Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model an improved Darcy model describing the natural convection in porous media. Besides their important theoretical meaning (f...Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model an improved Darcy model describing the natural convection in porous media. Besides their important theoretical meaning (for example, to analyze the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions to promoting the develop ment of computational heat and mass transfer. For instance, we can use them to check the accuracy,convergence and effectiveness of various numerical computational methods and to improve numerical calculation skills such as differential schemes and grid generation ways.展开更多
Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media.Besides their important theoretical meaning(f...Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media.Besides their important theoretical meaning(for example,in analyzing the non-Darcy and anisotropic effects on the convection),such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer.Some solutions considering the anisotropic effect of permeability have been given previously by the authors,and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.展开更多
The present study is focused on the unsteady two-phase flow of blood in a cylindrical region.Blood is taken as a counter-example of Brinkman type fluid containing magnetic(dust)particles.The oscillating pressure gradi...The present study is focused on the unsteady two-phase flow of blood in a cylindrical region.Blood is taken as a counter-example of Brinkman type fluid containing magnetic(dust)particles.The oscillating pressure gradient has been considered because for blood flow it is necessary to investigate in the form of a diastolic and systolic pressure.The transverse magnetic field has been applied externally to the cylindrical tube to study its impact on both fluids as well as particles.The system of derived governing equations based on Navier Stoke’s,Maxwell and heat equations has been generalized using the well-known Caputo–Fabrizio(C–F)fractional derivative.The considered fractional model has been solved analytically using the joint Laplace and Hankel(L&H)transformations.The effect of various physical parameters such as fractional parameter,Gr,M andγ on blood and magnetic particles has been shown graphically using the Mathcad software.The fluid behaviour is thinner in fractional order as compared to the classical one.展开更多
The viscous dissipation effect on forced convection in a porous saturated circular tube with an isoflux wall is investigated on the basis of the Brinkman flow model. For the thermally developing region, a numerical st...The viscous dissipation effect on forced convection in a porous saturated circular tube with an isoflux wall is investigated on the basis of the Brinkman flow model. For the thermally developing region, a numerical study is reported while a perturbation analysis is presented to find expressions for the temperature profile and the Nusselt number for the fully developed region. The fully developed Nusselt number found by numerical solution for the developing region is compared with that of asymptotic analysis and a good degree of agreement is observed.展开更多
During the manufacturing or processing of materials,large volumes of water of the required quality are often needed.Industrial water treatment and water purification is the process of removing impurities and pollution...During the manufacturing or processing of materials,large volumes of water of the required quality are often needed.Industrial water treatment and water purification is the process of removing impurities and pollution from the considered medium.To obtain liquid with specified quality parameters,complex systems of filters and treatment facilities are generally used.In this work,the cleaning process for a filtration column is studied.Three-dimensional numerical simulations of flow in a columnar array consisting of a porous medium are conducted.In particular,a model case corresponding to laboratory conditions is examined,with potassium salt being considered as a pollutant.It is assumed that the vertical column is a desalination system,as a result of which saturation and clogging of the pores of the medium occur;at the end of the operating cycle of such a filter,washing is required.Filtration modeling is implemented through the Brinkman approach taking into account density stratification.It is found that owing to density stratification and related effects,clean water moves in the central part of the filter,while contaminants near the side walls remain motionless for a long time.A solution to this problem is presented by changing the flow rate of supplied water.展开更多
In this paper, we have considered a fully developed flow of a viscous incompressible fluid in a rectangular porous duct saturated with the same fluid. The duct is heated from the bottom for forced and mixed convection...In this paper, we have considered a fully developed flow of a viscous incompressible fluid in a rectangular porous duct saturated with the same fluid. The duct is heated from the bottom for forced and mixed convection. The Brinkman model is used to simulate the momentum transfer in the porous duct. Using the momentum and thermal energy equations, the entropy generation has been obtained due to the heat transfer, viscous and Darcy dissipations. It is found from the mathematical analysis that the entropy generation is double when the viscous as well as the Darcy dissipations terms are taken in the thermal energy equation in comparison when the viscous as well as the Darcy dissipations terms are not taken in the thermal energy equation. This result clearly shows that there is no need of taking the viscous and Darcy dissipations terms in the thermal energy equation to obtain the entropy generation.展开更多
