Variable Viscosity Parameter Research Articles

MHD Williamson Nanofluid Flow over a Slender Elastic Sheet of Irregular Thickness in the Presence of Bioconvection.

Bioconvection phenomena for MHD Williamson nanofluid flow over an extending sheet of irregular thickness are investigated theoretically, and non-uniform viscosity and thermal conductivity depending on temperature are taken into account. The magnetic field of uniform strength creates a magnetohydrodynamics effect. The basic formulation of the model developed in partial differential equations which are later transmuted into ordinary differential equations by employing similarity variables. To elucidate the influences of controlling parameters on dependent quantities of physical significance, a computational procedure based on the Runge–Kutta method along shooting technique is coded in MATLAB platform. This is a widely used procedure for the solution of such problems because it is efficient with fifth-order accuracy and cost-effectiveness. The enumeration of the results reveals that Williamson fluid parameter , variable viscosity parameter and wall thickness parameter impart reciprocally decreasing effect on fluid velocity whereas these parameters directly enhance the fluid temperature. The fluid temperature is also improved with Brownian motion parameter and thermophoresis parameter . The boosted value of Brownian motion and Lewis number reduce the concentration of nanoparticles. The higher inputs of Peclet number and bioconvection Lewis number decline the bioconvection distribution. The velocity of non-Newtonian (Williamson nanofluid) is less than the viscous nanofluid but temperature behaves oppositely.

RETRACTED: Unsteady flow of three-dimensional Maxwell nanofluid with variables properties over a stretching surface

The present article focuses on the time-dependent three-dimensional Maxwell fluid flow with temperature-dependent fluid properties along the stretching sheet. The heat and mass transfer analysis are presented in the occurrence of activation energy, convective boundary condition, and non-uniform heat source/sink effect. The flow model is converted into a system of coupled ODEs with the help of a similarity transformation. The numerical built-in technique Bvp4c is employed to solve the obtained coupled ODEs. The graphical outcomes are obtained against the various parameters and discussed. It is seen from the graphs that fluid velocity diminishes for stronger values of relaxation parameter and shows an opposite trend for the variable viscosity parameter. Moreover, it is noted from the tabulated data that the heat and mass transfer rate reduces for the stronger values of unsteadiness and the variable viscosity parameter.

Numerical Solution of Transient Fe3O4-EG Nanofluid Flow past Couette Channel Associated with Radiation

The aim of the present paper is to analyze the transient Couette nanofluid flow of ethylene glycol(EG)-Ferrous oxide(Fe3O4) between two parallel plates in the presence of thermal radiation. Tiwari and Das nanofluid model is assumed to frame the governing equations. The novelty of the study is combining the effects of thermal radiation and Couette flow with pulsative pressure gradient. It is important because of its applications in the lubricant technology and advanced energy conversion systems operated at high temperature. The effects of dimensionless quantities such as radiation parameter(Rd=0.1 – 0.5), Biot number(Bi=1 4), nanoparticle volume fraction(), pressure gradient(A=1 3), amplitude pulse() stretching parameter() and viscosity variation parameter() are explored graphically. The main conclusion that can be drawn from the results is that high velocity region of steady state is strengthened near the upper plate with the growth in stretching parameter rather thermal radiation. The temperature near the upper plate enhances with thermal radiation. A vortex is formed in the upper half region of Couette channel with the increase in the phase angle, amplitude and pressure gradient. The temperature in the upper region of Couette channel, is significantly enhanced by the volume fraction of nanoparticles.

Two Dimensional Biomagnetic Fluid Flow and Heat Transfer over a Nonlinear Stretching Sheet with Temperature Dependent Viscosity

This investigated the flow and heat transfer of two dimensional biomagnetic fluid (blood) flow over a non-linear stretching sheet in the presence of magnetic dipole. It is assumed that the magnetic field is sufficiently strong enough to saturate the ferrofluid and variation of magnetization with temperature can be approximated by a linear function of temperature difference. The fluid viscosity is assumed to vary as an inverse linear function of the temperature. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformation. Numerical solutions are obtained by using bvp4c function technique in MATLAB software. The acquired results are shown graphically and were examined for several values of the dimensionless parameters. It is observed that for different values of ferromagnetic interaction parameter and variable viscosity parameter, the velocity distribution decreases while temperature distribution increases. The magnitude of skin friction coefficient and the rate of heat transfer decrease with the increasing values of radiation parameter and Prandtl number. The results are also compared for specific values of the parameters with others documented in literature.

