Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is investigated.The DarcyBrinkman model is used to characterize the fluid flow dynamics in porous materials.The analytical solutions are obtained for the unidirectional and completely developed flow.Based on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is solved.The eigenvalue problem is then solved by the spectral method.Finally,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing parameters.The results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the flow.Besides,the flow is the most unstable when the channel is vertically oriented.

Simulation of Variable Viscosity and Jeffrey Fluid Model for Blood Flow Through a Tapered Artery with a Stenosis

Non-Newtonian fluid model for blood flow through a tapered artery with a stenosis and variable viscosity by modeling blood as Jeffrey fluid has been studied in this paper. The Jeffrey fluid has two parameters, the relaxation time A1 and retardation time A2. The governing equations are simplified using the case of mild stenosis. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature profile, wall shear stress, shearing stress at the stenotsis throat and impedance of the artery are discussed. The results for Newtonian fluid are obtained as special case from this model.

BASIC EQUATIONS OF TURBULENT FLOW FOR VARIABLE DENSITY AND VARIABLE VISCOSITY NEWTONIAN FLUID IN OPEN CHANNEL

In this paper, using Navier-Stokes equations and Reynolds time-averaged rules, the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid have been presented, and the turbulent motional differential equations of variable density and variable viscosity Newtonian fluid in open channel have been further proposed. The concepts of the density turbulence stress and the viscosity turbulence stress have been firstly presented in the paper.

Nonlinear free thermal convection in a spherical shell:A variable viscosity model

In mantle convection models, the mantle viscosity is generally assumed constant or dependent on depth. In this paper, a laterally variable viscosity is introduced into mantle convection model in which the mantle viscosity consists of a constant background and latitude-dependent viscosity with small fluctuations. The features of toroidal field dependent on depth and Rayleigh number are discussed under two boundary conditions, i.e., the top rigid and bottom stress-free boundaries (R-F boundary for short) and both rigid ones (R-R boundary for short), respectively. The results show that the energy of toroidal field mainly concentrates in the middle and upper parts of a spherical shell, and the ratio of toroidal to total velocities amounts to only a few percents and hardly depends on Rayleigh number, while the convection patterns of toroidal field have been strongly affected by Rayleigh number. It is found that the convection patterns and velocities of toroidal field have obvious differences in latitudinal direction, which clearly reflects the effects of lateral mantle viscosity variations on the convection patterns. These preliminary results give us a possible hint to study some global tectonic phenomena, e.g. the asymmetry of the southern and northern hemispheres and the Earth's differential rotation.

Analytical Treatment of an Oldroyd 8-constant Fluid Between Coaxial Cylinders with Variable Viscosity

The flow of an Oldroyd 8-constant fluid between coaxial cylinders with variable viscosity is considered.The heat transfer analysis is also taken into account.An analytical solution of the non-linear problem is obtained usinghomotopy analysis method.The behavior of pertinent parameters is analyzed and depicted through graphs.

Extreme massive hydraulic fracturing in deep coalbed methane horizontal wells:A case study of the Linxing Block,eastern Ordos Basin,NW China

Deep coal seams show low permeability,low elastic modulus,high Poisson’s ratio,strong plasticity,high fracture initiation pressure,difficulty in fracture extension,and difficulty in proppants addition.We proposed the concept of large-scale stimulation by fracture network,balanced propagation and effective support of fracture network in fracturing design and developed the extreme massive hydraulic fracturing technique for deep coalbed methane(CBM)horizontal wells.This technique involves massive injection with high pumping rate+high-intensity proppant injection+perforation with equal apertures and limited flow+temporary plugging and diverting fractures+slick water with integrated variable viscosity+graded proppants with multiple sizes.The technique was applied in the pioneering test of a multi-stage fracturing horizontal well in deep CBM of Linxing Block,eastern margin of the Ordos Basin.The injection flow rate is 18 m^(3)/min,proppant intensity is 2.1 m^(3)/m,and fracturing fluid intensity is 16.5 m^(3)/m.After fracturing,a complex fracture network was formed,with an average fracture length of 205 m.The stimulated reservoir volume was 1987×10^(4)m^(3),and the peak gas production rate reached 6.0×10^(4)m^(3)/d,which achieved efficient development of deep CBM.

Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation

The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic（MHD） heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.

Numerical investigation of variable viscosities and thermal stratification effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of a chemical reaction

An analysis is presented to investigate the effects of variable viscosities and thermal stratification on the MHD mixed convective heat and mass transfer of a viscous, incompressible, and electrically conducting fluid past a porous wedge in the presence of a chemical reaction. The wall of the wedge is embedded in a uniform nonDarcian porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically with finite difference methods. Numerical calculations up to the thirdorder level of truncation are carried out for different values of dimensionless parameters. The results are presented graphically, and show that the flow field and other quantities of physical interest are significantly influenced by these parameters. The results are compared with those available in literature, and show excellent agreement.

