This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space R^(3). For regular initial data with m0E0 is suitable small, where m0 and E0 represent the upper bound of initial density ...This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space R^(3). For regular initial data with m0E0 is suitable small, where m0 and E0 represent the upper bound of initial density and initial energy, we prove that if ρ0 ∈ Lγ ∩ H3 with γ ∈ (1, 6), then the problem possesses a unique global classical solution on R^(3) × [0, T] with any T ∈ (0, ∞). It’s worth noting that both the vacuum states and possible random largeness of initial energy are allowed.展开更多
The time periodic electroosmotic between two infinitely extended microparallel flow of an incompressible micropolar fluid plates is studied. The analytical solutions of the velocity and microrotation are derived under...The time periodic electroosmotic between two infinitely extended microparallel flow of an incompressible micropolar fluid plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-Hiickel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and rnicrorotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.展开更多
Forced convection flow through a sinusoidally curved converging diverging channel in micropolar fluids has been investigated numerically. A simple coordinate transformation is employed to transform the complex wavy...Forced convection flow through a sinusoidally curved converging diverging channel in micropolar fluids has been investigated numerically. A simple coordinate transformation is employed to transform the complex wavy wall channel to a parallel plate channel, and the cubic spline alternating direction implicit method is then used to solve the flow patterns and heat transfer characteristics. The effects of the wavy geometry, vortex viscosity parameter and Reynolds number on skin friction coefficient and Nusselt number have been examined in detail. Results show that the flow through a sinusoidally curved converging diverging channel forms a strong forward flow and a reticular vortex within each wave for larger Reynolds number and wavy amplitudes. The heat transfer rate of a micropolar fluid is smaller than that of a Newtonian fluid, but the skin friction of a micropolar fluid is larger than that of a Newtonian fluid. Moreover, both Reynolds number and wavy amplitude tend to enhance the total heat transfer rate, irrespective of whether the fluids are Newtonian fluids or micropolar fluids.展开更多
Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental management.Determining the effectiveness of treatment methods in reducing po...Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental management.Determining the effectiveness of treatment methods in reducing pollution scales is made easier by analysing waste discharge concentrations.The waste discharge concentration analysis is useful for assessing how effectively wastewater treatment techniques reduce pollution levels.This study aims to explore the Casson micropolar fluid flow through two parallel plates with the influence of pollutant concentration and thermophoretic particle deposition.To explore the mass and heat transport features,thermophoretic particle deposition and thermal radiation are considered.The governing equations are transformed into ordinary differential equations with the help of suitable similarity transformations.The Runge-Kutta-Fehlberg’s fourthfifth order technique and shooting procedure are used to solve the reduced set of equations and boundary conditions.The integration of a neural network model based on the Levenberg-Marquardt algorithm serves to improve the accuracy of predictions and optimize the analysis of parameters.Graphical outcomes are displayed to analyze the characteristics of the relevant dimensionless parameters in the current problem.Results reveal that concentration upsurges as the micropolar parameter increases.The concentration reduces with an upsurge in the thermophoretic parameter.An upsurge in the external pollutant source variation and the local pollutant external source parameters enhances mass transport.The surface drag force declines for improved values of porosity and micropolar parameters.展开更多
This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The m...This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The motion of the fluid is taken as two-dimensional with the impact of a magnetic field in the normal direction. The variable, permeable, and stretching nature of sheet's surface sets the fluid into motion. Thermal and mass diffusions are controlled through the use of the Cattaneo–Christov flux model. A dataset is generated using MATLAB bvp4c package solver and employed to train an artificial neural network(ANN) based on the Levenberg–Marquardt back-propagation(LMBP) algorithm. It has been observed as an outcome of this study that the modeled problem achieves peak performance at epochs 637, 112, 4848, and 344 using ANN-LMBP. The linear velocity of the fluid weakens with progression in variable porous and magnetic factors.With an augmentation in magnetic factor, the micro-rotational velocity profiles are augmented on the domain 0 ≤ η < 1.5 due to the support of micro-rotations by Lorentz forces close to the sheet's surface, while they are suppressed on the domain 1.5 ≤ η < 6.0 due to opposing micro-rotations away from the sheet's surface. Thermal distributions are augmented with an upsurge in thermophoresis, Brownian motion, magnetic, and radiation factors, while they are suppressed with an upsurge in thermal relaxation parameter. Concentration profiles increase with an expansion in thermophoresis factor and are suppressed with an intensification of Brownian motion factor and solute relaxation factor. The absolute errors(AEs) are evaluated for all the four scenarios that fall within the range 10^(-3)–10^(-8) and are associated with the corresponding ANN configuration that demonstrates a fine degree of accuracy.展开更多