An analysis is presented with magnetohydrodynamics natural convective flow of a viscous Newtonian fluid saturated porous medium in a vertical slot. The flow in the porous media has been modeled using the Brinkman mode...An analysis is presented with magnetohydrodynamics natural convective flow of a viscous Newtonian fluid saturated porous medium in a vertical slot. The flow in the porous media has been modeled using the Brinkman model. The fully-developed two-dimensional flow from capped to open ends is considered for which a continuum of solutions is obtained. The influence of pertinent parame-ters on the flow is delineated and appropriate conclusions are drawn. The asymptotic behaviour and the volume flux are analyzed and incorporated graphically for the three-parameter family of solution.展开更多
The study of forced convection in a porous medium has aroused and still arouses today the interest of many scientists and industrialists. A considerable amount of work has been undertaken following the discovery of th...The study of forced convection in a porous medium has aroused and still arouses today the interest of many scientists and industrialists. A considerable amount of work has been undertaken following the discovery of the phenomenon. Solving a standard problem of forced convection in porous media comes down to predicting the temperature and velocity fields as well as the intensity of the flow as a function of the various parameters of the problem. A numerical study of the condensation in forced convection of a pure and saturated vapor on a vertical wall covered with a porous material is presented. The transfers in the porous medium and the liquid film are described respectively by the Darcy-Brinkman model and the classical boundary layer equations. The dimensionless equations are solved by an implicit finite difference method and the iterative Gauss-Seidel method. Our study makes it possible to examine and highlight the role of parameters such as: the Froude number and the thickness of the porous layer on the speed and the temperature in the porous medium. Given the objective of our study, the presentation of velocity and temperature profiles is limited in the porous medium. The results show that the Froude number does not influence the thermal field. The temperature increases with an increase in the thickness of the dimensionless porous layer. The decrease in the Froude number leads to an increase in the hydrodynamic field.展开更多
基金This work was supported by the National Natural Science Foundation of China (Giant Nos. 59846007,59925615) NKBRSF (Grant Nos. G1999022309, G2000026305). The authors are grateful to Prof. Liu Dengying, Prof. Zhao Tianshou, Liu Weiwei and Li Lina for
文摘Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model an improved Darcy model describing the natural convection in porous media. Besides their important theoretical meaning (for example, to analyze the non-Darcy and anisotropic effects on the convection), such analytical solutions can be the benchmark solutions to promoting the develop ment of computational heat and mass transfer. For instance, we can use them to check the accuracy,convergence and effectiveness of various numerical computational methods and to improve numerical calculation skills such as differential schemes and grid generation ways.
基金supported by the National Natural Science Foundation of China(Grant No.50246003)NKBRSF(Grant No.G2000026305).
文摘Some algebraically explicit analytical solutions are derived for the anisotropic Brinkman model―an improved Darcy model―describing the natural convection in porous media.Besides their important theoretical meaning(for example,in analyzing the non-Darcy and anisotropic effects on the convection),such analytical solutions can be the benchmark solutions that can promote the development of computational heat and mass transfer.Some solutions considering the anisotropic effect of permeability have been given previously by the authors,and this paper gives solutions including the anisotropic effect of thermal conductivity and the effect of heat sources.
文摘The present study is focused on the unsteady two-phase flow of blood in a cylindrical region.Blood is taken as a counter-example of Brinkman type fluid containing magnetic(dust)particles.The oscillating pressure gradient has been considered because for blood flow it is necessary to investigate in the form of a diastolic and systolic pressure.The transverse magnetic field has been applied externally to the cylindrical tube to study its impact on both fluids as well as particles.The system of derived governing equations based on Navier Stoke’s,Maxwell and heat equations has been generalized using the well-known Caputo–Fabrizio(C–F)fractional derivative.The considered fractional model has been solved analytically using the joint Laplace and Hankel(L&H)transformations.The effect of various physical parameters such as fractional parameter,Gr,M andγ on blood and magnetic particles has been shown graphically using the Mathcad software.The fluid behaviour is thinner in fractional order as compared to the classical one.
