Recent years have seen the development of a number of mathematical models for the description of the simultaneous transport of microorganisms and bioreactive solutes in porous media. Most models are based on the adve...Recent years have seen the development of a number of mathematical models for the description of the simultaneous transport of microorganisms and bioreactive solutes in porous media. Most models are based on the advection dispersion equation, with terms added to account for interactions with the surfaces of the solid matrix, transformations and microbial activities. Those models based on the advection dispersion equation have all been shown to represent laboratory experimental data adequately although various assumptions have been made concerning the pore scale distribution of bacteria. This paper provides an overview of the recent work on modelling the transport and fate of microorganisms and bioreactive solutes in porous media and examines the different assumptions regarding the pore scale distribution of microorganisms.展开更多
A new method - perturbative summation to infinite order is presented to obtain the anomalous dimension in the solution of the modified porous medium equation. The result is the same as that in the renormalization grou...A new method - perturbative summation to infinite order is presented to obtain the anomalous dimension in the solution of the modified porous medium equation. The result is the same as that in the renormalization group (RG) approach. It gives us an insight into the anomalous exponent in the asymptotic solution of the modified porous medium equation in the RG approach. Based on this discussion, we can see that the anomalous dimension appears naturally in the problem and the nonlinearity reflects the anomalous long-time behavior of the system.展开更多
Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is prove...Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is proved that the solutions of (1) tend to those of the following nonlinear parabolic equation time-asymptotically:展开更多
In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asympto...In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method （OHAM） for partial differ- ential equations （PDEs） is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional- order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.展开更多
The authors investigate the sensitivity of hydrostatic pressure of flows through porous media with respect to the position of the soil layers. Indeed, these induce discontinuities of the porosity which is a piecewise ...The authors investigate the sensitivity of hydrostatic pressure of flows through porous media with respect to the position of the soil layers. Indeed, these induce discontinuities of the porosity which is a piecewise constant coefficient K of the partial differential equation satisfied by the pressure u and it leads to the computation of the derivative of u with respect to changes in position of discontinuity surface of K.The analysis relies on a mixed formulation of the problem. Preliminary numerical simulations are given to illustrate the theory. An application to a simple inverse problem is also given.展开更多
The present study is carried out to see the thermal-diffusion(Dufour) and diffusion-thermo(Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface i...The present study is carried out to see the thermal-diffusion(Dufour) and diffusion-thermo(Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface in a porous medium. Optimal homotopy analysis method(OHAM) is best candidate to handle highly nonlinear system of differential equations obtained from boundary layer partial differential equations via appropriate transformations. Graphical illustrations depicting different physical arising parameters against velocity, temperature and concentration distributions with required discussion have also been added. Numerically calculated values of skin friction coefficient, local Nusselt and Sherwood numbers are given in the form of table and well argued. It is found that nanofluid velocity increases with increase in mixed convective and viscoelastic parameters but it decreases with the increasing values of porosity parameter. Also, it is observed that Dufour number has opposite behavior on temperature and concentration profiles.展开更多
The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bio- convection and mixed convection on the steady bo...The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bio- convection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conser- vation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative anal- ysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence beat, mass and motile micro-organism transfer rates.展开更多
文摘Recent years have seen the development of a number of mathematical models for the description of the simultaneous transport of microorganisms and bioreactive solutes in porous media. Most models are based on the advection dispersion equation, with terms added to account for interactions with the surfaces of the solid matrix, transformations and microbial activities. Those models based on the advection dispersion equation have all been shown to represent laboratory experimental data adequately although various assumptions have been made concerning the pore scale distribution of bacteria. This paper provides an overview of the recent work on modelling the transport and fate of microorganisms and bioreactive solutes in porous media and examines the different assumptions regarding the pore scale distribution of microorganisms.
文摘A new method - perturbative summation to infinite order is presented to obtain the anomalous dimension in the solution of the modified porous medium equation. The result is the same as that in the renormalization group (RG) approach. It gives us an insight into the anomalous exponent in the asymptotic solution of the modified porous medium equation in the RG approach. Based on this discussion, we can see that the anomalous dimension appears naturally in the problem and the nonlinearity reflects the anomalous long-time behavior of the system.
文摘Consider the systemwhich can be used to model the adiabatic gas flow through porous media. Here v is specific volume, u denotes velocity, s stands for entropy, p denotes pressure with pv <0 for v >0. It is proved that the solutions of (1) tend to those of the following nonlinear parabolic equation time-asymptotically:
文摘In this paper, we study the fractional-order biological population models （FI3PMs） with Malthusian~ Verhulst, and porous media laws. The fractional derivative is defined in Caputo sense. The optimal homotopy asymptotic method （OHAM） for partial differ- ential equations （PDEs） is extended and successfully implemented to solve FBPMs. Third-order approximate solutions are obtained and compared with the exact solutions. The numerical results unveil that the proposed extension in the OHAM for fractional- order differential problems is very effective and simple in computation. The results reveal the effectiveness with high accuracy and extremely efficient to handle most complicated biological population models.
文摘The authors investigate the sensitivity of hydrostatic pressure of flows through porous media with respect to the position of the soil layers. Indeed, these induce discontinuities of the porosity which is a piecewise constant coefficient K of the partial differential equation satisfied by the pressure u and it leads to the computation of the derivative of u with respect to changes in position of discontinuity surface of K.The analysis relies on a mixed formulation of the problem. Preliminary numerical simulations are given to illustrate the theory. An application to a simple inverse problem is also given.
文摘The present study is carried out to see the thermal-diffusion(Dufour) and diffusion-thermo(Soret) effects on the mixed convection boundary layer flow of viscoelastic nanofluid flow over a vertical stretching surface in a porous medium. Optimal homotopy analysis method(OHAM) is best candidate to handle highly nonlinear system of differential equations obtained from boundary layer partial differential equations via appropriate transformations. Graphical illustrations depicting different physical arising parameters against velocity, temperature and concentration distributions with required discussion have also been added. Numerically calculated values of skin friction coefficient, local Nusselt and Sherwood numbers are given in the form of table and well argued. It is found that nanofluid velocity increases with increase in mixed convective and viscoelastic parameters but it decreases with the increasing values of porosity parameter. Also, it is observed that Dufour number has opposite behavior on temperature and concentration profiles.
文摘The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bio- convection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conser- vation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative anal- ysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence beat, mass and motile micro-organism transfer rates.
