In the current critique, we deliberate the blood flow through narrowing vein with a steno- sis in the manifestation of heat and mass transmission. The non-Newtonian flora of blood in small veins are examined mathemati...In the current critique, we deliberate the blood flow through narrowing vein with a steno- sis in the manifestation of heat and mass transmission. The non-Newtonian flora of blood in small veins are examined mathematically by demonstrating the blood as Carreau fluid. The illustration for the blood flow is debated through an axially irregular but outward regular stenosis. Regularity in the dissemination of the fortification clipping stress and resistive impedance and their evolution with the emerging stenosis is a new significant feature of our investigation. Analytical solutions have been appraised for ＂velocity, tem- perature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat＂. The graphical consequences of different types of tapering arteries （i.e. ＂converging tapering, diverging tapering, non-tapered artery＂） have been studied for dissimilar constraints of attention. Rivulet shapes have been strategized for different parameters at the culmination of the article.展开更多
An analysis has been achieved to study the natural convection of a non-Newtonian fluid （namely a Carreau fluid） in a vertical channel with rhythmically contracting walls. The Navier-Stokes and the energy equations a...An analysis has been achieved to study the natural convection of a non-Newtonian fluid （namely a Carreau fluid） in a vertical channel with rhythmically contracting walls. The Navier-Stokes and the energy equations are reduced to a system of non- linear PDE by using the long wavelength approximation. The optimal homotopy analysis method （OHAM） is introduced to obtain the exact solutions for velocity and temperature fields. The convergence of the obtained OHAM solution is discussed explicitly. Numerical calculations are carried out for the pressure rise and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail.展开更多
This research is concerned with the mathematical modeling and analysis of blood flow in a tapered artery with stenosis. The analysis has been carried out in the presence of heat and mass transfer. Constitutive equatio...This research is concerned with the mathematical modeling and analysis of blood flow in a tapered artery with stenosis. The analysis has been carried out in the presence of heat and mass transfer. Constitutive equation of Carreau fluid has been invoked in the mathematical formulation. The representation of blood flow is considered through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall, shearing stress and resistive impectartce and their growth with the developirtg stenosis is given due attention. Solutions have been obtained for the velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. Graphical illustrations associated with the tapered arteries namely converging, diverging and non-tapered arteries are examined for different parameters of interest. Streamlines have been plotted and discussed.展开更多
The current article communicates a numerical investigation on laminar flow of dissipative generalized Newtonian Carreau nanofluid flowing through vertical conduit with converging and diverging plane walls.Thermal and ...The current article communicates a numerical investigation on laminar flow of dissipative generalized Newtonian Carreau nanofluid flowing through vertical conduit with converging and diverging plane walls.Thermal and concentration characteristics due to enthalpy change,activation energy,and non-linear thermal radiation have been examined in the presence of buoyancy forces.The channel walls for both temperature and volumetric fraction are assumed to be isothermal.The instability mechanism of nanofluids is reported using a two-phase nanofluid model,which works reasonably well for nanoparticle concentrations below a certain threshold.A Jeffery-Hamel(J-H)flow model is developed by assuming an incompressible purely radial flow of Carreau nanofluids with heat and mass transportation.Using the suitable non-dimensional variables,the resulting nonlinear partial differential equations are turned into a system of ordinary differential equations.The modified governing equations are then numerically solved using the built-in boundary value problem solver bvp4c,on the template form of commercial software MATLAB.The impacts of material,geometrical and thermophysical parameters governing the J-H problem are discussed and illustrated.Results indicate that higher buoyance forces incline the velocity profiles in converging enclosure,while a slight reduction is perceived in opposing forces.A significant decrease of wall heat transmission is reflected for larger values of activation energy and radiation parameter.For endorsing this communication,a comparison analysis is established with existing research and noticed a remarkable agreement.Practically,the flow inside converging and diverging channels are deployed in nuclear reactors that use plate-type nuclear energies,high heat-flux condensed heat exchangers,high-performance micro-electronic cooling systems,jets,rockets nozzles,and jet propulsion inlet.展开更多