Numerical analysis of multiphase flow of couple stress fluid thermally effected by moving surface

The study of multiphase flows gained much importance because of its extensive applications in nature and industry. These flows possess two or more thermodynamic phases, for example, one component phase (e.g., water vapors and water flow) or several components phase (e.g., water and oil flow). The most common example of multiphase flow in the context of the oil industry is petroleum. Further blood flow, porous structures, fluidized bed, bubbly flow in nuclear reactors, and fiber suspension in the paper industry are some significant examples of multiphase flows. In this paper, we considered the Couette flow of non-Newtonian (couple stress) fluid with variable magnetic field and thermal conductivity effects between parallel walls of the channel. The upper wall of the channel is in constant motion while the lower wall is in a fixed position. The variable viscosity effects with the suspension of hafnium particles are also discussed by taking Vogel’s viscosity case. The shooting method based on the R–K method is applied to obtain the numerical solution of the current problem. A comparison between Newtonian and non-Newtonian fluids is presented by sketching graphs. The variations in flow and temperature of fluid against various involved factors, including variable viscosity, wall temperature, thermal radiations, variable magnetic field, and thermal conductivity are sketched and also physically described. It is observed that variable viscosity parameter elevated both velocity and temperature profiles while wall temperature parameter decelerated both fields. Further, noticed that the variable thermal conductivity and variable magnetic field impede the velocity of the fluid and also retarded the temperature field. Our attempt is not just useful to investigate the mechanical and industrial multiphase flows but also delivers important results to fill the gap in the existing literature.

Effects of Temperature Dependent Viscosity and Thermal Conductivity of a Micropolar Fluid over a Stretching Surface with Radiation

The effects of temperature dependent viscosity and thermal conductivity of a micropolar fluid over a continuous moving stretching surface with radiation is examined. The micropolar model due to Eringen is used to describe the working fluid. The partial differentia equations governing problem under consideration have been transformed into a system of non linear differential equations by the similarity transformations and then solved numerically using shooting technique. Numerical results are carried out for various dimensionless parameters of the problem especially variable viscosity parameter, thermal conductivity parameter, micro-rotation parameter along with the Prandtl number. The results are presented graphically for velocity distribution, temperature distribution and micropolardistributions for various values of non-dimensional parameters. It is found that the effects of the parameters representing variable property of viscosity and thermal conductivity aresignificant

Computational analysis of the unsteady 3D chemically reacting MHD flow with the properties of temperature dependent transpose suspended Maxwell nanofluid

The current research explores an unsteady three-dimensional Maxwell nanofluid flow with variable viscosity and thermal conductivity through a stretching surface. The influence of Joule heating, heat generation/absorption, and chemical reaction are also incorporated in current investigation. By the utilization of suitable transformation, the flow model is transformed into coupled ordinary differential equations. The numerical solution of the coupled ODEs is adopted by the usage of Bvp4c built-in code in MATLAB software. The graphical findings are manipulated to present the features of heat and mass transfer for the different parameters. It is observed form the graphical description that the velocity of fluid declines for stronger estimation of Deborah number, because it provides resistance to fluid motion. Further, enhancement is arisen in the velocity of fluid by the increment of the variable viscosity parameter. It is examined from the tabulated data, that the Nusselt and Shewrood number displays reducing behavior for the unsteadiness parameter. Moreover, due to higher estimation of variable thermal conductivity parameter the heat transfer rate declines consequently.

An assessment of the mathematical model for estimating of entropy optimized viscous fluid flow towards a rotating cone surface

Entropy optimization in convective viscous fluids flow due to a rotating cone is explored. Heat expression with heat source/sink and dissipation is considered. Irreversibility with binary chemical reaction is also deliberated. Nonlinear system is reduced to ODEs by suitable variables. Newton built in shooting procedure is adopted for numerical solution. Salient features velocity filed, Bejan number, entropy rate, concentration and temperature are deliberated. Numerical outcomes for velocity gradient and mass and heat transfer rates are displayed through tables. Assessments between the current and previous published outcomes are in an excellent agreement. It is noted that velocity and temperature show contrasting behavior for larger variable viscosity parameter. Entropy rate and Bejan number have reverse effect against viscosity variable. For rising values of thermal conductivity variable both Bejan number and entropy optimization have similar effect.

