In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processe...In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.展开更多
The behavior of buoyancy-driven magnetohydrodynamic(MHD)nanofluid flows with temperature-sensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling,nuclear reactors,and me...The behavior of buoyancy-driven magnetohydrodynamic(MHD)nanofluid flows with temperature-sensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling,nuclear reactors,and metallurgical processes.This study focuses on the boundary layer flow of a Casson-based sodium alginate Fe3O4 nanofluid influenced by magnetic field-dependent viscosity and thermal radiation,as it interacts with a vertically stretching sheet under dissipative conditions.To manage the inherent nonlinearities,Lie group transformations are applied to reformulate the governing boundary layer equations into similarity forms.These reduced equations are then solved via the Spectral Quasi-Linearization Method(SQLM),ensuring high accuracy and computational efficiency.The analysis comprehensively explores the impact of key parameters-including mixed convection intensity,magnetic field strength,Casson fluid properties,temperature-dependent viscosity,thermal radiation,and viscous dissipation(Eckert number)-on flow characteristics and heat transfer rates.Findings reveal that increasing magnetic field-dependent viscosity diminishes both skin friction and thermal transport,while buoyancy effects enhance heat transfer but lower shear stress on the surface.This work provides critical insights into controlling heat and momentum transfer in Casson nanofluids,advancing the design of thermal management systems involving complex fluids under magnetic and buoyant forces.展开更多
Two intense quasi-linear mesoscale convective systems（QLMCSs） in northern China were simulated using the WRF（Weather Research and Forecasting） model and the 3D-Var（three-dimensional variational） analysis system ...Two intense quasi-linear mesoscale convective systems（QLMCSs） in northern China were simulated using the WRF（Weather Research and Forecasting） model and the 3D-Var（three-dimensional variational） analysis system of the ARPS（Advanced Regional Prediction System） model.A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures.Results indicate that,compared with calculating the results using two previous methods,the lightning density calculated using the new method presented in this study is in better accordance with observations.Based on the calculated lightning densities using the new method,it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs,where the surface wind field converged intensely.The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it,and their lightning events mainly occurred in regions with a large gradient of CAPE.Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions;the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different;and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions.展开更多
In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we ...In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.展开更多
The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assum...The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assumed to vibrate under an external harmonic electric force field and an analytical solution is proposed to obtain the nonlinear resonant frequencies. The results show good agreement with the numerical simulation and the obtained analytical frequency is com- pletely related to the curvature of the nanotube. Our model predicts that although the model is nonlinear in nature, the curved SWCNT could behave linearly in a certain amount of curvatures and this quasi-linear vibrational behavior of curved SWCNT is a function of aspect ratio, nonlocal parameter, and stiffness of the foundation.展开更多
This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classificati...This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classification results are presented, and some examples are given to show the main reduction procedure.展开更多
New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends ...New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.展开更多
In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using...In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.展开更多
Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not suppl...Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions展开更多
In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy prob...In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy problem admits a unique global smooth solution u∈C^∞（（0, T]; H^∞（R）） ∩ C（[0, T]; H^2（R）） ∩ C^1（[0, T]; L^2（R）） under suitable assumptions on the initial data.展开更多
This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exp...This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exponent,λ>0,p(?)r<p,p:=Np/N-p is the critical Sobolev exponent,μ>,0(?)t<p,p(?)q<p(t)=p(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.展开更多
This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix ...This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.展开更多
In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of cl...In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.展开更多
Existence of positive solution is established for boundary value problems of nonsingular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the non...Existence of positive solution is established for boundary value problems of nonsingular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the nonlinear alternative of Leray-Schauder method.展开更多
In this article, the author studies the iuitial （Dirichlet.） boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a...In this article, the author studies the iuitial （Dirichlet.） boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schroedinger equations on the unit cube. h global existence and uniqueness is established for a solution to this problem.展开更多