The study of peristaltic flow of a Carreau fluid in a non-uniform tube under the con- sideration of long wavelength is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave ...The study of peristaltic flow of a Carreau fluid in a non-uniform tube under the con- sideration of long wavelength is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave e. Numerical integration has been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated through graphs.展开更多
A sophisticated theoretical and mathematical model is proposed.It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and th...A sophisticated theoretical and mathematical model is proposed.It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux,thermal radiation,and viscous dissipation.Despite the fact that some properties of the fluid do not depend on the temperature,the fluid thermal conductivity is assumed to depend on the temperature.Based on accelerating the fluid elements,some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena.The contribution in this study is that a similar solution is obtained,in spite of the high nonlinearity of the Carreau model,especially,with the heat flux,variable conductivity,and viscous dissipation phenomena.Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number.Likewise,the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter.Finally,the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results.展开更多
The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated.Buongiornio nanoliquid model consists of thermophoresis and Bro...The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated.Buongiornio nanoliquid model consists of thermophoresis and Brownian movement aspects is opted for analysis.Energy expression is modeled subject to thermal radiation and viscous dissipation phenomenon.Concentration by zero mass flux condition is implemented.Consideration of chemical reaction and activation energy characterizes the mass transfer mechanism.Total entropy generation rate and Bejan number is formulated.The utilization of transformation variables reduces the PDEs into non-linear ODEs.The obtained nonlinear complex problems are computed numerically through Shooting scheme.The impact of involved variables like local Weissenberg number,magnetic parameter,thermal radiation parameter,Brownian motion parameter,thermophoresis parameter,buoyancy ratio parameter,mixed convection parameter,Prandtl parameter,Eckert number,Schmidt number,non-dimensional activation energy parameter,chemical reaction parameter,Brinkman number,dimensionless concentration ratio variable,diffusive variable and dimensionless temperature ratio variable on velocity,temperature,nanoparticles concentration,entropy generation,Bejan number,surface drag force and heat transfer rate are examined through graphs and tables.展开更多
The article investigates the influences of a variable thermal conductivity and wall slip on a peristaltic motion of Carreau nanofluid. The model is concerned with heat and mass transfer inside asymmetric channel. The ...The article investigates the influences of a variable thermal conductivity and wall slip on a peristaltic motion of Carreau nanofluid. The model is concerned with heat and mass transfer inside asymmetric channel. The blood is considered as the base Carreau non-Newtonian fluid and gold (Au) as nanoparticles stressed upon. The Fronchiener effect of the non-Darcian medium is taken in consideration. The system is stressed upon a strong magnetic field and the Hall currents are completed. The problem is modulated mathematically by a system of non-linear partial differential equations which describe the fluid velocity, temperature and concentration. The system is reformulated under the approximation of long wavelength and low Reynolds number. It is solved on using multi-step differential transform method (Ms-DTM) as a semi-analytical method. A gold nanoparticle has increased the temperature distribution which is of great importance in destroying the cancer cells.展开更多
For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, （bi）linear/（bi）linear and （bi）linear/constant element, is presented. The pressure projection stab...For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, （bi）linear/（bi）linear and （bi）linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r（Ω） norm and that of the pressure in the L r＇ （Ω） （1/r ＋ 1/r＇ = 1）. The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.展开更多