文摘The viscous dissipation effect on forced convection in a porous saturated circular tube with an isoflux wall is investigated on the basis of the Brinkman flow model. For the thermally developing region, a numerical study is reported while a perturbation analysis is presented to find expressions for the temperature profile and the Nusselt number for the fully developed region. The fully developed Nusselt number found by numerical solution for the developing region is compared with that of asymptotic analysis and a good degree of agreement is observed.
基金supported by a grant from the Russian Science Foundation(Project No.20-11-20125).
文摘During the manufacturing or processing of materials,large volumes of water of the required quality are often needed.Industrial water treatment and water purification is the process of removing impurities and pollution from the considered medium.To obtain liquid with specified quality parameters,complex systems of filters and treatment facilities are generally used.In this work,the cleaning process for a filtration column is studied.Three-dimensional numerical simulations of flow in a columnar array consisting of a porous medium are conducted.In particular,a model case corresponding to laboratory conditions is examined,with potassium salt being considered as a pollutant.It is assumed that the vertical column is a desalination system,as a result of which saturation and clogging of the pores of the medium occur;at the end of the operating cycle of such a filter,washing is required.Filtration modeling is implemented through the Brinkman approach taking into account density stratification.It is found that owing to density stratification and related effects,clean water moves in the central part of the filter,while contaminants near the side walls remain motionless for a long time.A solution to this problem is presented by changing the flow rate of supplied water.
文摘In this paper, we have considered a fully developed flow of a viscous incompressible fluid in a rectangular porous duct saturated with the same fluid. The duct is heated from the bottom for forced and mixed convection. The Brinkman model is used to simulate the momentum transfer in the porous duct. Using the momentum and thermal energy equations, the entropy generation has been obtained due to the heat transfer, viscous and Darcy dissipations. It is found from the mathematical analysis that the entropy generation is double when the viscous as well as the Darcy dissipations terms are taken in the thermal energy equation in comparison when the viscous as well as the Darcy dissipations terms are not taken in the thermal energy equation. This result clearly shows that there is no need of taking the viscous and Darcy dissipations terms in the thermal energy equation to obtain the entropy generation.
文摘An analysis is presented with magnetohydrodynamics natural convective flow of a viscous Newtonian fluid saturated porous medium in a vertical slot. The flow in the porous media has been modeled using the Brinkman model. The fully-developed two-dimensional flow from capped to open ends is considered for which a continuum of solutions is obtained. The influence of pertinent parame-ters on the flow is delineated and appropriate conclusions are drawn. The asymptotic behaviour and the volume flux are analyzed and incorporated graphically for the three-parameter family of solution.
文摘The study of forced convection in a porous medium has aroused and still arouses today the interest of many scientists and industrialists. A considerable amount of work has been undertaken following the discovery of the phenomenon. Solving a standard problem of forced convection in porous media comes down to predicting the temperature and velocity fields as well as the intensity of the flow as a function of the various parameters of the problem. A numerical study of the condensation in forced convection of a pure and saturated vapor on a vertical wall covered with a porous material is presented. The transfers in the porous medium and the liquid film are described respectively by the Darcy-Brinkman model and the classical boundary layer equations. The dimensionless equations are solved by an implicit finite difference method and the iterative Gauss-Seidel method. Our study makes it possible to examine and highlight the role of parameters such as: the Froude number and the thickness of the porous layer on the speed and the temperature in the porous medium. Given the objective of our study, the presentation of velocity and temperature profiles is limited in the porous medium. The results show that the Froude number does not influence the thermal field. The temperature increases with an increase in the thickness of the dimensionless porous layer. The decrease in the Froude number leads to an increase in the hydrodynamic field.