The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered.The governing par...The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered.The governing partial differential equations were transformed into a system of ordinary differential equations,which were then solved numerically using the shooting method.Results for the stretching velocity,the local Nusselt number,the temperature,and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to 1.Both assisting（heated plate） and opposing（cooled plate） flow regions are considered.It is found that dual solutions exist for both assisting and opposing flows.展开更多
The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The govern...The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations are then solved numerically by an algorithm based on the finite difference discretization. The results are further refined by Richardson＇s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields are predicted in tabular and graphical forms to show the important features of the solution. The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.展开更多
In 2018,Duan[1]studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid model.Due to the absence of heat conductivity,it is quite difficult to close the energy estimates.He consid...In 2018,Duan[1]studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid model.Due to the absence of heat conductivity,it is quite difficult to close the energy estimates.He considered the far-field states of the initial data to be constants;that is,lim x→±∞(v0,u0,w0,θ0)(x)=(1,0,0,1).He proved that the solution tends asymptotically to those constants.In this article,under the same hypothesis that the heat conductivity is zero,we consider the far-field states of the initial data to be different constants-that is,lim x→±∞(v0,u0,w0,θ0)(x)=(v±,u±,o,θ±)-and we prove that if both the initial perturbation and the strength of the rarefaction waves are assumed to be suitably small,the Cauchy problem admits a unique global solution that tends time-asymptotically toward the combination of two rarefaction waves from different families.展开更多
A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has b...A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter （referred to as the shape parameter）. The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis （stenosis throat） have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.展开更多
Compared with the classic flow on macroscale, flows in microchannels have some new phenomena such as the friction increase and the flow rate reduction. Papautsky and co-workers explained these phenomena by using a mic...Compared with the classic flow on macroscale, flows in microchannels have some new phenomena such as the friction increase and the flow rate reduction. Papautsky and co-workers explained these phenomena by using a micropolar fluid model where the effects of micro-rotation of fluid molecules were taken into account. But both the curl of velocity vector and the curl of micro-rotation gyration vector were given incorrectly in the Cartesian coordinates and then the micro-rotation gyration vector had only one component in the z-direction. Besides, the gradient term of the divergence of micro-rotation gyration vector was missed improperly in the angular moment equation. In this paper, the governing equations for laminar flows of micropolar fluid in rectangular microchannels are reconstructed. The numerical results of velocity profiles and micro-rotation gyrations are obtained by a procedure based on the Chebyshev collocation method. The micropolar effects on velocity and micro-rotation gyration are discussed in detail.展开更多
The dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The current predominately predictive modeling deals with the flow of the viscoelastic micropola...The dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The current predominately predictive modeling deals with the flow of the viscoelastic micropolar fluid in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov(C-C) heat and mass flux expressions. Besides, the thermal radiation effects are contributed in the energy equation and aspect of the radiation parameter, and the Prandtl number is specified by the one-parameter approach.The formulated expressions are converted to the dimensionless forms by relevant similarity functions. The analytical solutions to these expressions have been erected by the homotopy analysis method. The variations in physical quantities, including the velocity,the temperature, the effective local Nusselt number, the concentration of nanoparticles,and the local Sherwood number, have been observed under the influence of emerging parameters. The results have shown good accuracy compared with those of the existing literature.展开更多
The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is invest...The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.展开更多
Mathematical model for an unsteady,incompressible,electrically conducting micropolar fluid past a vertical plate through porous medium with constant plate velocity has been investigated in the present study.Heat absor...Mathematical model for an unsteady,incompressible,electrically conducting micropolar fluid past a vertical plate through porous medium with constant plate velocity has been investigated in the present study.Heat absorption,Joulian dissipation,and first-order chemical reaction is also considered.Under the assumption of low Reynolds number,the governing transport equations are rendered into non-dimensional form and the transformed first order differential equations are solved by employing an efficient finite element method.Influence of various flow parameters on linear velocity,microrotation velocity,temperature,and concentration are presented graphically.The effects of heat absorption and chemical reaction rate decelerate the flow is particularly near the wall.Skin friction and wall couple stress increases as heat absorption increases but the reverse phenomenon is observed in the case of chemical reaction rate.Wall mass transfer rate increases for chemical reaction and Sherwood number increases for heat absorption.Finite element study is very versatile in simulating unsteady micropolar rheo-materials processing transport phenomena.However,a relatively simple reaction effects restricted to first order.展开更多
Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical ...Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Futher, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.展开更多
A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection th...A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through yon Karman＇s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.展开更多
A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks.The consequences of the current flow problem are further extend...A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks.The consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis aspects.The energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass fluxes.The flow equations are converted into an ordinary differential model by employing the appropriate variables.The numerical solution is reported by using the MATLAB builtin bvp4c method.The consequences of engineering parameters on the flow velocity,the concentration,the microorganisms,and the temperature profiles are evaluated graphically.The numerical data for fascinating physical quantities,namely,the motile density number,the local Sherwood number,and the local Nusselt number,are calculated and executed against various parametric values.The microrotation magnitude reduces for increasing magnetic parameters.The intensity of the applied magnetic field may be utilized to reduce the angular rotation which occurs in the lubrication processes,especially in the suspension of flows.On the account of industrial applications,the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells.展开更多
This paper is concerned with the two-dimensional equations of incompress- ible micropolar fluid flows with mixed partial viscosity and angular viscosity. The global existence and uniqueness of smooth solution to the C...This paper is concerned with the two-dimensional equations of incompress- ible micropolar fluid flows with mixed partial viscosity and angular viscosity. The global existence and uniqueness of smooth solution to the Cauchy problem is established.展开更多
The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fl...The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters （i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter） are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M1. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.展开更多
The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method(OHAM) and fourth order Runge–Kutta numerical method. Comparis...The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method(OHAM) and fourth order Runge–Kutta numerical method. Comparison between OHAM and numerical method shows that OHAM is an exact and high efficient method for solving these kinds of problems. The results are presented to study the velocity and rotation profiles for different physical parameters such as Reynolds number, vortex viscosity parameter, spin gradient viscosity and microinertia density parameter. As an important outcome, the magnitude of the microrotation increases with an increase in the values of injection velocity while it decreases by increasing the values of suction velocity.展开更多
In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a s...In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.展开更多
基金supported by the Natural Science Foundation of Shandong Province of China(ZR2024MA033ZR2021QA049).
文摘This paper concerns the Cauchy problem of 3D compressible micropolar fluids in the whole space R^(3). For regular initial data with m0E0 is suitable small, where m0 and E0 represent the upper bound of initial density and initial energy, we prove that if ρ0 ∈ Lγ ∩ H3 with γ ∈ (1, 6), then the problem possesses a unique global classical solution on R^(3) × [0, T] with any T ∈ (0, ∞). It’s worth noting that both the vacuum states and possible random largeness of initial energy are allowed.
基金Supported by the National Natural Science Foundation of China(Nos.11472140 and 11362012)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(No.NJYT-13-A02)+1 种基金the Inner Mongolia Grassland Talent(No.12000-12102013)the Opening fund of State Key Laboratory of Nonlinear Mechanics
文摘The time periodic electroosmotic between two infinitely extended microparallel flow of an incompressible micropolar fluid plates is studied. The analytical solutions of the velocity and microrotation are derived under the Debye-Hiickel approximation. The effects of the related dimensionless parameters, e.g., the micropolar parameter, the frequency, the electrokinetic width, and the wall zeta potential ratio of the upper plate to the lower plate, on the electroosmotic velocity and rnicrorotation are investigated. The results show that the amplitudes of the velocity and the volume flow rate will drop to zero when the micropolar parameter increases from 0 to 1. The effects of the electrokinetic width and the frequency on the velocity of the micropolar fluid are similar to those of the Newtonian fluid. However, the dependence of the microrotation on the related parameters mentioned above is complex. In order to describe these effects clearly, the dimensionless microrotation strength and the penetration depth of the microrotation are defined, which are used to explain the variation of the microrotation. In addition, the effects of various parameters on the dimensionless stress tensor at the walls are studied.
