This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comp...This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper （Cu）, Silver （Ag）, Alumina （A1203） and Titanium Oxide （TiO2）. Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.展开更多
In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ...In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ=0 and 0〈μ〈 2N/n（m-1）＋2 or γ 〉 0 and 1/p-1 〈 μ 〈 2N/N（m-1）＋2 then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S（RN）, there exists an initial-value u0 ∈ C（RN） with limx→∞ uo（x）= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u（tβ, t）, Where β = 2-μ（m-1）/4.展开更多
The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition.At the end of the article,＂Darcy＇s law＂is rigorously derived from this m...The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition.At the end of the article,＂Darcy＇s law＂is rigorously derived from this model as the parameter ε tends to zero,which is independent of the coordinates towards the thickness.展开更多
The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian （Maxwell） fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtoni...The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian （Maxwell） fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in time domain. The results are also compared with those based on generalized Biot＇s theory. The results show that the influence of non-Newtonian effect on acoustic guided wave, especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.展开更多
In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material ...In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.展开更多
This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on...This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f（u）.展开更多
The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of soli...The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.展开更多
In this paper we study existence of solutions of a class of Cauchy problems for porous medium equations with strongly nonlinear sources or absorptions and convections when the initial trace is a Radon measure μ on RN.
Hydrate-based CO_(2) sequestration is an effective method for reducing the greenhouse effect,and the presence of porous media and NaCl can impact the formation characteristics of hydrates.This study uses the constant ...Hydrate-based CO_(2) sequestration is an effective method for reducing the greenhouse effect,and the presence of porous media and NaCl can impact the formation characteristics of hydrates.This study uses the constant volume temperature search method to investigate the effects of quartz sand particle size(0.006‒0.03 mm),water saturation(30%–90%),and NaCl concentration(1%‒9%)on the phase equilibrium and kinetics of CO_(2) hydrates within a temperature range of 273‒285 K and pressure range of 1.0‒3.5 MPa.The results indicate that a decrease in quartz sand particle size or an increase in NaCl concentration shifts the hydrate phase equilibrium curve towards lower temperatures and higher pressures,making hydrate generation conditions more demanding.In different particle size systems,there are no significant changes in the rate of CO_(2) hydrate formation or conversion rate.The highest hydrate conversion rate of 71.1%is observed in a 0.015 mm particle size system.With increasing water saturation,both the generation rate and conversion rate of CO_(2) hydrates show a trend of first increasing and then decreasing.Meanwhile,low concentrations of NaCl(1%–3%)are found to enhance the formation and conversion rates of CO_(2) hydrates.However,as NaCl concentration increases,the rate of CO_(2) hydrate formation and conversion rate decrease.展开更多
Amidst the rapid development of renewable energy,the intermittency and instability of energy supply pose severe challenges and impose higher requirements on energy storage systems.Among the various energy storage tech...Amidst the rapid development of renewable energy,the intermittency and instability of energy supply pose severe challenges and impose higher requirements on energy storage systems.Among the various energy storage technologies,the coupled approach of power-to-hydrogen(H2)and underground H2storage(UHS)offers advantages such as extended storage duration and large-scale capacity,making it highly promising for future development.However,during UHS,particularly in porous media,microbial metabolic processes such as methanogenesis,acetogenesis,and sulfate reduction may lead to H2consumption and the production of byproducts.These microbial activities can impact the efficiency and safety of UHS both positively and negatively.Therefore,this paper provides a comprehensive review of experimental,numerical,and field studies on microbial interactions in UHS within porous media,aiming to capture research progress and elucidate microbial effects.It begins by outlining the primary types of UHS and the key microbial metabolic processes involved.Subsequently,the paper introduces the experimental approaches for investigating gas-water-rock-microbe interactions and interfacial properties,the models and simulators used in numerical studies,and the procedures implemented in field trials.Furthermore,it analyzes and discusses microbial interactions and their positive and negative impacts on UHS in porous media,focusing on aspects such as H2consumption,H2flow,and storage safety.Based on these insights,recommendations for site selection,engineering operations,and on-site monitoring of UHS,as well as potential future research directions,are provided.展开更多
In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to...In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.展开更多
