Taking account of the thermal-diffusion (Soret) and the diffusion-themo (Dufour) effects, the properties of the heat and mass transfers in a strongly endothermic chemical reaction system for a porous medium are numeri...Taking account of the thermal-diffusion (Soret) and the diffusion-themo (Dufour) effects, the properties of the heat and mass transfers in a strongly endothermic chemical reaction system for a porous medium are numerically studied. Through the theory of the thermodynamics of irreversible processes, a coupled mathematical model describing the heat and mass transfers in aporous system for the calcination of limestone is formulated. The governing partial differential equations are numerically solved by the implicitly finite volume method through decomposing the equations to a set of coupled differential equations. The results indicate that when the convectional velocity is lower or when the initial temperature of the feeding gas is higher, Soret and Dufour effects can’t be ignored. The distribution figures for the temperature field of the gas in the system, the concentration field of the product gas and the solid conversion ratio are provided.展开更多
This article studies the Soret and Dufour effects on the magnetohydrody- namic （MHD） flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructe...This article studies the Soret and Dufour effects on the magnetohydrody- namic （MHD） flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.展开更多
The Soret and Dufour effects on unsteady MHD mixed convection flow past an infinite radiative vertical porous plate embedded in a porous medium in the presence of chemical reaction have been studied. A uniform magneti...The Soret and Dufour effects on unsteady MHD mixed convection flow past an infinite radiative vertical porous plate embedded in a porous medium in the presence of chemical reaction have been studied. A uniform magnetic field acts perpendicular to the porous surface. The Rosseland approximation has been used to describe the radiative heat flux in energy equation. The governing equations are solved numerically by applying explicit finite difference Method. The effects of various parameters on the velocity, temperature and concentration fields have been examined with the help of graphs.展开更多
This research explored the effects of an angled magnetic field, Brownian motion, and thermophoresis on the flow of an electrically conducting and chemically reacting Casson nanofluid under the influence of the Soret-D...This research explored the effects of an angled magnetic field, Brownian motion, and thermophoresis on the flow of an electrically conducting and chemically reacting Casson nanofluid under the influence of the Soret-Dufour mechanism. A set of partial differential equations is generated by the flow mode. The governing partial differential equations are solved numerically using the spectral collocation method after being transformed to self-similar forms. The effect of various fluid parameters on the velocity profile, temperature profile, and nanoparticle concentration is addressed. A quantitative agreement is observed when previous findings are compared to the current results. The skin friction, local Nusselt number, and local Sherwood number are also examined, and the results are presented in the table. This study discovered that the inclined magnetic field has a significant impact on the flow of the electrically conducting fluid by delaying its mobility within the boundary layer. The plastic dynamic viscosity, which acts as a barrier to fluid flow, is shown to degenerate the fluid velocity when the Casson parameter is increased. As a consequence, the findings may be used to improve thermal science instruments and increase industrial output.展开更多
The motion of incompressible fluid of a variable fluid viscosity and variable thermal conductivity with thermal radiation, Dufour, Soret with heat and mass transfer over a linearly moving porous vertical semi-infinite...The motion of incompressible fluid of a variable fluid viscosity and variable thermal conductivity with thermal radiation, Dufour, Soret with heat and mass transfer over a linearly moving porous vertical semi-infinite plate with suction is investigated. The governing equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations with dimensionless variables and solved numerically using shooting method with Runge-Kutta fourth-order method and Newton-Raphson’s interpolation scheme implemented in MATLAB. The result showed that with increase in Dufour and Soret parameter, fluid velocity increases and temperature increases with increase in variation of Dufour while, temperature decreases with increase in Soret. The effects of variable fluid viscosity, variable thermal conductivity, thermal radiation, Soret, Dufour, Prandtl and Schmidt parameters on the dimensionless velocity, temperature and concentration profiles are shown graphically.展开更多
The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompres...The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid past an infinite vertical porous plate under oscillatory suction velocity and thermal radiation. The Dufour （diffusion thermo） and Soret （thermal diffusion） effects are taken into account. The problem is solved numerically using the finite element method for the velocity, the temperature, and the concentration field. The expression for the skin friction, the rate of heat and mass transfer is obtained. The results are presented numerically through graphs and tables for the externally cooled plate （Gr 〉 0） and the externally heated plate （Gr 〈 0） to observe the effects of various parameters encountered in the equations.展开更多
This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the ...This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.展开更多