By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of t...By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.展开更多
In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate init...In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.展开更多
The optimal design of heating and cooling systems must take into account heat radiation which is a non-linear process.In this study,the mixed convection in a radiative magnetohydrodynamic Eyring-Powell copperwater nan...The optimal design of heating and cooling systems must take into account heat radiation which is a non-linear process.In this study,the mixed convection in a radiative magnetohydrodynamic Eyring-Powell copperwater nanofluid over a stretching cylinder was investigated.The energy balance is modeled,taking into account the non-linear thermal radiation and a thermal slip condition.The effects of the embedded flow parameters on the fluid properties,as well as on the skin friction coefficient and heat transfer rate,are analyzed.Unlike in many existing studies,the recent spectral quasi-linearization method is used to solve the coupled nonlinear boundary-value problem.The computational result shows that increasing the nanoparticle volume fraction,thermal radiation parameter and heat generation parameter enhances temperature profile.We found that the velocity slip parameter and the fluid material parameter enhance the skin friction.A comparison of the current numerical results with existing literature for some limiting cases shows excellent agreement.展开更多
A study is presented for magnetohydrodynamics （MHD） flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar mode...A study is presented for magnetohydrodynamics （MHD） flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar model introduced by Eringen is used to describe the working fluid. The transformed self similar ordinary differential equations together with the associated boundary conditions are solved numerically by an algorithm based on quasi-linearization and multilevel discretization. The effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigations may be beneficial in the flow and thermal control of polymeric processing.展开更多
In this paper, the problem of unsteady laminar boundary-layer flow and heat transfer of a viscous income-pressible fluid over stretching sheet is studied numerically. The unsteadiness in the flow and temperature is ca...In this paper, the problem of unsteady laminar boundary-layer flow and heat transfer of a viscous income-pressible fluid over stretching sheet is studied numerically. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. A similarity transformation is used to reduce the governing boundary-layer equations to couple higher order non-linear ordinary differential equations. These equations are numerically solved using quasi-linearization technique. The effect of the governing parameters unsteadiness parameter and Prandtl number on velocity and temperature profile is discussed. Besides the numerical results for the local skin friction coefficient and local Nusselt number are presented. The computed results are compared with previously reported work.展开更多
文摘In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.
文摘The behavior of buoyancy-driven magnetohydrodynamic(MHD)nanofluid flows with temperature-sensitive viscosity plays a pivotal role in high-performance thermal systems such as electronics cooling,nuclear reactors,and metallurgical processes.This study focuses on the boundary layer flow of a Casson-based sodium alginate Fe3O4 nanofluid influenced by magnetic field-dependent viscosity and thermal radiation,as it interacts with a vertically stretching sheet under dissipative conditions.To manage the inherent nonlinearities,Lie group transformations are applied to reformulate the governing boundary layer equations into similarity forms.These reduced equations are then solved via the Spectral Quasi-Linearization Method(SQLM),ensuring high accuracy and computational efficiency.The analysis comprehensively explores the impact of key parameters-including mixed convection intensity,magnetic field strength,Casson fluid properties,temperature-dependent viscosity,thermal radiation,and viscous dissipation(Eckert number)-on flow characteristics and heat transfer rates.Findings reveal that increasing magnetic field-dependent viscosity diminishes both skin friction and thermal transport,while buoyancy effects enhance heat transfer but lower shear stress on the surface.This work provides critical insights into controlling heat and momentum transfer in Casson nanofluids,advancing the design of thermal management systems involving complex fluids under magnetic and buoyant forces.
基金supported jointly by the National Key Basic Research and Development (973) Program of China (Grant No. 2014CB441401)the National Natural Science Foundation of China (Grant Nos. 41405007, 41175043, 41475002, and 41205027)
文摘Two intense quasi-linear mesoscale convective systems（QLMCSs） in northern China were simulated using the WRF（Weather Research and Forecasting） model and the 3D-Var（three-dimensional variational） analysis system of the ARPS（Advanced Regional Prediction System） model.A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures.Results indicate that,compared with calculating the results using two previous methods,the lightning density calculated using the new method presented in this study is in better accordance with observations.Based on the calculated lightning densities using the new method,it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs,where the surface wind field converged intensely.The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it,and their lightning events mainly occurred in regions with a large gradient of CAPE.Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions;the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different;and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions.
文摘In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.
