations.
{"title":"Nonsimilar modeling analysis of Carreau–Yasuda mixed convective flow in a porous medium subjected to Soret and Dufour influences","authors":"Jifeng Cui, Qurat‐Ul‐Ain Ashraf, Wenhao Cheng, Umer Farooq, Muzamil Hussain","doi":"10.1002/zamm.202100603","DOIUrl":"https://doi.org/10.1002/zamm.202100603","url":null,"abstract":"This nonsimilar convection study is about the flow of Carreau–Yasuda (CY) nanofluid model above a vertically extendible surface. Convection in a fluid‐filled permeable medium has given due consideration because of its relevance in a variety of applications, including insulation, relocation of water from geothermal reservoirs, storage of nuclear waste, renewable energy, mechanical engineering, and enhanced oil reservoir recovery. By virtue of linear stretching and buoyancy effects, flow in a stationary fluid is induced along a vertical porous surface. In x‐momentum equation, linear buoyancy in the context of temperature and concentration is taken into consideration. Modeling of energy expression is done in the presence of Dufour and Soret influences. Governing differential system describing convection equations is changed into nonlinear partial differential system (PDE) by implementing applicable nonsimilar transformations. By making use of analytical local nonsimilarity (LNS) technique and bvp4c (numerical finite difference‐based algorithm), the transformed dimensionless nonsimilar structure is simulated numerically. At the end, the alteration of important nondimensional numbers is studied on transport quantities such as temperature, concentration and velocity field. The repercussions of relevant parameters on drag coefficient, Nusselt number and Sherwood number have been tabulated. Numerical simulations of nonsimilar model suggests that the velocity profile reduces due to rise in the values of Weissenberg number, porosity and suction parameter. The temperature profile is increased in comparison with the higher estimates, Eckert, and Dufour numbers. Because of larger values of Soret and Prandtl number, an increase in concentration profile is seen. Friction coefficient and Nusselt number increases with respect to higher estimations of porosity parameter, Weissenberg number and Prandtl number respectively, whereas they decrease against Dufour and Eckert variations.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"13 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86791700","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}
In this paper, the frequency stability analysis of a fluid conveying cantilever viscoelastic carbon nanotube (CNT) in the Kelvin–Voigt material model with slip boundary condition (BC) regime on a viscoelastic Pasternak foundation and under axial load has been performed based on nonlocal Euler–Bernoulli thin beam theory. The governing partial differential equation of motion (EOM) and its associated BCs have been derived using the Hamilton principle. The governing EOM has been converted into an ordinary differential equation using mode summation technique and solved by applying the extended Galerkin method. Then, the frequency stability analysis has been carried out for the vibrational response of CNT in the state‐space form. The obtained results have been validated with the literature works. The effect of changes of various parameters like elastic stiffness, shear stiffness and damping coefficients of foundation, nonlocal scale‐effect parameter of the nanotube, fluid flow Knudsen number, mass ratio, structural damping of the nanotube and applied axial force have been investigated in terms of frequency to predict the occurrence of different instability modes for the system. It is concluded that flutter and divergence instabilities in the vibration of the viscoelastic CNT are significantly affected by changes of different above‐mentioned parameters.
{"title":"Frequency stability analysis of a cantilever viscoelastic CNT conveying fluid on a viscoelastic Pasternak foundation and under axial load based on nonlocal elasticity theory","authors":"A. Mamandi","doi":"10.1002/zamm.202100536","DOIUrl":"https://doi.org/10.1002/zamm.202100536","url":null,"abstract":"In this paper, the frequency stability analysis of a fluid conveying cantilever viscoelastic carbon nanotube (CNT) in the Kelvin–Voigt material model with slip boundary condition (BC) regime on a viscoelastic Pasternak foundation and under axial load has been performed based on nonlocal Euler–Bernoulli thin beam theory. The governing partial differential equation of motion (EOM) and its associated BCs have been derived using the Hamilton principle. The governing EOM has been converted into an ordinary differential equation using mode summation technique and solved by applying the extended Galerkin method. Then, the frequency stability analysis has been carried out for the vibrational response of CNT in the state‐space form. The obtained results have been validated with the literature works. The effect of changes of various parameters like elastic stiffness, shear stiffness and damping coefficients of foundation, nonlocal scale‐effect parameter of the nanotube, fluid flow Knudsen number, mass ratio, structural damping of the nanotube and applied axial force have been investigated in terms of frequency to predict the occurrence of different instability modes for the system. It is concluded that flutter and divergence instabilities in the vibration of the viscoelastic CNT are significantly affected by changes of different above‐mentioned parameters.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"54 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83883676","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}
Based on Eringen's nonlocal elastic theory, the vibration characteristics and critical buckling load of porous functionally graded rectangular nanoplates under thermomechanical load are studied. The material properties of porous FGM nanoplates are characterized by Voigt mixing power rate and arbitrarily distributed porous model, and the correlation between material and temperature is further considered, the temperature distribution along with the thickness direction is uniform. The numerical solution of the vibration and critical buckling loads of porous functionally graded material (FGM) rectangular nanoplates under thermo‐mechanical loading are investigated using the numerical solution method‐differential transformation method (DTM), and the governing differential equations are established in the classical plate theory and Hamilton system. The effects of boundary conditions, nonlocal parameters, gradient index, temperature rise, porosity, compression load, and aspect ratio on the vibration and critical buckling load of porous FGM nanoplates under thermo‐mechanical loading effects are mainly investigated utilizing arithmetic examples.