Comparative analysis of Yamada-Ota and Xue models for hybrid nanofluid flow amid two concentric spinning disks with variable thermophysical characteristics

The surprising features of carbon nanotubes such as featherweight, mechanical permanence, outstanding electrical and thermal conductivities, and physicochemical aptness make them impeccable material for electrochemical contraptions. Having such astounding physiognomies in mind our purpose in this study is to make a comparison of the performance of Yamada-Ota and Xue models for a nanofluid flow amidst two rotating disks in a spongy medium. The majority of nanofluid flow models in the available literature considered constant thermal conductivity and viscosity. Nevertheless, here the whole scenario is deliberated with variable characteristics. The novelty of the envisaged mathematical model is enriched considering the chemical species of both types amalgamated with the entropy generation minimization analysis keeping in view the liquid and gaseous states. The numerical solution of the governing system is obtained by using the bvp4c function of the MATLAB software. The graphical outcomes of arising parameters solid nanoparticles volume fraction (0.005≤φ2≤0.06), variable viscosity (−5≤θr≤2.5), thermal conductivity (1.0≤ε≤2.0), surface catalyzed parameter (0.0≤Kvs≤0.3), homogeneous reaction parameter (0.3≤Kc≤0.7), heterogeneous reaction parameter (0.3≤Ks≤0.7), Brinkman number (0.2≤Br≤0.6), and temperature difference parameter (0.5≤α1≤1.2), versus associated profiles are analyzed logically. It is examined that for positive values of variable viscosity parameter (gases) the axial velocity declines, nevertheless, an increase in velocity distribution is seen for negative values of variable viscosity parameter (liquids).

Entropy generation analysis of Falkner–Skan flow of Maxwell nanofluid in porous medium with temperature-dependent viscosity

Entropy generation analysis in steady two-dimensional, viscous, incompressible forced convective Falkner–Skan flow of Maxwell nanofluid over a static wedge embedded in a porous medium with temperature-dependent viscosity is examined. The Buongiorno’s model has been utilised, to get the flow governing higher-order coupled nonlinear partial differential equations (PDEs) from mass, momentum, energy and concentration conservations. Suitable transformations have been done to convert governing PDEs into the coupled non-linear ODEs along with no-slip boundary conditions, which are then solved using the MATLAB programme bvp4c. The influences of diverse flow governing parameters on various flow properties and quantities of physical interest are displayed in graphical mode and discussed. It is found that entropy generation reduces only with Eckert number (Ec), while more entropy is generated for pressure gradient parameter (m), local Deborah number ( $$\beta )$$ , variable viscosity parameter ( $$\delta $$ ) and permeability parameter (K). Entropy generation due to heat transfer irreversibility is prominent with increase in m and $$\delta $$ , but it is not so for other parameters. The drag force on the wedge surface become stronger with $$\beta $$ and m, but it reduces with $$\delta $$ . Rates of heat transfer and mass transfer enhance with m and $$\delta $$ . In addition, surface drag force and heat transfer rate diminish with Brownian motion parameter (Nb) and thermophoresis parameter (Nt).

Variable thermo-physical characteristics of Carreau fluid flow by means of stretchable paraboloid surface with activation energy and heat generation

The present study is based on the flow of two dimensional Carreau fluid with heat generation and activation energy over the surface of paraboloid. The thermophysical properties such as viscosity, thermal conductivity and thermal diffusivity are chosen to be temperature dependent. The stretching in the fluid layers is presumed at the surface of object. This problem is modified by using law of conversation of momentum, mass, heat and concentration. The governing PDEs are transformed into dimensionless form by using appropriate similarity transformations. The numerical and graphical results are obtained via solving the ordinary differential equations by “RK4” technique with shooting method through MATLAB software. The impacts of key parameters on velocity, temperature and concentration fields are solved numerically and graphically. The power law index and variable viscosity parameter shows increment in velocity field. The temperature of fluid rises due to high values of heat source parameter while temperature shows reduction with Prandtl number. The cause of increment in concentration of fluid is due to activation energy and thermal diffusivity parameter.