Aerogel nanoporous materials possess high porosity, high specific surface area, and extremely low density due to their unique nanoscale network structure. Moreover, their effective thermal conductivity is very low, ma...Aerogel nanoporous materials possess high porosity, high specific surface area, and extremely low density due to their unique nanoscale network structure. Moreover, their effective thermal conductivity is very low, making them a new type of lightweight and highly efficient nanoscale super-insulating material. However, prediction of their effective thermal conductivity is challenging due to their uneven pore size distribution. To investigate the internal heat transfer mechanism of aerogel nanoporous materials, this study constructed a cross-aligned and cubic pore model(CACPM) based on the actual pore arrangement of SiO_(2) aerogel. Based on the established CACPM, the effective thermal conductivity expression for the aerogel was derived by simultaneously considering gas-phase heat conduction, solid-phase heat conduction, and radiative heat transfer. The derived expression was then compared with available experimental data and the Wei structure model. The results indicate that, according to the model established in this study for the derived thermal conductivity formula of silica aerogel, for powdery silica aerogel under the conditions of T = 298 K, a_(2)= 0.85, D_(1)= 90 μm, ρ = 128 kg/m^(3), within the pressure range of 0–10^(5)Pa, the average deviation between the calculated values and experimental values is 10.51%. In the pressure range of 10^(3)–10^(4)Pa, the deviation between calculated values and experimental values is within 4%. Under these conditions, the model has certain reference value in engineering verification. This study also makes a certain contribution to the research of aerogel thermal conductivity heat transfer models and calculation formulae.展开更多
Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the prese...Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.展开更多
It is very important to design the optimum starting time of water injection for the development of low permeability reservoirs. In this type of reservoir the starting time of water injection will be affected by a rese...It is very important to design the optimum starting time of water injection for the development of low permeability reservoirs. In this type of reservoir the starting time of water injection will be affected by a reservoir pressure-sensitive effect. In order to optimize the starting time of water injection in low permeability reservoirs, this effect of pressure change on rock permeability of low permeability reservoirs was, at first, studied by physical simulation. It was shown that the rock permeability decreases exponentially with an increase in formation pressure. Secondly, we conducted a reservoir engineering study, from which we obtained analytic relationships between formation pressure, oil production rate, water production rate and water injection rate. After our physical, theoretical and economical analyses, we proposed an approach which takes the pressure-sensitive effect into consideration and designed the optimum starting time of water injection, based on the principle of material balance. Finally, the corresponding software was developed and applied to one block of the Jiangsu Oilfield. It is shown that water injection, in advance of production, can decrease the adverse impact of the pressure-sensitive effect on low permeability reservoir development. A water-flooding project should be preferably initiated in advance of production for no more than one year and the optimum ratio of formation pressure to initial formation pressure should be maintained at a level between 1.05 and 1.2.展开更多
This paper deals with the singularity and global regularity tor a class oI nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principl...This paper deals with the singularity and global regularity tor a class oI nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up Occurs.展开更多
This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the react...This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.展开更多
We would like to acknowledge the misprinted terms in our published paper“Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a micro...We would like to acknowledge the misprinted terms in our published paper“Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel”[Chin.Phys.B 22124702(2013)].Since only two misprints exist and the main results of the published paper are correct,we present the correct equations in this erratum.展开更多
This research presents the applications of entropy generation phenomenon in incompressible flow of Jeffrey nanofluid in the presence of distinct thermal features. The novel aspects of various features, such as Joule h...This research presents the applications of entropy generation phenomenon in incompressible flow of Jeffrey nanofluid in the presence of distinct thermal features. The novel aspects of various features, such as Joule heating, porous medium,dissipation features, and radiative mechanism are addressed. In order to improve thermal transportation systems based on nanomaterials, convective boundary conditions are introduced. The thermal viscoelastic nanofluid model is expressed in terms of differential equations. The problem is presented via nonlinear differential equations for which analytical expressions are obtained by using the homotopy analysis method(HAM). The accuracy of solution is ensured. The effective outcomes of all physical parameters associated with the flow model are carefully examined and underlined through various curves. The observations summarized from current analysis reveal that the presence of a permeability parameter offers resistance to the flow. A monotonic decrement in local Nusselt number is noted with Hartmann number and Prandtl number.Moreover, entropy generation and Bejan number increases with radiation parameter and fluid parameter.展开更多
基金supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia
文摘This article concentrates on the steady magnetohydrodynamic （MHD） flow of viscous nanofluid. The flow is caused by a permeable exponentially stretching surface. An incompressible fluid fills the porous space. A comparative study is made for the nanoparticles namely Copper （Cu）, Silver （Ag）, Alumina （A1203） and Titanium Oxide （TiO2）. Water is treated as a base fluid. Convective type boundary conditions are employed in modeling the heat transfer process. The non-linear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations. The obtained equations are then solved for the development of series solutions. Convergence of the obtained series solutions is explicitly discussed. The effects of different parameters on the velocity and temperature profiles are shown and analyzed through graphs.