{"title":"Analysis of vibration and critical buckling load of porous functionally graded material rectangular nanoplates under thermo‐mechanical loading","authors":"Weibin Wang, Zhaochun Teng","doi":"10.1002/zamm.202200073","DOIUrl":"https://doi.org/10.1002/zamm.202200073","url":null,"abstract":"Based on Eringen's nonlocal elastic theory, the vibration characteristics and critical buckling load of porous functionally graded rectangular nanoplates under thermomechanical load are studied. The material properties of porous FGM nanoplates are characterized by Voigt mixing power rate and arbitrarily distributed porous model, and the correlation between material and temperature is further considered, the temperature distribution along with the thickness direction is uniform. The numerical solution of the vibration and critical buckling loads of porous functionally graded material (FGM) rectangular nanoplates under thermo‐mechanical loading are investigated using the numerical solution method‐differential transformation method (DTM), and the governing differential equations are established in the classical plate theory and Hamilton system. The effects of boundary conditions, nonlocal parameters, gradient index, temperature rise, porosity, compression load, and aspect ratio on the vibration and critical buckling load of porous FGM nanoplates under thermo‐mechanical loading effects are mainly investigated utilizing arithmetic examples.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"21 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83202891","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}
Natural convection of a chemically reacting hybrid nanofluid in a closed wavy‐walled cavity embedded in a porous medium is investigated with an inclined magnetic field. The left wall of the cavity is assumed to be wavy and the walls are maintained at the surrounding temperature. Governing equations are transformed into dimensionless equations which are solved using the finite difference method. To validate the solving procedure, a grid sensitivity test and a comparison with published results have been carried out. Streamlines, isotherms, and isolines of concentration are discussed for varying Rayleigh number (Ra), Hartmann number (Ha), Frank‐Kamenetskii number (Fk), Darcy number (Da), combined buoyancy parameter (N), and nanoparticle volume fractions (φ1 and φ2). Streamlines show clockwise and anticlockwise vortices irrespective of the parameters. For Fk = 0.5, the maximum stream function (ψmax) is 0.64 and the maximum temperature (θmax) is 0.20 while for Fk = 2, ψmax and θmax are 4.08 and 1.36, respectively. Besides, for Ha = 0, ψmax and θmax are 1.61 and 0.379, however, for Ha = 100, ψmax is 0.90 and θmax is 0.377. Maximum temperature is increased with an increase in Ra, N, and Fk, whereas it is decreased with the augmentation of Ha and Da. Isolines of concentration show reverse characteristics of temperature. An increase in Ra, Da, and Fk enhances the intensity of streamlines but the opposite is observed for higher Ha, N and volume fractions. Moreover, the eyes of the vortices are distorted in the direction of the magnetic field.
