This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multipli...This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.展开更多
In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-simi...In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-similar coupled ordinary differential equation. The transformed conservations equations were solved by using new algorithm. Basically, this new algorithm depends mainly on the Taylor expansion application with the coefficients of power series resulting from integrating the order differential equation. Results obtained from new algorithm are compared with the results of numerical Range-Kutta fourth-order algorithm with help of the shooting algorithm. The comparison revealed that the resulting solutions were excellent agreement. Thermo-diffusion and diffusion-thermo effects were investigated to analyze the behavior of temperature and concentration profile. Also the influences of the first order chemical reaction and the rate of mass and heat transfer were studied. The computed analytical solution result for the velocity, temperature and concentration distribution with the effect of various important dimensionless parameters was analyzed and discussed graphically.展开更多
In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the...In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the continuous dependence on the density <i><span style="white-space:nowrap;"><i>ρ</i></span></i> and the coefficient of thermal conductivity <i>K</i>. These results show that small changes for these coefficients can’t cause tremendous changes for the solutions.展开更多
The dependencies of fluxes and forces were paid close attention to the phenomenological theory of Onsager.But in such a case,it seems that the Onsager's reciprocal relations are not necessarily fulfilled.In this w...The dependencies of fluxes and forces were paid close attention to the phenomenological theory of Onsager.But in such a case,it seems that the Onsager's reciprocal relations are not necessarily fulfilled.In this work,the problem of thermo-diffusion was chosen as an example and a combination of the first and the second law of thermodynamics was adopted to describe the reversible and the irreversible process.Accordingly,the Gibbs-Duhem relation was found to be followed by not only the equilibrium but also the non-equilibrium thermodynamics,i.e.,the dependency of forces needs to be considered during the derivation of evolution equations.After that,a comparative study between the previous thermodynamic extremal principle(TEP)incorporating only the constraint from fluxes and the present TEP incorporating the constraints from both fluxes and forces was carried out.For the former,the well-known Dufour effect cannot be described,whereas,for the latter,both the well-known Soret effect and the Dufour effect can be predicted.Furthermore,the phenomenological equations were uniquely determined using the present TEP,and Onsager's reciprocal relations were found to be followed,thus solving the problem of the n-fold arbitrariness for the kinetic coefficients pointed out previously.The present work not only extends the TEP to non-isothermal thermodynamics but also might provide guidance for modeling dissipation systems with constraints from both fluxes and forces.展开更多
The major concern of proffered study based on the inquisitive analysis of entropy approach based on 3-D Prandtl fluid influenced by modified advanced heat conduction along with mass diffusion models.Moreover,influence...The major concern of proffered study based on the inquisitive analysis of entropy approach based on 3-D Prandtl fluid influenced by modified advanced heat conduction along with mass diffusion models.Moreover,influence of Hall and also slip forces and heat transmission characteristics are featured under the combined outcomes appertaining to radiations and viscous dissipation are taken into account in this investigation.This article also examined the combined impacts of thermal conductivity change together with variable mass diffusion co-efficient within the heat and mass transport in the occurrence of Prandtl fluid.Flow demeanor is examined across the bidirectional extendable sheet.Numerical simulations based on 3-D flow configured by extending surface are carried out by using OHAM.Simulated PDEs expressed as ODEs with the utilization of dimensionless variables.Simulated outcomes are validated graphically obtained by varying values of emerging constraints through previous published results and seen in desirable agreement.The influence of distinct parameters associated with this current study like Brownian and diffusion constraint,temperature and also concentration difference,Eckert number,Hall as well as ion slip parameters,Brinkman number,magnetic constraint,radiation and Prandtl fluid constraint are sketched for temperature,velocity field along xy-axes,concentration and entropy generation rate.It is noticed that velocity distribution along x-axes is an increasing function of magnetic constraint,Prandtl fluid and also elastic constraint whilst contrast impact is seen along y-axes.Moreover,temperature as well as concentration profile decays for Prandtl number,thermal and also concentration relaxation time constraint respectively whereas both profiles enhanced for distinct considered parameters.Entropy declines for ion-slip parameter whilst enhanced for Bejan number.Entropy behavior as well as Bejan number effect under various parameters is sketched graphically and enhanced behavior is depicted for entropy for considered constraint whilst Bejan number enhanced for diffusion parameter and also concentration difference constraint whereas declined behavior demonstrated for other considered parameters.The innovative component in the current study lies in the integration of multiple factors towards the Prandtl fluid model framework,forcing its boundaries beyond widespread conventional applications.Extending the Prandtl fluid model in 3D allows more comprehensive demonstration of the under consideration physical system.展开更多
The current paper explores the behavior of the thermal radiation on the time-independent flow of mi-cropolar fluid past a vertical stretching surface with the interaction of a transverse magnetic field.The ef-fect of ...The current paper explores the behavior of the thermal radiation on the time-independent flow of mi-cropolar fluid past a vertical stretching surface with the interaction of a transverse magnetic field.The ef-fect of thermo-diffusion(Soret)along with the heat source is incorporated to enhance the thermal prop-erties.Also,the convective solutal condition is considered that affects the mass transfer phenomenon.The transformed equations are modeled using suitable similarity transformation.However,the complex cou-pled equations are handled mathematically employing the Runge-Kutta-Felhberg method.The behavior of characterizing parameters on the flow phenomena as well as the engineering coefficients are displayed via graphs and the validation of the current outcome is reported with the previously published results in particular cases.展开更多
基金Sponsored by the NNSF of China(11031003,11271066,11326158)a grant of Shanghai Education Commission(13ZZ048)Chinese Universities Scientific Fund(CUSF-DH-D-2013068)
文摘This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.