In this work, the Micropolar fluid flow and heat and mass transfer past a horizontal nonlinear stretching sheet through porous medium is studied including the Soret-Dufour effect in the presence of suction. A uniform ...In this work, the Micropolar fluid flow and heat and mass transfer past a horizontal nonlinear stretching sheet through porous medium is studied including the Soret-Dufour effect in the presence of suction. A uniform magnetic field is applied transversely to the direction of the flow. The governing differential equations of the problem have been transformed into a system of non-dimensional differential equations which are solved numerically by Nachtsheim-Swigert iteration technique along with the sixth order Runge-Kutta integration scheme. The velocity, microrotation, temperature and concentration profiles are presented for different parameters. The present problem finds significant applications in hydromagnetic control of conducting polymeric sheets, magnetic materials processing, etc.展开更多
The present study deals with MHD (magneto hydrodynamics) mixed convection flow of a Casson fluid over an exponentially stretching sheet with the effects of Soret and Dufour, thermal radiation, chemical reaction. The g...The present study deals with MHD (magneto hydrodynamics) mixed convection flow of a Casson fluid over an exponentially stretching sheet with the effects of Soret and Dufour, thermal radiation, chemical reaction. The governing partial differential equations are converted into ordinary differential equations by using similarity transformations. These equations are then solved numerically by applying finite difference scheme known as the Keller Box method. The effects of various parameters on velocity, temperature and concentration profiles are presented graphically to interpret and the results are discussed.展开更多
The Dufour and Soret effects on the unsteady twodimensional magnetonyaro dynamics （MHD） doublediffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a nonDarcy porous me...The Dufour and Soret effects on the unsteady twodimensional magnetonyaro dynamics （MHD） doublediffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a nonDarcy porous medium are investigated numeri cally. The governing nonlinear dimensionless equations are solved by an implicit finite difference scheme of the CrankNicolson type with a tridiagonal matrix manipulation. The effects of various parameters entering into the problem on the unsteady dimension less velocity, temperature, and concentration profiles are studied in detail. Furthermore, the time variation of the skin friction coefficient, the Nusselt number, and the Sherwood number is presented and analyzed. The results show that the unsteady velocity, tem perature, and concentration profiles are substantially influenced by the Dufour and Soret effects. When the Dufour number increases or the Soret number decreases, both the skin friction and the Sherwood number decrease, while the Nusselt number increases. It is found that, when the magnetic parameter increases, the velocity and the temperature decrease in the boundary layer.展开更多
Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall ...Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall current and constant heat flux. It is considered that the porous plate is subjected to constant heat flux. The obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocities, temperature and concentration distributions are obtained for various parameters by the above mentioned technique. The local and average shear stresses, Nusselt number as well as Sherwood number are also investigated. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The obtained results are illustrated with the help of graphs to observe the effects of various legitimate parameters.展开更多
An analysis of two-dimensional steady magneto-hydrodynamic free convection flow of an electrically conducting, viscous, incompressible fluid past an inclined stretching porous plate in the presence of a uniform magnet...An analysis of two-dimensional steady magneto-hydrodynamic free convection flow of an electrically conducting, viscous, incompressible fluid past an inclined stretching porous plate in the presence of a uniform magnetic field and thermal radiation with heat generation is made. Both the Dufour and Soret effects are considered for a hydrogen-air mixture as the non-chemically reacting fluid pair. The equations governing the flow, temperature and concentration fields are reduced to a system of joined non-linear ordinary differential equations by similarity transformation. Non-linear differential equations are integrated numerically by using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Finally the significance of physical parameters which are of engineering interest are examined both in graphical and tabular form.展开更多
The primary aim of this research endeavor is to examine the characteristics of magnetohydrodynamicWilliamson nanofluid flow past a nonlinear stretching surface that is immersed in a permeable medium.In the current ana...The primary aim of this research endeavor is to examine the characteristics of magnetohydrodynamicWilliamson nanofluid flow past a nonlinear stretching surface that is immersed in a permeable medium.In the current analysis,the impacts of Soret and Dufour(cross-diffusion effects)have been attentively taken into consideration.Using appropriate similarity variable transformations,the governing nonlinear partial differential equations were altered into nonlinear ordinary differential equations and then solved numerically using the Runge Kutta Fehlberg-45 method along with the shooting technique.Numerical simulations were then perceived to show the consequence of various physical parameters on the plots of velocity,temperature,and concentration