基金supported by National Natural Science Foundation of Chinasupported by Specialized Research Fund for the Doctoral Program of Higher Educationsupported by Graduate Innovation Fund of Jilin University (20101045)
文摘In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut - △um ＋ yup = 0,where γ≥0,m〉 1and P〉m＋2/N We will show that if γ=0 and 0〈μ〈 2N/n（m-1）＋2 or γ 〉 0 and 1/p-1 〈 μ 〈 2N/N（m-1）＋2 then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S（RN）, there exists an initial-value u0 ∈ C（RN） with limx→∞ uo（x）= 0 such that φ is an w-limit point of the rescaled solutions tμ/2u（tβ, t）, Where β = 2-μ（m-1）/4.
基金National NaturalScience Foundation of China(10171113 and 10471156)Natural Science Foundation of Guangdong(4009793)
文摘The article studies the homogenization of a stationary Navier-Stokes fluid in porous medium with thin film under Dirichlet boundary condition.At the end of the article,＂Darcy＇s law＂is rigorously derived from this model as the parameter ε tends to zero,which is independent of the coordinates towards the thickness.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.40974067,40674059 and 10534040)the State Key Laboratory of Acoustics,Chinese Academy of Sciences(Grant No.200807)Scientific Forefront and Interdisciplinary Innovation Project of Jilin University(Grant No.200903319)
文摘The property of acoustic guided waves generated in a fluid-filled borehole surrounded by a non-Newtonian （Maxwell） fluid-saturated porous formation with a permeable wall is investigated. The influence of non-Newtonian effects on acoustic guided waves such as Stoneley waves, pseudo-Rayleigh waves, flexural waves, and screw waves propagations in a fluid-filled borehole is demonstrated based on the generalized Biot-Tsiklauri model by calculating their velocity dispersion and attenuation coefficients. The corresponding acoustic waveforms illustrate their properties in time domain. The results are also compared with those based on generalized Biot＇s theory. The results show that the influence of non-Newtonian effect on acoustic guided wave, especially on the attenuation coefficient of guided wave propagation in borehole is noticeable.
文摘In this paper, the effects of both rotation and magnetic field of the peristaltic transport of a second-order fluid through a porous medium in a channel are studied analytically and computed numerically. The material is represented by the constitutive equations for a second-order fluid. Closed-form solutions under the consideration of long wavelength and low Reynolds number is presented. The analytical expressions for the pressure gradient, pressure rise, friction force, stream function, shear stress, and velocity are obtained in the physical domain. The effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow in the wave frame are analyzed theoretically and computed numerically. Numerical results are given and illustrated graphically in each case considered. Comparison was made with the results obtained in the presence and absence of rotation, magnetic field, and porosity. The results indicate that the effects of the non-dimensional wave amplitude, porosity, magnetic field, rotation, and the dimensionless time-mean flow are very pronounced in the phenomena.
基金The project is supported by NSFC(11271154)Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Educationby the 985 Program of Jilin University
文摘This paper deals with a class of porous medium equation ut=△u^m＋f（u）with homogeneous Dirichlet boundary conditions. The blow-up criteria is established by using the method of energy under the suitable condition on the function f（u）.