文摘In this paper, the magneto hydrodynamic (MHD) flow of viscous fluid in a channel with non-parallel plates is studied. The governing partial differential equation was transformed into a system of dimensionless non-similar coupled ordinary differential equation. The transformed conservations equations were solved by using new algorithm. Basically, this new algorithm depends mainly on the Taylor expansion application with the coefficients of power series resulting from integrating the order differential equation. Results obtained from new algorithm are compared with the results of numerical Range-Kutta fourth-order algorithm with help of the shooting algorithm. The comparison revealed that the resulting solutions were excellent agreement. Thermo-diffusion and diffusion-thermo effects were investigated to analyze the behavior of temperature and concentration profile. Also the influences of the first order chemical reaction and the rate of mass and heat transfer were studied. The computed analytical solution result for the velocity, temperature and concentration distribution with the effect of various important dimensionless parameters was analyzed and discussed graphically.
文摘In this paper, we establish the structural stability for the linear differential equations of thermo-diffusion in a semi-infinite pipe flow. Using the technology of a second-order differential inequality, we prove the continuous dependence on the density <i><span style="white-space:nowrap;"><i>ρ</i></span></i> and the coefficient of thermal conductivity <i>K</i>. These results show that small changes for these coefficients can’t cause tremendous changes for the solutions.
基金the Natural Science Foundation of China(No.51975474,No.52304414)the Fundamental Research Funds for the Central Universities(No.3102019JC001).
文摘The dependencies of fluxes and forces were paid close attention to the phenomenological theory of Onsager.But in such a case,it seems that the Onsager's reciprocal relations are not necessarily fulfilled.In this work,the problem of thermo-diffusion was chosen as an example and a combination of the first and the second law of thermodynamics was adopted to describe the reversible and the irreversible process.Accordingly,the Gibbs-Duhem relation was found to be followed by not only the equilibrium but also the non-equilibrium thermodynamics,i.e.,the dependency of forces needs to be considered during the derivation of evolution equations.After that,a comparative study between the previous thermodynamic extremal principle(TEP)incorporating only the constraint from fluxes and the present TEP incorporating the constraints from both fluxes and forces was carried out.For the former,the well-known Dufour effect cannot be described,whereas,for the latter,both the well-known Soret effect and the Dufour effect can be predicted.Furthermore,the phenomenological equations were uniquely determined using the present TEP,and Onsager's reciprocal relations were found to be followed,thus solving the problem of the n-fold arbitrariness for the kinetic coefficients pointed out previously.The present work not only extends the TEP to non-isothermal thermodynamics but also might provide guidance for modeling dissipation systems with constraints from both fluxes and forces.
文摘The major concern of proffered study based on the inquisitive analysis of entropy approach based on 3-D Prandtl fluid influenced by modified advanced heat conduction along with mass diffusion models.Moreover,influence of Hall and also slip forces and heat transmission characteristics are featured under the combined outcomes appertaining to radiations and viscous dissipation are taken into account in this investigation.This article also examined the combined impacts of thermal conductivity change together with variable mass diffusion co-efficient within the heat and mass transport in the occurrence of Prandtl fluid.Flow demeanor is examined across the bidirectional extendable sheet.Numerical simulations based on 3-D flow configured by extending surface are carried out by using OHAM.Simulated PDEs expressed as ODEs with the utilization of dimensionless variables.Simulated outcomes are validated graphically obtained by varying values of emerging constraints through previous published results and seen in desirable agreement.The influence of distinct parameters associated with this current study like Brownian and diffusion constraint,temperature and also concentration difference,Eckert number,Hall as well as ion slip parameters,Brinkman number,magnetic constraint,radiation and Prandtl fluid constraint are sketched for temperature,velocity field along xy-axes,concentration and entropy generation rate.It is noticed that velocity distribution along x-axes is an increasing function of magnetic constraint,Prandtl fluid and also elastic constraint whilst contrast impact is seen along y-axes.Moreover,temperature as well as concentration profile decays for Prandtl number,thermal and also concentration relaxation time constraint respectively whereas both profiles enhanced for distinct considered parameters.Entropy declines for ion-slip parameter whilst enhanced for Bejan number.Entropy behavior as well as Bejan number effect under various parameters is sketched graphically and enhanced behavior is depicted for entropy for considered constraint whilst Bejan number enhanced for diffusion parameter and also concentration difference constraint whereas declined behavior demonstrated for other considered parameters.The innovative component in the current study lies in the integration of multiple factors towards the Prandtl fluid model framework,forcing its boundaries beyond widespread conventional applications.Extending the Prandtl fluid model in 3D allows more comprehensive demonstration of the under consideration physical system.
文摘The current paper explores the behavior of the thermal radiation on the time-independent flow of mi-cropolar fluid past a vertical stretching surface with the interaction of a transverse magnetic field.The ef-fect of thermo-diffusion(Soret)along with the heat source is incorporated to enhance the thermal prop-erties.Also,the convective solutal condition is considered that affects the mass transfer phenomenon.The transformed equations are modeled using suitable similarity transformation.However,the complex cou-pled equations are handled mathematically employing the Runge-Kutta-Felhberg method.The behavior of characterizing parameters on the flow phenomena as well as the engineering coefficients are displayed via graphs and the validation of the current outcome is reported with the previously published results in particular cases.