文摘Forced convection flow through a sinusoidally curved converging diverging channel in micropolar fluids has been investigated numerically. A simple coordinate transformation is employed to transform the complex wavy wall channel to a parallel plate channel, and the cubic spline alternating direction implicit method is then used to solve the flow patterns and heat transfer characteristics. The effects of the wavy geometry, vortex viscosity parameter and Reynolds number on skin friction coefficient and Nusselt number have been examined in detail. Results show that the flow through a sinusoidally curved converging diverging channel forms a strong forward flow and a reticular vortex within each wave for larger Reynolds number and wavy amplitudes. The heat transfer rate of a micropolar fluid is smaller than that of a Newtonian fluid, but the skin friction of a micropolar fluid is larger than that of a Newtonian fluid. Moreover, both Reynolds number and wavy amplitude tend to enhance the total heat transfer rate, irrespective of whether the fluids are Newtonian fluids or micropolar fluids.
文摘Assessing the behaviour and concentration of waste pollutants deposited between two parallel plates is essential for effective environmental management.Determining the effectiveness of treatment methods in reducing pollution scales is made easier by analysing waste discharge concentrations.The waste discharge concentration analysis is useful for assessing how effectively wastewater treatment techniques reduce pollution levels.This study aims to explore the Casson micropolar fluid flow through two parallel plates with the influence of pollutant concentration and thermophoretic particle deposition.To explore the mass and heat transport features,thermophoretic particle deposition and thermal radiation are considered.The governing equations are transformed into ordinary differential equations with the help of suitable similarity transformations.The Runge-Kutta-Fehlberg’s fourthfifth order technique and shooting procedure are used to solve the reduced set of equations and boundary conditions.The integration of a neural network model based on the Levenberg-Marquardt algorithm serves to improve the accuracy of predictions and optimize the analysis of parameters.Graphical outcomes are displayed to analyze the characteristics of the relevant dimensionless parameters in the current problem.Results reveal that concentration upsurges as the micropolar parameter increases.The concentration reduces with an upsurge in the thermophoretic parameter.An upsurge in the external pollutant source variation and the local pollutant external source parameters enhances mass transport.The surface drag force declines for improved values of porosity and micropolar parameters.
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through large Research Group Project (Grant No. RGP2/198/45)Project supported by Prince Sattam bin Abdulaziz University (Grant No. PSAU/2025/R/1446)。
文摘This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The motion of the fluid is taken as two-dimensional with the impact of a magnetic field in the normal direction. The variable, permeable, and stretching nature of sheet's surface sets the fluid into motion. Thermal and mass diffusions are controlled through the use of the Cattaneo–Christov flux model. A dataset is generated using MATLAB bvp4c package solver and employed to train an artificial neural network(ANN) based on the Levenberg–Marquardt back-propagation(LMBP) algorithm. It has been observed as an outcome of this study that the modeled problem achieves peak performance at epochs 637, 112, 4848, and 344 using ANN-LMBP. The linear velocity of the fluid weakens with progression in variable porous and magnetic factors.With an augmentation in magnetic factor, the micro-rotational velocity profiles are augmented on the domain 0 ≤ η < 1.5 due to the support of micro-rotations by Lorentz forces close to the sheet's surface, while they are suppressed on the domain 1.5 ≤ η < 6.0 due to opposing micro-rotations away from the sheet's surface. Thermal distributions are augmented with an upsurge in thermophoresis, Brownian motion, magnetic, and radiation factors, while they are suppressed with an upsurge in thermal relaxation parameter. Concentration profiles increase with an expansion in thermophoresis factor and are suppressed with an intensification of Brownian motion factor and solute relaxation factor. The absolute errors(AEs) are evaluated for all the four scenarios that fall within the range 10^(-3)–10^(-8) and are associated with the corresponding ANN configuration that demonstrates a fine degree of accuracy.
基金the financial supports received in the form of fundamental research grant scheme (FRGS)the financial supports received in the form of research university grant (GUP)
文摘The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were considered.The governing partial differential equations were transformed into a system of ordinary differential equations,which were then solved numerically using the shooting method.Results for the stretching velocity,the local Nusselt number,the temperature,and the velocity profiles are presented for various values of the mixed convection parameter λ and material parameter K when the Prandtl number is equal to 1.Both assisting（heated plate） and opposing（cooled plate） flow regions are considered.It is found that dual solutions exist for both assisting and opposing flows.