基金Supported by the National Natural Science Foundation of China under Grant No 51305080
文摘The effect of the solid matrix and porosity of the porous medium are first introduced to the study of power-law nanofluids, and the Marangoni boundary layer flow with heat generation is investigated. Two cases of solid matrix of porous medium including glass balls and aluminum foam are considered. The governing partial differential equations are simplified by dimensionless variables and similarity transformations, and are solved numerically by using a shooting method with the fourth-fifth-order Runge-Kutta integration technique. It is indicated that the increase of the porosity leads to the enhancement of heat transfer in the surface of the Marangoni boundary layer flow.
文摘In this paper we study existence of solutions of a class of Cauchy problems for porous medium equations with strongly nonlinear sources or absorptions and convections when the initial trace is a Radon measure μ on RN.
基金the National Natural Science Foundation of China(NSFC 21676145)Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD,China).
文摘Hydrate-based CO_(2) sequestration is an effective method for reducing the greenhouse effect,and the presence of porous media and NaCl can impact the formation characteristics of hydrates.This study uses the constant volume temperature search method to investigate the effects of quartz sand particle size(0.006‒0.03 mm),water saturation(30%–90%),and NaCl concentration(1%‒9%)on the phase equilibrium and kinetics of CO_(2) hydrates within a temperature range of 273‒285 K and pressure range of 1.0‒3.5 MPa.The results indicate that a decrease in quartz sand particle size or an increase in NaCl concentration shifts the hydrate phase equilibrium curve towards lower temperatures and higher pressures,making hydrate generation conditions more demanding.In different particle size systems,there are no significant changes in the rate of CO_(2) hydrate formation or conversion rate.The highest hydrate conversion rate of 71.1%is observed in a 0.015 mm particle size system.With increasing water saturation,both the generation rate and conversion rate of CO_(2) hydrates show a trend of first increasing and then decreasing.Meanwhile,low concentrations of NaCl(1%–3%)are found to enhance the formation and conversion rates of CO_(2) hydrates.However,as NaCl concentration increases,the rate of CO_(2) hydrate formation and conversion rate decrease.
基金supported by the European Union's“Horizon Europe programme”—LOC3G(Grant No.101129729)the Henan Center for Outstanding Overseas Scientists(Grant No.GZS2024001)。
文摘Amidst the rapid development of renewable energy,the intermittency and instability of energy supply pose severe challenges and impose higher requirements on energy storage systems.Among the various energy storage technologies,the coupled approach of power-to-hydrogen(H2)and underground H2storage(UHS)offers advantages such as extended storage duration and large-scale capacity,making it highly promising for future development.However,during UHS,particularly in porous media,microbial metabolic processes such as methanogenesis,acetogenesis,and sulfate reduction may lead to H2consumption and the production of byproducts.These microbial activities can impact the efficiency and safety of UHS both positively and negatively.Therefore,this paper provides a comprehensive review of experimental,numerical,and field studies on microbial interactions in UHS within porous media,aiming to capture research progress and elucidate microbial effects.It begins by outlining the primary types of UHS and the key microbial metabolic processes involved.Subsequently,the paper introduces the experimental approaches for investigating gas-water-rock-microbe interactions and interfacial properties,the models and simulators used in numerical studies,and the procedures implemented in field trials.Furthermore,it analyzes and discusses microbial interactions and their positive and negative impacts on UHS in porous media,focusing on aspects such as H2consumption,H2flow,and storage safety.Based on these insights,recommendations for site selection,engineering operations,and on-site monitoring of UHS,as well as potential future research directions,are provided.
基金supported by the National Science Foundation of China(1067121290820302)the National Science Foundation of Hunan Province
文摘In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51764046 and 52160013)the Inner Mongolia Autonomous Region Postgraduate Research Innovation Project of China (Grant No. S20231165Z)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region of China (Grant Nos. 2023RCTD016 and 2024RCTD008)。
文摘Aerogel nanoporous materials possess high porosity, high specific surface area, and extremely low density due to their unique nanoscale network structure. Moreover, their effective thermal conductivity is very low, making them a new type of lightweight and highly efficient nanoscale super-insulating material. However, prediction of their effective thermal conductivity is challenging due to their uneven pore size distribution. To investigate the internal heat transfer mechanism of aerogel nanoporous materials, this study constructed a cross-aligned and cubic pore model(CACPM) based on the actual pore arrangement of SiO_(2) aerogel. Based on the established CACPM, the effective thermal conductivity expression for the aerogel was derived by simultaneously considering gas-phase heat conduction, solid-phase heat conduction, and radiative heat transfer. The derived expression was then compared with available experimental data and the Wei structure model. The results indicate that, according to the model established in this study for the derived thermal conductivity formula of silica aerogel, for powdery silica aerogel under the conditions of T = 298 K, a_(2)= 0.85, D_(1)= 90 μm, ρ = 128 kg/m^(3), within the pressure range of 0–10^(5)Pa, the average deviation between the calculated values and experimental values is 10.51%. In the pressure range of 10^(3)–10^(4)Pa, the deviation between calculated values and experimental values is within 4%. Under these conditions, the model has certain reference value in engineering verification. This study also makes a certain contribution to the research of aerogel thermal conductivity heat transfer models and calculation formulae.