In this work, the peristaltic motion of a nano non-Newtonian fluid which obeys Carreau model through a porous medium inside an asymmetric channel is investigated. The hall current effects with Joule heating and viscou...In this work, the peristaltic motion of a nano non-Newtonian fluid which obeys Carreau model through a porous medium inside an asymmetric channel is investigated. The hall current effects with Joule heating and viscous dissipation are considered. The problem is modulated mathematically by a set of nonlinear partial differential equations which describe the conservation of mass, momentum, energy and concentration of nanoparticles. The non-dimensional form of these equations is simplified under the assumption of long wavelength and low Reynolds number, and then resulting equations of coupled nonlinear differential equations are tackled numerically with appropriate boundary conditions. Graphical results are presented for dimensionless velocity, temperature, concentration and pressure gradient in order to illustrate the variations of various parameters of this problem on these obtained solutions.展开更多
This paper constructs a mathematical model for blood flow through an artery with mild stenosis. Constitutive equations for Carreau fluid are employed in the mathematical modeling. Analysis has been carried out in the ...This paper constructs a mathematical model for blood flow through an artery with mild stenosis. Constitutive equations for Carreau fluid are employed in the mathematical modeling. Analysis has been carried out in the presence of constant magnetic field. Symmetric and asymmetric shapes of stenosis are taken. Governing flow model is computed for the series solution. Whe flow quantities of interest, for instance, axial velocity, pressure gradient, pressure drop, impedance and shear stress at the walls of stenotic artery are described for various pertinent parameters entering into the problem.展开更多
The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model ha...The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10^-3 ml/h in the human ductus efferentes when We = 0.5 and e is near by 0.25.展开更多
This examination emphasizes the analysis of thermal transmission of Carreau fluid flow on a permeable sensor surface equipped with radiation,Joule heating,an internal heat source,and a magnetic field.With the above ef...This examination emphasizes the analysis of thermal transmission of Carreau fluid flow on a permeable sensor surface equipped with radiation,Joule heating,an internal heat source,and a magnetic field.With the above effects and assumptions,the equations that administer the flow are formulated.A configured system of equations is productively reduced to a system of ordinary differential equations.The reduced system is then dealt with using the Runge–Kutta-Fehlberg fourth–fifth order tool equipped by the shooting technique.Derived numerical solutions are utilized to plot graphs and tables.The conclusion of the study outlines some important findings such as the power law index,the thermal radiation parameter and the heat source parameter enhance the thermal panel whereas the Weissenberg number deescalates the same.The power law index and permeable velocity decrease the velocity panel significantly.Diagrammatic representation of streamlines of the flow has been given to strengthen the study.A detailed description has been produced about the results obtained in the study.展开更多
Present communication is devoted to analyze thermal characteristics of Carreau liquid flowing on variably thickened non-uniformly rotating disk.Mathematical formulation is constructed in view of complex coupled partia...Present communication is devoted to analyze thermal characteristics of Carreau liquid flowing on variably thickened non-uniformly rotating disk.Mathematical formulation is constructed in view of complex coupled partial differential system.Afterwards,boundary layer approach is executed for comprehensive examination of under consideration phenomenon with in boundary layer region.Karman’s transformation is capitalized to convert the attained PDE’s into ordinary differential equations system.Solution of attained ODE’s system is solved numerically by implementing Keller-Box scheme.Influence of protuberant involved parameters on momentum and thermal distributions is illustrated through sketches.In addition,impact of flow concerning parameters on wall shear stress and thermal flux is also evaluated.The assurance of present finding is done by making agreement with published results and by restricting considered problem to Newtonian case.Here,we observed that radially and tangentially directed wall drag lessen with growing magnitude of power law exponent index.Moreover,the consequence of disk thickness parameter grows stresses along radial direction whereas opposite behavior is depicted in case of tangentially directed friction and heat flux factors.展开更多