文摘The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field is analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions are reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations are then solved numerically by an algorithm based on the finite difference discretization. The results are further refined by Richardson＇s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields are predicted in tabular and graphical forms to show the important features of the solution. The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.
基金supported by Hubei Natural Science(2019CFB834).The second author was supported by the NSFC(11971193).
文摘In 2018,Duan[1]studied the case of zero heat conductivity for a one-dimensional compressible micropolar fluid model.Due to the absence of heat conductivity,it is quite difficult to close the energy estimates.He considered the far-field states of the initial data to be constants;that is,lim x→±∞(v0,u0,w0,θ0)(x)=(1,0,0,1).He proved that the solution tends asymptotically to those constants.In this article,under the same hypothesis that the heat conductivity is zero,we consider the far-field states of the initial data to be different constants-that is,lim x→±∞(v0,u0,w0,θ0)(x)=(v±,u±,o,θ±)-and we prove that if both the initial perturbation and the strength of the rarefaction waves are assumed to be suitably small,the Cauchy problem admits a unique global solution that tends time-asymptotically toward the combination of two rarefaction waves from different families.
文摘A micropolar model for axisymmetric blood flow through an axially nonsymmetreic but radially symmetric mild stenosis tapered artery is presented. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter （referred to as the shape parameter）. The model is also used to study the effect of the taper angle Ф. Flow parameters such as the velocity, the resistance to flow （the resistance impedance）, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis （stenosis throat） have been computed for different values of the shape parameter n, the taper angle Ф, the coupling number N and the micropolar parameter m. It is shown that the resistance to flow decreases with increasing the shape parameter n and the micropolar parameter m while it increases with increasing the coupling number N. So, the magnitude of the resistance impedance is higher for a micropolar fluid than that for a Newtonian fluid model. Finally, the velocity profile, the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis are discussed for different values of the parameters involved on the problem.
基金The project was supported by the National Natural Science Foundation of China (10472054). The English text was polished by Boyi Wang
文摘Compared with the classic flow on macroscale, flows in microchannels have some new phenomena such as the friction increase and the flow rate reduction. Papautsky and co-workers explained these phenomena by using a micropolar fluid model where the effects of micro-rotation of fluid molecules were taken into account. But both the curl of velocity vector and the curl of micro-rotation gyration vector were given incorrectly in the Cartesian coordinates and then the micro-rotation gyration vector had only one component in the z-direction. Besides, the gradient term of the divergence of micro-rotation gyration vector was missed improperly in the angular moment equation. In this paper, the governing equations for laminar flows of micropolar fluid in rectangular microchannels are reconstructed. The numerical results of velocity profiles and micro-rotation gyrations are obtained by a procedure based on the Chebyshev collocation method. The micropolar effects on velocity and micro-rotation gyration are discussed in detail.
文摘The dynamics of non-Newtonian fluids along with nanoparticles is quite interesting with numerous industrial applications. The current predominately predictive modeling deals with the flow of the viscoelastic micropolar fluid in the presence of nanoparticles. A progressive amendment in the heat and concentration equations is made by exploiting the Cattaneo-Christov(C-C) heat and mass flux expressions. Besides, the thermal radiation effects are contributed in the energy equation and aspect of the radiation parameter, and the Prandtl number is specified by the one-parameter approach.The formulated expressions are converted to the dimensionless forms by relevant similarity functions. The analytical solutions to these expressions have been erected by the homotopy analysis method. The variations in physical quantities, including the velocity,the temperature, the effective local Nusselt number, the concentration of nanoparticles,and the local Sherwood number, have been observed under the influence of emerging parameters. The results have shown good accuracy compared with those of the existing literature.
文摘The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.
文摘Mathematical model for an unsteady,incompressible,electrically conducting micropolar fluid past a vertical plate through porous medium with constant plate velocity has been investigated in the present study.Heat absorption,Joulian dissipation,and first-order chemical reaction is also considered.Under the assumption of low Reynolds number,the governing transport equations are rendered into non-dimensional form and the transformed first order differential equations are solved by employing an efficient finite element method.Influence of various flow parameters on linear velocity,microrotation velocity,temperature,and concentration are presented graphically.The effects of heat absorption and chemical reaction rate decelerate the flow is particularly near the wall.Skin friction and wall couple stress increases as heat absorption increases but the reverse phenomenon is observed in the case of chemical reaction rate.Wall mass transfer rate increases for chemical reaction and Sherwood number increases for heat absorption.Finite element study is very versatile in simulating unsteady micropolar rheo-materials processing transport phenomena.However,a relatively simple reaction effects restricted to first order.