{"title":"Magnetohydrodynamic natural convection of a reacting hybrid nanofluid in a porous wavy‐walled cavity","authors":"N. C. Roy, S. Monira","doi":"10.1002/zamm.202200476","DOIUrl":"https://doi.org/10.1002/zamm.202200476","url":null,"abstract":"Natural convection of a chemically reacting hybrid nanofluid in a closed wavy‐walled cavity embedded in a porous medium is investigated with an inclined magnetic field. The left wall of the cavity is assumed to be wavy and the walls are maintained at the surrounding temperature. Governing equations are transformed into dimensionless equations which are solved using the finite difference method. To validate the solving procedure, a grid sensitivity test and a comparison with published results have been carried out. Streamlines, isotherms, and isolines of concentration are discussed for varying Rayleigh number (Ra), Hartmann number (Ha), Frank‐Kamenetskii number (Fk), Darcy number (Da), combined buoyancy parameter (N), and nanoparticle volume fractions (φ1 and φ2). Streamlines show clockwise and anticlockwise vortices irrespective of the parameters. For Fk = 0.5, the maximum stream function (ψmax) is 0.64 and the maximum temperature (θmax) is 0.20 while for Fk = 2, ψmax and θmax are 4.08 and 1.36, respectively. Besides, for Ha = 0, ψmax and θmax are 1.61 and 0.379, however, for Ha = 100, ψmax is 0.90 and θmax is 0.377. Maximum temperature is increased with an increase in Ra, N, and Fk, whereas it is decreased with the augmentation of Ha and Da. Isolines of concentration show reverse characteristics of temperature. An increase in Ra, Da, and Fk enhances the intensity of streamlines but the opposite is observed for higher Ha, N and volume fractions. Moreover, the eyes of the vortices are distorted in the direction of the magnetic field.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"2 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80923415","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}
The current investigation is concerned with the effect of chemical reactions and radiation on unsteady free convective flow through a porous medium via an infinitely oscillating vertical plate. The primary goal of this study is to investigate the effects of first‐order homogeneous chemical reactions and thermal radiation on mass flow and heat transmission characteristics. The closed‐form Laplace transformation method is used to obtain exact solutions to the governing equations for concentration, energy and momentum. The impact of various non‐dimensional parameters on fluid velocity, temperature and concentration is graphically depicted. Furthermore, 3‐dimensional surface plots for the Nusselt number and Sherwood number are provided, and the equation for skin friction is derived and demonstrated in tabular form. Investigation simulates that the skin friction increases as the chemical reaction parameter hikes, whereas the fluid concentration reduces as the chemical reaction parameter increases. Further, it was revealed that the augmentation of the radiation parameter decreased the temperature and velocity pattern. It is seen that the primary and secondary velocities reduce due to the increment of the chemical reaction parameter.
{"title":"Chemical reaction and radiation impact on unsteady free convective flow through a porous medium past an infinite oscillatory vertical plate","authors":"D. J. Saikia, N. Ahmed","doi":"10.1002/zamm.202200579","DOIUrl":"https://doi.org/10.1002/zamm.202200579","url":null,"abstract":"The current investigation is concerned with the effect of chemical reactions and radiation on unsteady free convective flow through a porous medium via an infinitely oscillating vertical plate. The primary goal of this study is to investigate the effects of first‐order homogeneous chemical reactions and thermal radiation on mass flow and heat transmission characteristics. The closed‐form Laplace transformation method is used to obtain exact solutions to the governing equations for concentration, energy and momentum. The impact of various non‐dimensional parameters on fluid velocity, temperature and concentration is graphically depicted. Furthermore, 3‐dimensional surface plots for the Nusselt number and Sherwood number are provided, and the equation for skin friction is derived and demonstrated in tabular form. Investigation simulates that the skin friction increases as the chemical reaction parameter hikes, whereas the fluid concentration reduces as the chemical reaction parameter increases. Further, it was revealed that the augmentation of the radiation parameter decreased the temperature and velocity pattern. It is seen that the primary and secondary velocities reduce due to the increment of the chemical reaction parameter.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"15 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84966039","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}
Naeem Ullah, D. N. K. Marwat, Montaha Mohamed Ibrahim Mohamed, Sana Ben Moussa
A generalized model of flow of viscous thin film has been presented and the film is maintained over a porous, moving and non‐flat sheet. We categorically emphasized on the nonuniform and nonlinear kinematics of the sheet and deformation of thin film and variation of all quantities specified at the boundaries are taken of exponential type. The combined effects of deformation of both thin film and sheet along with the nonlinear kinematics of sheet have been analyzed on the characteristics of flow. The governing partial differential equations are transformed into ordinary differential equations (ODEs) by using similarity transformations and the final problem of ODEs is solved with the help of bvp4c technique, whereas, the result for the velocity and skin friction are graphed for different values of the injection (suction), stretching (shrinking) and deformation (contraction/expansion) of both thin film and sheet parameters. Note that the increasing, decreasing, uniform, linear, nonlinear and boundary layer behaviors of the velocity profiles and skin friction are noted for multiple choices of the parameters. Moreover, flows in upstream and downstream directions have been observed for different values and diverse nature of the parameters.