Effect of variable liquid properties on peristaltic transport of Rabinowitsch liquid in convectively heated complaint porous channel

The present paper emphasizes the peristaltic mechanism of Rabinowitsch liquid in a complaint porous channel under the influence of variable liquid properties and convective heat transfer.The effect of inclination on the complaint channel walls has been taken into account.The viscosity of the liquid varies across the thickness of the complaint channel,whereas,thermal conductivity varies concerning temperature.The nonlinear governing equations are solved by using perturbation technique under the long wavelength and small Reynold’s number approximations.The expressions for axial velocity,temperature,the coefficient of heat transfer and streamlines are obtained and analyzed graphically.The above said physiological phenomena are investigated for a specific set of relevant parameters on dilatant,Newtonian and pseudoplastic fluid models.The results presented here shows that the presence of variable viscosity,porous parameter and slip parameter significantly affects the flow quantities of dilatant,Newtonian and pseudoplastic fluid models.The investigation further reveals that an increase in the value of variable viscosity and porous parameters enhances the occurrence of trapping phenomenon.Moreover,the size of trapped bolus can be eliminated with suitably adjusting the angle of inclination parameter.

Group solution for an unsteady non-Newtonian Hiemenz flow with variable fluid properties and suction/injection

The theoretic transformation group approach is applied to address the problem of unsteady boundary layer flow of a non-Newtonian fluid near a stagnation point with variable viscosity and thermal conductivity. The application of a two- parameter group method reduces the number of independent variables by two, and consequently the governing partial differential equations with the boundary conditions transformed into a system of ordinary differential equations with the appropriate corresponding conditions. Two systems of ordinary differential equations have been solved numerically using a fourth-order Runge-Kutta algorithm with a shooting technique. The effects of various parameters governing the problem are investigated.

Study on Periodic MHD Flow with Temperature Dependent Viscosity and Thermal Conductivity past an Isothermal Oscillating Cylinder

Temperature dependent viscosity and thermal conducting heat and mass transfer flow with chemical reaction and periodic magnetic field past an isothermal oscillating cylinder have been considered. The partial dimensionless equations governing the flow have been solved numerically by applying explicit finite difference method with the help Compaq visual 6.6a. The obtained outcome of this inquisition has been discussed for different values of well-known flow parameters with different time steps and oscillation angle. The effect of chemical reaction and periodic MHD parameters on the velocity field, temperature field and concentration field, skin-friction, Nusselt number and Sherwood number have been studied and results are presented by graphically. The novelty of the present problem is to study the streamlines by taking into account periodic magnetic field.

A Numerical Tackling on Sakiadis Flow with Thermal Radiation

Momentum and energy laminar boundary layers of an incompressible fluid with thermal radiation about a moving plate in a quiescent ambient fluid are investigated numerically. Also, it has been underlined that the analysis of the roles of both velocity and temperature gradient at infinity is of key relevance for our results.

A Clot Model Examination: with Impulsion of Nanoparticles under Influence of Variable Viscosity and Slip Effects

In this speculative analysis, our main focused is to address the neurotic condition that occurs due to accumulation of blood components on the wall of the artery that results in blood coagulation. Specifically, to perceive this phenomena clot model is considered. To discuss this analysis mathematical model is formed in the presence of the effective thermal conductivity and variable viscosity of base fluid. Appropriate slip conditions are employed to obtain the close form solutions of temperature and velocity profile. The graphical illustrations have been presented for the assessment of pressure rise, pressure gradient and velocity profile. The effects of several parameters on the flow quantities for theoretical observation are investigated. At the end, the results confirmed that the impulsion of copper and silver nanoparticles as drug agent enlarges the amplitude of the velocity and hence nanoparticles play an important role in engineering and biomedical applications such as drug delivery system.

Irreversibility analysis of unsteady couette flow with variable viscosity

This paper investigates numerically the inherent irreversibility in unsteady generalized Couette flow between two parallel plates with variable viscosity. The nonlinear governing equations are derived from the Navier-Stokes equations and solved numerically using a semi-discretization finite difference method together with the Runge-Kutta-Fehlberg integration scheme. The profiles of velocity and the temperature obtained are used to compute the entropy generation number, Bejan number, skin friction and Nusselt number. The effects of embedded parameters on entire flow structure are presented graphically and discussed quantitatively.