文摘The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assumed to vibrate under an external harmonic electric force field and an analytical solution is proposed to obtain the nonlinear resonant frequencies. The results show good agreement with the numerical simulation and the obtained analytical frequency is com- pletely related to the curvature of the nanotube. Our model predicts that although the model is nonlinear in nature, the curved SWCNT could behave linearly in a certain amount of curvatures and this quasi-linear vibrational behavior of curved SWCNT is a function of aspect ratio, nonlocal parameter, and stiffness of the foundation.
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.SJ08A05
文摘This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classification results are presented, and some examples are given to show the main reduction procedure.
基金supported by the National Natural Science Foundation of China under Grant No. 10671156the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968
文摘New classes of exact solutions of the quasi-linear diffusion-reaction equations are obtained by seeking for the high-order conditional Lie-Baeklund symmetries of the considered equations. The method used here extends the approaches of derivative-dependent functional separation of variables and the invariant subspace. Behavior to some solutions such as blow-up and quenching is also described.
基金Supported by the Natural Science Foundations of Zhejiang Province(102009) Supported by the Zhejiang Educational Offlce(20020305) Supported by Huzhou Teacher's College(02101A)
文摘In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.
文摘Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions
基金Supported by the National Natural Science Foundation of China(10371073)
文摘In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy problem admits a unique global smooth solution u∈C^∞（（0, T]; H^∞（R）） ∩ C（[0, T]; H^2（R）） ∩ C^1（[0, T]; L^2（R）） under suitable assumptions on the initial data.
基金This research is supported by the National Natural Science Foundation of China(l0171036) and the Natural Science Foundation of South-Central University For Nationalities(YZZ03001).
文摘This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exponent,λ>0,p(?)r<p,p:=Np/N-p is the critical Sobolev exponent,μ>,0(?)t<p,p(?)q<p(t)=p(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.
文摘This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.
文摘In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.
文摘Existence of positive solution is established for boundary value problems of nonsingular for a class quasi-linear ordinary differential equation on the semi-infinite interval. The results are obtained by using the nonlinear alternative of Leray-Schauder method.
文摘In this article, the author studies the iuitial （Dirichlet.） boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schroedinger equations on the unit cube. h global existence and uniqueness is established for a solution to this problem.
基金Project supported by the National Natural Science Foundation of China(Grant No.10671156)the Natural Science Foundation of Shaanxi Province of China(Grant No.SJ08A05)
文摘By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.
文摘In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.
文摘The optimal design of heating and cooling systems must take into account heat radiation which is a non-linear process.In this study,the mixed convection in a radiative magnetohydrodynamic Eyring-Powell copperwater nanofluid over a stretching cylinder was investigated.The energy balance is modeled,taking into account the non-linear thermal radiation and a thermal slip condition.The effects of the embedded flow parameters on the fluid properties,as well as on the skin friction coefficient and heat transfer rate,are analyzed.Unlike in many existing studies,the recent spectral quasi-linearization method is used to solve the coupled nonlinear boundary-value problem.The computational result shows that increasing the nanoparticle volume fraction,thermal radiation parameter and heat generation parameter enhances temperature profile.We found that the velocity slip parameter and the fluid material parameter enhance the skin friction.A comparison of the current numerical results with existing literature for some limiting cases shows excellent agreement.
基金Project supported by the Higher Education Commission of Pakistan
文摘A study is presented for magnetohydrodynamics （MHD） flow and heat transfer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar model introduced by Eringen is used to describe the working fluid. The transformed self similar ordinary differential equations together with the associated boundary conditions are solved numerically by an algorithm based on quasi-linearization and multilevel discretization. The effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigations may be beneficial in the flow and thermal control of polymeric processing.
文摘In this paper, the problem of unsteady laminar boundary-layer flow and heat transfer of a viscous income-pressible fluid over stretching sheet is studied numerically. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. A similarity transformation is used to reduce the governing boundary-layer equations to couple higher order non-linear ordinary differential equations. These equations are numerically solved using quasi-linearization technique. The effect of the governing parameters unsteadiness parameter and Prandtl number on velocity and temperature profile is discussed. Besides the numerical results for the local skin friction coefficient and local Nusselt number are presented. The computed results are compared with previously reported work.