文摘Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.
基金Projects 2003BA613-07-05 supported by the Program of National "Fifteen" Science and Technology 04E7029 by the CNPC Innovation Foundation
文摘It is very important to design the optimum starting time of water injection for the development of low permeability reservoirs. In this type of reservoir the starting time of water injection will be affected by a reservoir pressure-sensitive effect. In order to optimize the starting time of water injection in low permeability reservoirs, this effect of pressure change on rock permeability of low permeability reservoirs was, at first, studied by physical simulation. It was shown that the rock permeability decreases exponentially with an increase in formation pressure. Secondly, we conducted a reservoir engineering study, from which we obtained analytic relationships between formation pressure, oil production rate, water production rate and water injection rate. After our physical, theoretical and economical analyses, we proposed an approach which takes the pressure-sensitive effect into consideration and designed the optimum starting time of water injection, based on the principle of material balance. Finally, the corresponding software was developed and applied to one block of the Jiangsu Oilfield. It is shown that water injection, in advance of production, can decrease the adverse impact of the pressure-sensitive effect on low permeability reservoir development. A water-flooding project should be preferably initiated in advance of production for no more than one year and the optimum ratio of formation pressure to initial formation pressure should be maintained at a level between 1.05 and 1.2.
基金supported in part by NSFC(11571243)Sichuan Youth Science and Technology Foundation(2014JQ0003)+1 种基金Fundamental Research Funds for the Central Universities(2682016CX116)Project of Education Department of Sichuan Province(14226423)
文摘This paper deals with the singularity and global regularity tor a class oI nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up Occurs.
基金supported in part by NSF of China(11001189),supported by NSF of China(11371384)supported in part by NSF of Chongqing(cstc2013jcyjA0940)in part by NSF of Fuling(FLKJ,2013ABA2036)
文摘This article deals with the global existence and blow-up of positive solution of a nonlinear diffusion equation with nonlocal source and nonlocal nonlinear boundary condition. We investigate the influence of the reaction terms, the weight functions and the nonlinear terms in the boundary conditions on global existence and blow up for this equation. Moreover, we establish blow-up rate estimates under some appropriate hypotheses.
文摘We would like to acknowledge the misprinted terms in our published paper“Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel”[Chin.Phys.B 22124702(2013)].Since only two misprints exist and the main results of the published paper are correct,we present the correct equations in this erratum.
基金supported by Taif University Researchers Supporting Project(Grant No.TURSP-2020/217),Taif University,Taif,Saudi Arabia。
文摘This research presents the applications of entropy generation phenomenon in incompressible flow of Jeffrey nanofluid in the presence of distinct thermal features. The novel aspects of various features, such as Joule heating, porous medium,dissipation features, and radiative mechanism are addressed. In order to improve thermal transportation systems based on nanomaterials, convective boundary conditions are introduced. The thermal viscoelastic nanofluid model is expressed in terms of differential equations. The problem is presented via nonlinear differential equations for which analytical expressions are obtained by using the homotopy analysis method(HAM). The accuracy of solution is ensured. The effective outcomes of all physical parameters associated with the flow model are carefully examined and underlined through various curves. The observations summarized from current analysis reveal that the presence of a permeability parameter offers resistance to the flow. A monotonic decrement in local Nusselt number is noted with Hartmann number and Prandtl number.Moreover, entropy generation and Bejan number increases with radiation parameter and fluid parameter.