CPSM Simulation of the Variable Properties’ Role in MHD Non-Newtonian Micropolar Nanofluid Flow Over a Stretching Porous Sheet (Flow Filtration)

In this manuscript, to modify the fluid thermophysical properties, the alumina suspended nanoparticles were immersed in two different kinds of base fluids, ethylene glycol with Prandtl number (Pr = 204) and water with (Pr = 6.785). The combination between Powell–Eyring model and micropolar fluid was utilized to describe a 2D steady nanofluid flow along a stretching permeable sheet. An inconvenience through a porous material was illustrated by Darcy–Forchheimer (D–F) expression. As it is known, the nanofluid thermophysical properties are not constants especially in the presence of heat transfer; hence, the viscosity and thermal conductivity were employed as variable functions of the temperature and nanoparticle concentration. As well as in the present work, the microrotation and spin gradient viscosities, which were always constant in all the above studies, have been employed as variable functions of the temperature. The governing mathematical equations have been calculated numerically via the Chebyshev pseudospectral method/Mathematica code. A perfect agreement was obtained between some numerical outcomes and previous published data. Also, the present numerical outcomes for the distributions of temperature, concentration, velocities, skin friction, wall couple stress, Nusselt and Sherwood numbers are represented in tabular form and by drawing against different controlling parameters in the ranges $$ \phi (0 - 20\% ),A(0.01 - 1),\,n(0 - 5),\,\beta_{1} ,\,\beta_{1} ,\,\beta_{3} \,(0 - 0.7),\,$$ $$ {\text{Fr}},\,{\text{Da,}}\,K_{c} ,\,{\text{Sc}}\,(0.1 - 2),\,\Delta \,(0.1 - 10),S\,( - 1\, - \,1)$$ , and $$ M(0 - 20)$$ . In this article, it is confirmed that utilizing the nanofluid viscosity/thermal conductivity as a variable function of both the nanoparticle concentration and the temperature had a great importance and is a vital factor to reinforce the rate of heat transfer. Finally, a new result was gotten in this work; when the variable microrotation viscosity parameter rose, the angular velocity profile raised.

Modeling Heat Transfer Enhancement of Ferrofluid (Fe3O4–H2O) Flow in a Microchannel Filled with a Porous Medium

Heat transfer characteristics and hydrodynamical properties of ferrofluid through microchannels with non-uniform permeable walls temperature and filled with porous media plays an important role in modern microfluidic applications, such as solar collectors, nuclear reactors, micro-electro-chemical cell transport, micro heat exchanging, microchip cooling, and electronic equipment. Therefore, this paper presents the investigation of ferrofluid (Fe3O4-H2O) heat transfer characteristics as well as hydrodynamical properties in a permeable microchannel with non-uniform permeable walls. The semi-discretization finite difference method is utilized to solve the highly non-linear partial differential equations that govern the momentum and energy equations. Accordingly, the numerical outcomes reveal that the ferrofluid velocity and temperature profiles indicate a rising trend as the pressure gradient parameter, the variable viscosity parameter, the Darcy number, the Eckert number, and Prandtl number increase. The Reynolds number, which is a suction/injection parameter, shows a contrary influence on the ferrofluid velocity and temperature whereas nanoparticles volume fraction and the Forchheimer constant show a decreasing effect on the ferrofluid velocity and temperature. The outcomes also depict that the coefficient of skin friction at the cold wall of the microchannel is larger for higher values of the nanoparticles volume fraction, the variable viscosity parameter, the Darcy number, and the Eckert number. Besides, the coefficient of skin friction at the hot wall rises with the Darcy number, and the Prandtl number. Furthermore, the heat transfer rate at both cold and hot walls of the microchannel increases as the variable viscosity parameter, the Darcy number, the Eckert number, and the Prandtl number increase. The nanoparticles volume fraction and Darcy number show a retarding effect on the heat transfer rate at both walls of the microchannel.