文摘Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Futher, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.
文摘A numerical study is carried out for the axisymmetric steady laminar incompressible flow of an electrically conducting micropolar fluid between two infinite parallel porous disks with the constant uniform injection through the surface of the disks. The fluid is subjected to an external transverse magnetic field. The governing nonlinear equations of motion are transformed into a dimensionless form through yon Karman＇s similarity transformation. An algorithm based on a finite difference scheme is used to solve the reduced coupled ordinary differential equations under associated boundary conditions. The effects of the Reynolds number, the magnetic parameter, the micropolar parameter, and the Prandtl number on the flow velocity and temperature distributions are discussed. The results agree well with those of the previously published work for special cases. The investigation predicts that the heat transfer rate at the surfaces of the disks increases with the increases in the Reynolds number, the magnetic parameter, and the Prandtl number. The shear stresses decrease with the increase in the injection while increase with the increase in the applied magnetic field. The shear stress factor is lower for micropolar fluids than for Newtonian fluids, which may be beneficial in the flow and thermal control in the polymeric processing.
文摘A numerical analysis is performed to analyze the bioconvective double diffusive micropolar non-Newtonian nanofluid flow caused by stationary porous disks.The consequences of the current flow problem are further extended by incorporating the Brownian and thermophoresis aspects.The energy and mass species equations are developed by utilizing the Cattaneo and Christov model of heat-mass fluxes.The flow equations are converted into an ordinary differential model by employing the appropriate variables.The numerical solution is reported by using the MATLAB builtin bvp4c method.The consequences of engineering parameters on the flow velocity,the concentration,the microorganisms,and the temperature profiles are evaluated graphically.The numerical data for fascinating physical quantities,namely,the motile density number,the local Sherwood number,and the local Nusselt number,are calculated and executed against various parametric values.The microrotation magnitude reduces for increasing magnetic parameters.The intensity of the applied magnetic field may be utilized to reduce the angular rotation which occurs in the lubrication processes,especially in the suspension of flows.On the account of industrial applications,the constituted output can be useful to enhance the energy transport efficacy and microbial fuel cells.
文摘This paper is concerned with the two-dimensional equations of incompress- ible micropolar fluid flows with mixed partial viscosity and angular viscosity. The global existence and uniqueness of smooth solution to the Cauchy problem is established.
文摘The triple-diffusive convection in a micropolar ferromagnetic fluid layer heated and soluted from below is considered in the presence of a transverse uniform magnetic field. An exact solution is obtained for a flat fluid layer contained between two free boundaries. A linear stability analysis and a normal mode analysis method are carried out to study the onset convection. For stationary convection, various parameters such as the medium permeability, the solute gradients, the non-buoyancy magnetization, and the micropolar parameters （i.e., the coupling parameter, the spin diffusion parameter, and the micropolar heat conduction parameter） are analyzed. The critical magnetic thermal Rayleigh number for the onset of instability is determined numerically for a sufficiently large value of the buoyancy magnetization parameter M1. The principle of exchange of stabilities is found to be true for the micropolar fluid heated from below in the absence of the micropolar viscous effect, the microinertia, and the solute gradients. The micropolar viscous effect, the microinertia, and the solute gradient introduce oscillatory modes, which are non-existent in their absence. Sufficient conditions for the non-existence of overstability are also obtained.
文摘The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method(OHAM) and fourth order Runge–Kutta numerical method. Comparison between OHAM and numerical method shows that OHAM is an exact and high efficient method for solving these kinds of problems. The results are presented to study the velocity and rotation profiles for different physical parameters such as Reynolds number, vortex viscosity parameter, spin gradient viscosity and microinertia density parameter. As an important outcome, the magnitude of the microrotation increases with an increase in the values of injection velocity while it decreases by increasing the values of suction velocity.
基金supported by Scientific Research of the University of Rijeka(13.14.1.3.03)
文摘In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.