The pulsatile flow of blood in a tapered narrow artery with overlapping time-dependent stenosis is mathematically analyzed, modeling blood as Caxreau fluid. Perturbation method is employed for solving the resulting no...The pulsatile flow of blood in a tapered narrow artery with overlapping time-dependent stenosis is mathematically analyzed, modeling blood as Caxreau fluid. Perturbation method is employed for solving the resulting nonlinear system of equations along with the appropriate boundary conditions. The analytic solutions to the pressure gradient, velocity distribution, flow rate, wall shear stress and longitudinal impedance to flow axe obtained in the asymptotic form. The variation of the aforesaid flow quantities with respect to various physical parameters such as maximum depth of the stenosis, angle of tapering of the artery, power law index, Reynolds number, pulsatile amplitude of the flow and Weissenberg number is investigated. It is found that the wall shear stress and longitudinal impedance to flow increase with the increase of the angle of tapering of the artery, the maximum depth of the stenosis and pulsatile Reynolds number and these decrease with the increase of the amplitude of the flow, power law index and Weis- senberg number. The mean velocity of blood decreases significantly with the increase of the artery radius, maximum depth of the stenosis, angle of tapering of the artery.展开更多
The effect of permeable walls and magnetic field on the peristaltic flow of a Carreau fluid in a tapered asymmetric channel is studied. The tapered asymmetric channel is normally created due to the intra-uterine fluid...The effect of permeable walls and magnetic field on the peristaltic flow of a Carreau fluid in a tapered asymmetric channel is studied. The tapered asymmetric channel is normally created due to the intra-uterine fluid flow induced by myometrial contractions and it was simulated by asymmetric peristaltic fluid flow in a two-dimensional infinite non-uniform channel. The analysis has been performed under long wavelength and low- Reynolds number assumptions to linearize the governing flow equations. A series solution in respect of a small Weissenberg number is obtained for the stream function, axial pressure gradient and shear stress. Time average of pressure rise and frictional force on the upper wall has also been computed using numerical integration. The results have been presented graphically for the various interested physical parameters. It is observed that for Carreau fluids the peristalsis works as a pump against a greater pressure rise compared with a Newtonian fluid, while there exists no significant difference in free pumping flux for Newtonian and Carreau fluids in the tapered asymmetric channel.展开更多
文摘In the current critique, we deliberate the blood flow through narrowing vein with a steno- sis in the manifestation of heat and mass transmission. The non-Newtonian flora of blood in small veins are examined mathematically by demonstrating the blood as Carreau fluid. The illustration for the blood flow is debated through an axially irregular but outward regular stenosis. Regularity in the dissemination of the fortification clipping stress and resistive impedance and their evolution with the emerging stenosis is a new significant feature of our investigation. Analytical solutions have been appraised for ＂velocity, tem- perature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat＂. The graphical consequences of different types of tapering arteries （i.e. ＂converging tapering, diverging tapering, non-tapered artery＂） have been studied for dissimilar constraints of attention. Rivulet shapes have been strategized for different parameters at the culmination of the article.
文摘An analysis has been achieved to study the natural convection of a non-Newtonian fluid （namely a Carreau fluid） in a vertical channel with rhythmically contracting walls. The Navier-Stokes and the energy equations are reduced to a system of non- linear PDE by using the long wavelength approximation. The optimal homotopy analysis method （OHAM） is introduced to obtain the exact solutions for velocity and temperature fields. The convergence of the obtained OHAM solution is discussed explicitly. Numerical calculations are carried out for the pressure rise and the features of the flow and temperature characteristics are analyzed by plotting graphs and discussed in detail.
文摘This research is concerned with the mathematical modeling and analysis of blood flow in a tapered artery with stenosis. The analysis has been carried out in the presence of heat and mass transfer. Constitutive equation of Carreau fluid has been invoked in the mathematical formulation. The representation of blood flow is considered through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall, shearing stress and resistive impectartce and their growth with the developirtg stenosis is given due attention. Solutions have been obtained for the velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat. Graphical illustrations associated with the tapered arteries namely converging, diverging and non-tapered arteries are examined for different parameters of interest. Streamlines have been plotted and discussed.
基金the Deanship of Scientific Research at King Khalid University for funding this work through the General Research Project under grant number(R.G.P1/181/43).