The effect of variable viscosity on the flow and heat transfer of a viscous Agwater and Cu-water nanofluids

A numerical study is carried out to study the effects of the temperature dependent viscosity on the flow and heat transfer of a nanofluid over a flat surface in the presence of viscous dissipation. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, and are solved numerically by the Keller-box method. The numerical results indicate that the effect of nanoparticle volume fraction is to increase the heat transfer and hence enhance the thermal boundary layer thickness. This is true even in the presence of variable viscosity and the viscous dissipation. Furthermore, the results obtained for heat transfer characteristics with nanoparticles reveal many interesting behaviors that warrant further study on the effects of the ＂nano-solid-particles＂.

Effects of thermal radiation on MHD viscous fluid flow and heat transfer over nonlinear shrinking porous sheet

This paper investigates the effects of thermal radiation on the magnetohy- drodynamic （MHD） flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent viscosity and the thermal conductivity are also assumed to vary as an inverse function and a linear function of the temperature, respectively. A generalized similarity transfor- mation is used to reduce the governing partial differential equations to their nonlinear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concern with the velocity and temperature profiles as well as the local skin-friction coefficient and the rate of the heat transfer at the porous sheet for different values of several physical parameters of interest.

Effects of groove on behavior of flow between hydro-viscous drive plates

The flow between a grooved and a flat plate was presented to investigate the effects of groove on the behavior of hydro-viscous drive. The flow was solved by using computational fluid dynamics (CFD) code, Fluent. Parameters related to the flow, such as velocity, pressure, temperature, axial force and viscous torque, are obtained. The results show that pressure at the upstream notch is negative, pressure at the downstream notch is positive and pressure along the film thickness is almost the same. Dynamic pressure peak decreases as groove depth or groove number increases, but increases as output rotary speed increases. Consequently, the groove depth is suggested to be around 0.4 mm. Both the groove itself and groove parameters (i.e. groove depth, groove number) have little effect on the flow temperature. Circumferential pressure gradient induced by the groove weakens the viscous torque on the grooved plate (driven plate) greatly. It has little change as the groove depth increases. However, it decreases dramatically as the groove number increases. The experiment results show that the trend of experimental temperature and pressure are the same with numerical results. And the output rotary speed also has relationship with input flow rate and flow temperature.

Variable viscosity effects on the flow of MHD hybrid nanofluid containing dust particles over a needle with Hall current——a Xue model exploration

This study scrutinizes the flow of engine oil-based suspended carbon nanotubes magnetohydrodynamics(MHD)hybrid nanofluid with dust particles over a thin moving needle following the Xue model.The analysis also incorporates the effects of variable viscosity with Hall current.For heat transfer analysis,the effects of the Cattaneo–Christov theory and heat generation/absorption with thermal slip are integrated into the temperature equation.The Tiwari–Das nanofluid model is used to develop the envisioned mathematical model.Using similarity transformation,the governing equations for the flow are translated into ordinary differential equations.The bvp4c method based on Runge–Kutta is used,along with a shooting approach.Graphs are used to examine and depict the consequences of significant parameters on involved profiles.The results revealed that the temperature of the fluid and boundary layer thickness is diminished as the solid volume fraction is raised.Also,with an enhancement in the variable viscosity parameter,the velocity distribution becomes more pronounced.The results are substantiated by assessing them with an available study.

Rheological Analysis of CNT Suspended Nanofluid with Variable Viscosity: Numerical Solution

In this article, we discuss the two-dimensional stagnation-point flow of carbon nanotubes towards a stretching sheet with water as the base fluid under the influence temperature dependent viscosity. Similarity transformations are used to simplify the governing boundary layer equations for nanofluid. This is the first article on the stagnation point flow of CNTs over a stretching sheet with variable viscosity. A well known Reynold's model of viscosity is used. Single wall CNTs are used with water as a base fluid. The resulting nonlinear coupled equations with the relevant boundary conditions are solved numerically using shooting method. The influence of the flow parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are explored and presented in forms of graphs and interpreted physically.

Inclined magnetic field and variable viscosity effects on bioconvection of Casson nanofluid slip flow over non linearly stretching sheet

In pursuit of improved thermal transportation,the slip flow of Casson nanofluid is considered in the existence of an inclined magnetic field and radiative heat flux flow over a nonlinear stretching sheet.The viscosity of the fluid is considered as a function of temperature along with the convective thermal boundary condition.Numerical solutions are obtained via Runge-Kutta along with the shooting technique method for the chosen boundary values problem.To see the physical insights of the problem,some graphs are plotted for various flow and embedded parameters on temperature function,micro-organism distribution,velocity,and volume fraction of nanoparticles.A decline is observed in the velocity and the temperature for Casson fluid.Thermophoresis and Brownian motion incremented the temperature profile.It is also found that thermal transportation can be enhanced in the presence of nanoparticles and the bioconvection of microorganisms.Present results are useful in the various sectors of engineering and for heat exchangers working in various technological processors.The main findings of the problem are validated and compared with those in the existing literature as a limiting case.