Steady Marangoni instabilities in variable-viscosity liquid layer in the presence of insoluble surfactant

The ability to control the complex convective flow patterns is important and one of the factors that alter the dynamics of the surface tension is surface-active agents or surfactants. Surfactants affect the surface tension at the free upper surface by producing tangential stress. This study theoretically examines the onset of steady instabilities in a thin nondeformable and deformable variable-viscosity liquid layer in the presence of insoluble surfactant. The surface tension at the free surface is assumed to be linearly dependent on temperature and concentration gradients. The dynamic viscosity is assumed to be exponentially dependent on temperature. The stability problems are governed by the systems of nonlinear partial differential equations consisting of continuity, momentum and energy equations. Linear stability analysis consisting of scaling, perturbation of infinitesimal disturbances and superposition in normal modes are used to transform the system of partial differential equations into system of ordinary differential equations. The exact analytical solutions are derived and the marginal curves are illustrated to show effects of some controlling parameters particularly the variable viscosity and elasticity parameter. Viscosity variation and elasticity parameter of surfactant act as destabilizer while the Biot number and Lewis number stabilize. For deformable surface, convection sets in at long wavelength for liquid with variable viscosity but convection occurs at short wavelength for constant viscosity liquid.

Induced MHD impact on exponentially varying viscosity of Williamson fluid flow with variable conductivity and diffusivity

In this study, we assumed a thermal energy system with variable controlling properties which effect the entire system. One of the best applications of thermal energy system is heat exchanger. A good heat exchanger is a big challenge over the past years, due to enlarged public request on improving energy efficiency and decreasing energy. Normally, heat exchangers are used in the transmission of heat between two or more fluids [46]. Furthermore, the analysis of MHD flow of an electrically conducting fluid due to the thermal system is significant in current metallurgy and metal-working methods. Due to large amount of applications, variable thermo-physical properties of induced magnetic field in Williamson fluid flow is studied. The achieved system is partial differential, which is converted into ordinary differential equations by using the transformations. Then the attained system is solved by using shooting method. The thermal extrusion system contains velocity, concentration, and temperature fields. The associated controlling parameters contain small parameter, magnetic field, the reciprocal magnetic Prandtl number, variable viscosity parameter, Williamson parameter, small concentration parameter and Schmidt number. The outlined results deliver good thermal impact on entire system for minor and big values of these pertinent parameters. Williamson fluid model is executed to examine the properties of shear thinning fluids. It is noticed that a big reduction is noticed in velocity profile for large values of variable viscosity parameter, Williamson parameter and magnetic parameter. Moreover, the reciprocal magnetic Prandtl number reduces the magnetic profile. The temperature and concentration small parameters show enhanced impact on temperature and concentration profiles. Comparison of present thermal system is considered for limited values of these parameters.

Flow over a Needle Moving in a Stream of Dissipative Fluid Having Variable Viscosity and Thermal Conductivity

In this article, the boundary layer flow around a thin needle is examined. Non-constant thermal conductivity as well as viscosity is the art of present study. Governing equations are modeled in the presence of frictional heating and are simplified by utilizing boundary layer assumptions. To obtain a self-similar solution, boundary layer equations are further transformed into dimensionless forms by utilizing axisymmetric similarity variables. For further investigation of the problem, attained self-similar nonlinear equations with suitable boundary conditions are solved numerically using MATLAB bvp5c. A comparative study with existing findings is carried out. Impact of velocity ratio parameter, size of the needle, variable viscosity parameter, Prandtl number, fluid friction and variable thermal conductivity parameters on dimensionless velocity, skin friction coefficient, temperature and local Nusselt number are investigated through graphical analysis. It is observed that flow with variable viscosity and thermal conductivity is significantly different and realistic in comparison with constant properties-based flow. It is also noted that the temperature of the fluid and the thickness of the thermal boundary layer are related directly to reduction in needle size. Further, considerable enhancement is observed in heat transfer rate for the variable properties case.