文摘The current article communicates a numerical investigation on laminar flow of dissipative generalized Newtonian Carreau nanofluid flowing through vertical conduit with converging and diverging plane walls.Thermal and concentration characteristics due to enthalpy change,activation energy,and non-linear thermal radiation have been examined in the presence of buoyancy forces.The channel walls for both temperature and volumetric fraction are assumed to be isothermal.The instability mechanism of nanofluids is reported using a two-phase nanofluid model,which works reasonably well for nanoparticle concentrations below a certain threshold.A Jeffery-Hamel(J-H)flow model is developed by assuming an incompressible purely radial flow of Carreau nanofluids with heat and mass transportation.Using the suitable non-dimensional variables,the resulting nonlinear partial differential equations are turned into a system of ordinary differential equations.The modified governing equations are then numerically solved using the built-in boundary value problem solver bvp4c,on the template form of commercial software MATLAB.The impacts of material,geometrical and thermophysical parameters governing the J-H problem are discussed and illustrated.Results indicate that higher buoyance forces incline the velocity profiles in converging enclosure,while a slight reduction is perceived in opposing forces.A significant decrease of wall heat transmission is reflected for larger values of activation energy and radiation parameter.For endorsing this communication,a comparison analysis is established with existing research and noticed a remarkable agreement.Practically,the flow inside converging and diverging channels are deployed in nuclear reactors that use plate-type nuclear energies,high heat-flux condensed heat exchangers,high-performance micro-electronic cooling systems,jets,rockets nozzles,and jet propulsion inlet.
文摘The study of peristaltic flow of a Carreau fluid in a non-uniform tube under the con- sideration of long wavelength is presented. The flow is investigated in a wave frame of reference moving with velocity of the wave e. Numerical integration has been used to obtain the graphical results for pressure rise and frictional forces. The effects of various emerging parameters are investigated through graphs.
文摘A sophisticated theoretical and mathematical model is proposed.It is verified that this model can estimate and monitor the detailed behavior for the steady Carreau fluid flow past a nonlinear stretching surface and the predicted phenomena due to the presence of heat flux,thermal radiation,and viscous dissipation.Despite the fact that some properties of the fluid do not depend on the temperature,the fluid thermal conductivity is assumed to depend on the temperature.Based on accelerating the fluid elements,some of the kinetic energy for the fluid can be turned to the internal heating energy in the form of viscous dissipation phenomena.The contribution in this study is that a similar solution is obtained,in spite of the high nonlinearity of the Carreau model,especially,with the heat flux,variable conductivity,and viscous dissipation phenomena.Some of the major significant findings of this study can be observed from the reduction in the fluid velocity with enhancing the Weissenberg number.Likewise,the increase in the sheet temperature is noted with increasing the Eckert number while the reverse behavior is observed for increasing both the radiation parameter and the conductivity parameter.Finally,the accuracy and trust in the proposed numerical method are validated after benchmarking for our data onto the earlier results.
文摘The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated.Buongiornio nanoliquid model consists of thermophoresis and Brownian movement aspects is opted for analysis.Energy expression is modeled subject to thermal radiation and viscous dissipation phenomenon.Concentration by zero mass flux condition is implemented.Consideration of chemical reaction and activation energy characterizes the mass transfer mechanism.Total entropy generation rate and Bejan number is formulated.The utilization of transformation variables reduces the PDEs into non-linear ODEs.The obtained nonlinear complex problems are computed numerically through Shooting scheme.The impact of involved variables like local Weissenberg number,magnetic parameter,thermal radiation parameter,Brownian motion parameter,thermophoresis parameter,buoyancy ratio parameter,mixed convection parameter,Prandtl parameter,Eckert number,Schmidt number,non-dimensional activation energy parameter,chemical reaction parameter,Brinkman number,dimensionless concentration ratio variable,diffusive variable and dimensionless temperature ratio variable on velocity,temperature,nanoparticles concentration,entropy generation,Bejan number,surface drag force and heat transfer rate are examined through graphs and tables.