{"title":"Steady flow of thin film over porous moving and non‐flat sheet with nonlinear kinematics of exponential type","authors":"Naeem Ullah, D. N. K. Marwat, Montaha Mohamed Ibrahim Mohamed, Sana Ben Moussa","doi":"10.1002/zamm.202300057","DOIUrl":"https://doi.org/10.1002/zamm.202300057","url":null,"abstract":"A generalized model of flow of viscous thin film has been presented and the film is maintained over a porous, moving and non‐flat sheet. We categorically emphasized on the nonuniform and nonlinear kinematics of the sheet and deformation of thin film and variation of all quantities specified at the boundaries are taken of exponential type. The combined effects of deformation of both thin film and sheet along with the nonlinear kinematics of sheet have been analyzed on the characteristics of flow. The governing partial differential equations are transformed into ordinary differential equations (ODEs) by using similarity transformations and the final problem of ODEs is solved with the help of bvp4c technique, whereas, the result for the velocity and skin friction are graphed for different values of the injection (suction), stretching (shrinking) and deformation (contraction/expansion) of both thin film and sheet parameters. Note that the increasing, decreasing, uniform, linear, nonlinear and boundary layer behaviors of the velocity profiles and skin friction are noted for multiple choices of the parameters. Moreover, flows in upstream and downstream directions have been observed for different values and diverse nature of the parameters.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"13 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79429580","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}
N. Khan, Basmah H. Alshammari, A. Noor, Siwar Ben Haj Hassine
Variable properties like thermal conductivity and variable thickness of the disk are analyzed for the Jeffery nanofluid and gyrotactic microorganisms in rotating system taking into account the Cattaneo‐Christov heat flux, velocity slip and thermal radiation effects. Zero mass flux is assumed at the disk surface for the better and high accuracy of the out‐turn. The governing equations of the problem are transformed into nonlinear ordinary differential equations by introducing the appropriate similarity transformations which are solved analytically by the homotopy analysis method. The effects of all the parameters are given in detail through the graphs.
{"title":"Performance of variable characteristics on MHD Jeffery nanofluid over spinning disk with Cattaneo‐Christov heat flux and microswimmers","authors":"N. Khan, Basmah H. Alshammari, A. Noor, Siwar Ben Haj Hassine","doi":"10.1002/zamm.202200247","DOIUrl":"https://doi.org/10.1002/zamm.202200247","url":null,"abstract":"Variable properties like thermal conductivity and variable thickness of the disk are analyzed for the Jeffery nanofluid and gyrotactic microorganisms in rotating system taking into account the Cattaneo‐Christov heat flux, velocity slip and thermal radiation effects. Zero mass flux is assumed at the disk surface for the better and high accuracy of the out‐turn. The governing equations of the problem are transformed into nonlinear ordinary differential equations by introducing the appropriate similarity transformations which are solved analytically by the homotopy analysis method. The effects of all the parameters are given in detail through the graphs.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"1 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82669807","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}
Nanomaterials having excellent thermal properties are employed in producing energy, extrusion processes, engineering processes, nuclear interactions, industrial domains and aero‐spaces, etc. Therefore, current study scrutinizes the aspects of entropy optimization and Ohmic heating on MHD peristalsis of fourth‐grade nanoliquid in a channel. Flexible channel walls retain concentration, thermal slip and velocity conditions. The consequences of viscous dissipation and Arrhenius activation have been accounted. The lubrication approximation is used in mathematical modelling. Nanofluid model is used by considering thermophoresis and Brownian motion. Furthermore, thermal radiation features are included in the energy equation. By using an appropriate similarity transformation, a system of PDEs is simplified to a solvable system of ODEs. Numerical techniques are used to solve the problem of governance. Detailed exploration of the sundry variables of concern on the flow quantities like velocity profile, nanoparticle concentration, temperature and entropy of the system is graphically examined. Heat transfer is examined in tabular form. Based on the derived outcomes, the velocity rises via thermal Grashof and slip variables. Further, an increment in Brownian motion and radiation parameters shows opposite behaviour on temperature.
{"title":"Mathematical modelling for peristaltic flow of fourth‐grade nanoliquid with entropy generation","authors":"Z. Nisar, T. Hayat, A. Alsaedi, S. Momani","doi":"10.1002/zamm.202300034","DOIUrl":"https://doi.org/10.1002/zamm.202300034","url":null,"abstract":"Nanomaterials having excellent thermal properties are employed in producing energy, extrusion processes, engineering processes, nuclear interactions, industrial domains and aero‐spaces, etc. Therefore, current study scrutinizes the aspects of entropy optimization and Ohmic heating on MHD peristalsis of fourth‐grade nanoliquid in a channel. Flexible channel walls retain concentration, thermal slip and velocity conditions. The consequences of viscous dissipation and Arrhenius activation have been accounted. The lubrication approximation is used in mathematical modelling. Nanofluid model is used by considering thermophoresis and Brownian motion. Furthermore, thermal radiation features are included in the energy equation. By using an appropriate similarity transformation, a system of PDEs is simplified to a solvable system of ODEs. Numerical techniques are used to solve the problem of governance. Detailed exploration of the sundry variables of concern on the flow quantities like velocity profile, nanoparticle concentration, temperature and entropy of the system is graphically examined. Heat transfer is examined in tabular form. Based on the derived outcomes, the velocity rises via thermal Grashof and slip variables. Further, an increment in Brownian motion and radiation parameters shows opposite behaviour on temperature.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"3 1","pages":""},"PeriodicalIF":2.3,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81826374","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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