Radiative MHD flow of hybrid nanofluid past a porous stretching cylinder for heat transfer enhancement

AbstractThe current study investigates heat transfer enhancement due to the radiative magnetohydrodynamics (MHD) flow of a hybrid nanofluid past a porous stretching cylinder under the influence of variable viscosity as well as suction. The nonlinear partial differential equations governing the proposed physical model are transformed into nonlinear ordinary differential equations by applying suitable similarity transformation. The scaled‐down system is solved numerically by the fourth‐order Runge–Kutta method along with shooting technique for the achievement of asymptotic boundary condition. The velocity and temperature profiles are obtained for various physical factors of the problem, namely, magnetic interaction factor , Reynolds number , volume fraction factor of copper , variable viscosity , and radiation factor , together with suction , by fixing the Prandtl number of the core fluid (ethylene glycol) constant at 25.825. The numerical values of skin friction and the rate of heat transfer are obtained and tabulated. To validate the proposed physical model, numerical simulations are provided with comparison. The paper highlights the effects of physical factors, namely, radiation, variable viscosity, and suction parameters, on the flow of a hybrid nanoflluid for heat transfer enhancement.

The Effect of Variable Viscosity on Unsteady Free Convective Fluid Flow over a Stretching Surface in the Presence of Thermal Radiation and Viscous Dissipation

The unsteady free convective flow of an incompressible, viscous, electrically conducting fluid over a vertical stretching surface with variable viscosity and thermal radiation in the presence of viscous dissipation is considered. The fluid is assumed to be gray, absorbing emitting but non-scattering medium. Thus, the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The viscosity of the fluid is assumed to be an inverse linear function of temperature. Specifically, the study is aimed at determining the effects of variable viscosity parameter ( ), Eckert number ( ), and radiation parameter ( ) on temperature distribution profiles, while holding the Prandtl number constant that is corresponding to air. The specific energy equation governing the fluid flow is solved numerically by the finite difference method. The nonlinear partial differential equation is solved numerically by the finite difference method. MATLAB code is used to solve the Forward Time and Centered Space (FTCS) scheme. Further, stability and consistency analyses are performed on the FTCS scheme to determine the convergence of the scheme. Results for temperature distribution profiles are presented graphically for different values of variable viscosity ( ), Eckert number ( ), radiation parameter ( ). The findings are that an increase in variable viscosity and Eckert number causes an enhancement of temperature distribution profiles whereas an increase in radiation parameter leads to a decrease in temperature distribution profiles. The FTCS scheme was found to be unconditionally stable and consistent. The results obtained in this study follow expected trends and are in good agreement with some previous studies.

Investigation of irreversibilities in a microchannel by differing viscosity, including buoyancy forces and suction/injection

AbstractSingle‐phase Poiseuille flow considering oxides of copper‐water nanoliquid in the upright microchannel with uneven viscosity causes the production of inbuilt irreversibility in the system. This is reported in the present investigation involving the buoyancy force with suction/injection at the walls by taking into account different shapes of nanoparticles. The equations so obtained being highly nonlinear is attempted to solve via Runge–Kutta–Fehlberg shooting scheme. Flow and heat transmission characteristics are explored by considering the nanoparticle's shape. The result exemplifies that the viscosity variation parameter escalates the flow profile as well as temperature profile. The thermal radiation and Biot number boost the let go of thermal energy, which leads to system cooling. The temperature profile for nanoparticle shape factor upholds the fact that temperature is high for lamina‐shaped nanoparticles and least for spherical‐shaped nanoparticles. Also, the Biot number, radiation parameter, and nanoparticle volume fraction serve in lowering the entropy, which augments the exergetic effectiveness of the system.

Natural convection of fluid with variable viscosity and viscous dissipation from a heated vertical wavy surface in presence of magnetic field

ABSTRACT
 
 The present numerical work describes the effect of the temperature dependent variable viscosity and viscous dissipation on natural convection heat transfer boundary layer flow of a viscous incompressible electrically conducting fluid along a vertical wavy surface in presence of a transverse magnetic field. The wavy surface is maintained at uniform wall temperature that is higher than that of the ambient. A simple coordinate transformation is employed to transform the wavy surface into a flat plate. A marching finite difference scheme is used for present analysis. The numerical results, including the developments of the skin friction coefficients, the local Nusselt number, the streamlines as well as the isotherms are presented and discussed in detail. The results of this investigation illustrated that the skin friction coefficient increase with an increase of the variable viscosity and viscous dissipation parameter, while the local Nusselt number at the heated surface decrease with increasing values of variable viscosity, intensity of magnetic field and viscous dissipation parameter.