文摘The article investigates the influences of a variable thermal conductivity and wall slip on a peristaltic motion of Carreau nanofluid. The model is concerned with heat and mass transfer inside asymmetric channel. The blood is considered as the base Carreau non-Newtonian fluid and gold (Au) as nanoparticles stressed upon. The Fronchiener effect of the non-Darcian medium is taken in consideration. The system is stressed upon a strong magnetic field and the Hall currents are completed. The problem is modulated mathematically by a system of non-linear partial differential equations which describe the fluid velocity, temperature and concentration. The system is reformulated under the approximation of long wavelength and low Reynolds number. It is solved on using multi-step differential transform method (Ms-DTM) as a semi-analytical method. A gold nanoparticle has increased the temperature distribution which is of great importance in destroying the cancer cells.
基金Project supported by the Key Technology Research and Development Program of Sichuan Province of China(No.05GG006-006-2)
文摘For a generalized quasi-Newtonian flow, a new stabilized method focused on the low-order velocity-pressure pairs, （bi）linear/（bi）linear and （bi）linear/constant element, is presented. The pressure projection stabilized method is extended from Stokes problems to quasi-Newtonian flow problems. The theoretical framework developed here yields an estimate bound, which measures error in the approximate velocity in the W 1,r（Ω） norm and that of the pressure in the L r＇ （Ω） （1/r ＋ 1/r＇ = 1）. The power law model and the Carreau model are special ones of the quasi-Newtonian flow problem discussed in this paper. Moreover, a residual-based posterior bound is given. Numerical experiments are presented to confirm the theoretical results.
文摘In this work, the peristaltic motion of a nano non-Newtonian fluid which obeys Carreau model through a porous medium inside an asymmetric channel is investigated. The hall current effects with Joule heating and viscous dissipation are considered. The problem is modulated mathematically by a set of nonlinear partial differential equations which describe the conservation of mass, momentum, energy and concentration of nanoparticles. The non-dimensional form of these equations is simplified under the assumption of long wavelength and low Reynolds number, and then resulting equations of coupled nonlinear differential equations are tackled numerically with appropriate boundary conditions. Graphical results are presented for dimensionless velocity, temperature, concentration and pressure gradient in order to illustrate the variations of various parameters of this problem on these obtained solutions.
文摘This paper constructs a mathematical model for blood flow through an artery with mild stenosis. Constitutive equations for Carreau fluid are employed in the mathematical modeling. Analysis has been carried out in the presence of constant magnetic field. Symmetric and asymmetric shapes of stenosis are taken. Governing flow model is computed for the series solution. Whe flow quantities of interest, for instance, axial velocity, pressure gradient, pressure drop, impedance and shear stress at the walls of stenotic artery are described for various pertinent parameters entering into the problem.
文摘The aim of this study is to explain theoretically the role of ciliary motion on the transport of epididymal fluid through the ductus efferentes of the male reproductive track. For this purpose, a mathematical model has been developed for the flow of a non-Newtonian fluid in an axisymmetric tube due to metachronal wave of cilia motion for the more realistic consequences. Carreau viscous fluid model is considered to see the rheological effects on the pumping characteristics of the flow. Regular perturbation method has been employed to obtain the analytical expressions for the stream function, the velocity field and a relation between the pressure difference and the volume flow rate. It is found that the volume flow rate is influenced significantly by Weissenberg number We and the cilia length parameter ε. The computational results are presented graphically to see the effects of various physical parameters. Finally, the analysis is applied and compared with the observed value of the flow rate of spermatic fluid in the ductus efferentes of the male reproductive track. The volume flow rate is reported closed to the estimated value 6 × 10^-3 ml/h in the human ductus efferentes when We = 0.5 and e is near by 0.25.