of the nanofluid flow.Boosting the magnetic,Williamson,porosity,and stretching sheet index parameters,the velocity of the fluid flow decreases.The temperature is enhanced as theWilliamson and Brownian motion parameters upsurge,but it decreases as the Prandtl,thermophoresis,stretching sheet index,and Dufour parameters escalate.The concentration distribution decreases as the thermophoresis andmagnetic parameters upsurge,but it escalates as the Soret,Schmidt,Brownian motion,and stretching sheet index parameters increase.Skin friction coefficient boosted as the stretching sheet index and magnetic parameters enhanced against the Williamson parameter.The findings from this study have been contrasted with earlier findings on local Nusselt numbers,which show substantial support and endorse the existing approach’s validity.The numerical values of the local Sherwood number gradually increase as the Schmidt,Soret,stretching sheet index,and thermophoresis parameters are upsurged.展开更多
基金Project(50174015) supported by the National Natural Science Foundation of China
文摘Taking account of the thermal-diffusion (Soret) and the diffusion-themo (Dufour) effects, the properties of the heat and mass transfers in a strongly endothermic chemical reaction system for a porous medium are numerically studied. Through the theory of the thermodynamics of irreversible processes, a coupled mathematical model describing the heat and mass transfers in aporous system for the calcination of limestone is formulated. The governing partial differential equations are numerically solved by the implicitly finite volume method through decomposing the equations to a set of coupled differential equations. The results indicate that when the convectional velocity is lower or when the initial temperature of the feeding gas is higher, Soret and Dufour effects can’t be ignored. The distribution figures for the temperature field of the gas in the system, the concentration field of the product gas and the solid conversion ratio are provided.
基金supported by the Deanship of Scientific Research (DSR) of King Abdulaziz University of Saudi Arabia
文摘This article studies the Soret and Dufour effects on the magnetohydrody- namic （MHD） flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.
文摘The Soret and Dufour effects on unsteady MHD mixed convection flow past an infinite radiative vertical porous plate embedded in a porous medium in the presence of chemical reaction have been studied. A uniform magnetic field acts perpendicular to the porous surface. The Rosseland approximation has been used to describe the radiative heat flux in energy equation. The governing equations are solved numerically by applying explicit finite difference Method. The effects of various parameters on the velocity, temperature and concentration fields have been examined with the help of graphs.
文摘This research explored the effects of an angled magnetic field, Brownian motion, and thermophoresis on the flow of an electrically conducting and chemically reacting Casson nanofluid under the influence of the Soret-Dufour mechanism. A set of partial differential equations is generated by the flow mode. The governing partial differential equations are solved numerically using the spectral collocation method after being transformed to self-similar forms. The effect of various fluid parameters on the velocity profile, temperature profile, and nanoparticle concentration is addressed. A quantitative agreement is observed when previous findings are compared to the current results. The skin friction, local Nusselt number, and local Sherwood number are also examined, and the results are presented in the table. This study discovered that the inclined magnetic field has a significant impact on the flow of the electrically conducting fluid by delaying its mobility within the boundary layer. The plastic dynamic viscosity, which acts as a barrier to fluid flow, is shown to degenerate the fluid velocity when the Casson parameter is increased. As a consequence, the findings may be used to improve thermal science instruments and increase industrial output.
文摘The motion of incompressible fluid of a variable fluid viscosity and variable thermal conductivity with thermal radiation, Dufour, Soret with heat and mass transfer over a linearly moving porous vertical semi-infinite plate with suction is investigated. The governing equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations with dimensionless variables and solved numerically using shooting method with Runge-Kutta fourth-order method and Newton-Raphson’s interpolation scheme implemented in MATLAB. The result showed that with increase in Dufour and Soret parameter, fluid velocity increases and temperature increases with increase in variation of Dufour while, temperature decreases with increase in Soret. The effects of variable fluid viscosity, variable thermal conductivity, thermal radiation, Soret, Dufour, Prandtl and Schmidt parameters on the dimensionless velocity, temperature and concentration profiles are shown graphically.
文摘The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid past an infinite vertical porous plate under oscillatory suction velocity and thermal radiation. The Dufour （diffusion thermo） and Soret （thermal diffusion） effects are taken into account. The problem is solved numerically using the finite element method for the velocity, the temperature, and the concentration field. The expression for the skin friction, the rate of heat and mass transfer is obtained. The results are presented numerically through graphs and tables for the externally cooled plate （Gr 〉 0） and the externally heated plate （Gr 〈 0） to observe the effects of various parameters encountered in the equations.
文摘This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.