基金Department of Science and Technology,Government of India under DST-FIST Program(Ref No.SR/FST/MS-I/2018-2023)for supporting the Department of Mathematics,Kuvempu University,Shankaraghatta。
文摘This examination emphasizes the analysis of thermal transmission of Carreau fluid flow on a permeable sensor surface equipped with radiation,Joule heating,an internal heat source,and a magnetic field.With the above effects and assumptions,the equations that administer the flow are formulated.A configured system of equations is productively reduced to a system of ordinary differential equations.The reduced system is then dealt with using the Runge–Kutta-Fehlberg fourth–fifth order tool equipped by the shooting technique.Derived numerical solutions are utilized to plot graphs and tables.The conclusion of the study outlines some important findings such as the power law index,the thermal radiation parameter and the heat source parameter enhance the thermal panel whereas the Weissenberg number deescalates the same.The power law index and permeable velocity decrease the velocity panel significantly.Diagrammatic representation of streamlines of the flow has been given to strengthen the study.A detailed description has been produced about the results obtained in the study.
文摘Present communication is devoted to analyze thermal characteristics of Carreau liquid flowing on variably thickened non-uniformly rotating disk.Mathematical formulation is constructed in view of complex coupled partial differential system.Afterwards,boundary layer approach is executed for comprehensive examination of under consideration phenomenon with in boundary layer region.Karman’s transformation is capitalized to convert the attained PDE’s into ordinary differential equations system.Solution of attained ODE’s system is solved numerically by implementing Keller-Box scheme.Influence of protuberant involved parameters on momentum and thermal distributions is illustrated through sketches.In addition,impact of flow concerning parameters on wall shear stress and thermal flux is also evaluated.The assurance of present finding is done by making agreement with published results and by restricting considered problem to Newtonian case.Here,we observed that radially and tangentially directed wall drag lessen with growing magnitude of power law exponent index.Moreover,the consequence of disk thickness parameter grows stresses along radial direction whereas opposite behavior is depicted in case of tangentially directed friction and heat flux factors.
文摘The pulsatile flow of blood in a tapered narrow artery with overlapping time-dependent stenosis is mathematically analyzed, modeling blood as Caxreau fluid. Perturbation method is employed for solving the resulting nonlinear system of equations along with the appropriate boundary conditions. The analytic solutions to the pressure gradient, velocity distribution, flow rate, wall shear stress and longitudinal impedance to flow axe obtained in the asymptotic form. The variation of the aforesaid flow quantities with respect to various physical parameters such as maximum depth of the stenosis, angle of tapering of the artery, power law index, Reynolds number, pulsatile amplitude of the flow and Weissenberg number is investigated. It is found that the wall shear stress and longitudinal impedance to flow increase with the increase of the angle of tapering of the artery, the maximum depth of the stenosis and pulsatile Reynolds number and these decrease with the increase of the amplitude of the flow, power law index and Weis- senberg number. The mean velocity of blood decreases significantly with the increase of the artery radius, maximum depth of the stenosis, angle of tapering of the artery.
文摘The effect of permeable walls and magnetic field on the peristaltic flow of a Carreau fluid in a tapered asymmetric channel is studied. The tapered asymmetric channel is normally created due to the intra-uterine fluid flow induced by myometrial contractions and it was simulated by asymmetric peristaltic fluid flow in a two-dimensional infinite non-uniform channel. The analysis has been performed under long wavelength and low- Reynolds number assumptions to linearize the governing flow equations. A series solution in respect of a small Weissenberg number is obtained for the stream function, axial pressure gradient and shear stress. Time average of pressure rise and frictional force on the upper wall has also been computed using numerical integration. The results have been presented graphically for the various interested physical parameters. It is observed that for Carreau fluids the peristalsis works as a pump against a greater pressure rise compared with a Newtonian fluid, while there exists no significant difference in free pumping flux for Newtonian and Carreau fluids in the tapered asymmetric channel.