文摘In this work, the Micropolar fluid flow and heat and mass transfer past a horizontal nonlinear stretching sheet through porous medium is studied including the Soret-Dufour effect in the presence of suction. A uniform magnetic field is applied transversely to the direction of the flow. The governing differential equations of the problem have been transformed into a system of non-dimensional differential equations which are solved numerically by Nachtsheim-Swigert iteration technique along with the sixth order Runge-Kutta integration scheme. The velocity, microrotation, temperature and concentration profiles are presented for different parameters. The present problem finds significant applications in hydromagnetic control of conducting polymeric sheets, magnetic materials processing, etc.
文摘The present study deals with MHD (magneto hydrodynamics) mixed convection flow of a Casson fluid over an exponentially stretching sheet with the effects of Soret and Dufour, thermal radiation, chemical reaction. The governing partial differential equations are converted into ordinary differential equations by using similarity transformations. These equations are then solved numerically by applying finite difference scheme known as the Keller Box method. The effects of various parameters on velocity, temperature and concentration profiles are presented graphically to interpret and the results are discussed.
文摘The Dufour and Soret effects on the unsteady twodimensional magnetonyaro dynamics （MHD） doublediffusive free convective flow of an electrically conducting fluid past a vertical plate embedded in a nonDarcy porous medium are investigated numeri cally. The governing nonlinear dimensionless equations are solved by an implicit finite difference scheme of the CrankNicolson type with a tridiagonal matrix manipulation. The effects of various parameters entering into the problem on the unsteady dimension less velocity, temperature, and concentration profiles are studied in detail. Furthermore, the time variation of the skin friction coefficient, the Nusselt number, and the Sherwood number is presented and analyzed. The results show that the unsteady velocity, tem perature, and concentration profiles are substantially influenced by the Dufour and Soret effects. When the Dufour number increases or the Soret number decreases, both the skin friction and the Sherwood number decrease, while the Nusselt number increases. It is found that, when the magnetic parameter increases, the velocity and the temperature decrease in the boundary layer.
文摘Unsteady MHD natural convective heat and mass transfer flow through a semi-infinite vertical porous plate in a rotating system have been investigated with the combined Soret and Dufour effects in the presence of Hall current and constant heat flux. It is considered that the porous plate is subjected to constant heat flux. The obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocities, temperature and concentration distributions are obtained for various parameters by the above mentioned technique. The local and average shear stresses, Nusselt number as well as Sherwood number are also investigated. The stability conditions and convergence criteria of the explicit finite difference scheme are established for finding the restriction of the values of various parameters to get more accuracy. The obtained results are illustrated with the help of graphs to observe the effects of various legitimate parameters.
文摘An analysis of two-dimensional steady magneto-hydrodynamic free convection flow of an electrically conducting, viscous, incompressible fluid past an inclined stretching porous plate in the presence of a uniform magnetic field and thermal radiation with heat generation is made. Both the Dufour and Soret effects are considered for a hydrogen-air mixture as the non-chemically reacting fluid pair. The equations governing the flow, temperature and concentration fields are reduced to a system of joined non-linear ordinary differential equations by similarity transformation. Non-linear differential equations are integrated numerically by using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Finally the significance of physical parameters which are of engineering interest are examined both in graphical and tabular form.
文摘The primary aim of this research endeavor is to examine the characteristics of magnetohydrodynamicWilliamson nanofluid flow past a nonlinear stretching surface that is immersed in a permeable medium.In the current analysis,the impacts of Soret and Dufour(cross-diffusion effects)have been attentively taken into consideration.Using appropriate similarity variable transformations,the governing nonlinear partial differential equations were altered into nonlinear ordinary differential equations and then solved numerically using the Runge Kutta Fehlberg-45 method along with the shooting technique.Numerical simulations were then perceived to show the consequence of various physical parameters on the plots of velocity,temperature,and concentration of the nanofluid flow.Boosting the magnetic,Williamson,porosity,and stretching sheet index parameters,the velocity of the fluid flow decreases.The temperature is enhanced as theWilliamson and Brownian motion parameters upsurge,but it decreases as the Prandtl,thermophoresis,stretching sheet index,and Dufour parameters escalate.The concentration distribution decreases as the thermophoresis andmagnetic parameters upsurge,but it escalates as the Soret,Schmidt,Brownian motion,and stretching sheet index parameters increase.Skin friction coefficient boosted as the stretching sheet index and magnetic parameters enhanced against the Williamson parameter.The findings from this study have been contrasted with earlier findings on local Nusselt numbers,which show substantial support and endorse the existing approach’s validity.The numerical values of the local Sherwood number gradually increase as the Schmidt,Soret,stretching sheet index,and thermophoresis parameters are upsurged.
