Flow Of Third Grade Fluid Research Articles

Transient Flow and Heat Transfer Characteristics of non-Newtonian Supercritical Third-Grade Fluid (CO2) past a Vertical Cylinder

Abstract The present study deals with the time-dependent natural convective supercritical third-grade fluid flow past a vertical cylinder. A new thermodynamic model for the supercritical carbon di-oxide (CO2) has been derived. In this model the thermal expansion coefficient is characterized as a function of pressure, temperature and compressibility factor. This model uses the Redlich-Kwong equation of state (RK-EOS). The numerically calculated thermal expansion coefficient values of CO2 are validated with available experimental results. The governing non-linear coupled partial differential equations are solved by using Crank-Nicolson method. The obtained numerical data is described in terms of velocity, temperature, skin-friction and Nusselt number through the graphs and tables for the different set of physical parameters. It is observed that the unsteady velocity is an increasing function of reduced pressure and reduced temperature; whereas it is a decreasing function with respect to third-grade fluid parameter. The temperature field is enhanced near the critical point for the increasing values of third-grade fluid parameter. In supercritical fluid region for the increasing values of reduced pressure and reduced temperature, the skin-friction values are magnified against time. Also, the average heat transfer rate decreases for increasing values of third-grade fluid parameter.

Effect of Nonlinear Convection on Stratified Flow of Third Grade Fluid with Revised Fourier-Fick Relations

Here thermal dependence conductivity and nonlinear convection features in third-grade liquid flow bounded by moving surface having varying thickness are formulated. Stagnation point flow is considered. Revised Fourier-Fick relations and double stratification phenomena are utilized for modeling energy and concentration expressions. Mathematical model of considered physical problem is achieved by implementing the idea of boundary layer theory. The acquired partial differential system is transformed into ordinary ones by employing relevant variables. The homotopic scheme yield convergent solutions of governing nonlinear expressions. Graphs are constructed for distinct values of physical constraints to elaborate the heat/mass transportation mechanisms.

Impact of nanoparticles on flow of a special non-Newtonian third-grade fluid over a porous heated shrinking sheet with nonlinear radiation

Abstract This research peruses the characteristics of heat and mass transfern of a special non-Newtonian third-grade fluid over a porous convectively-heated shrinking sheet filled with nanoparticles. The Buongiorno model is used for the special non-Newtonian third-grade fluid that includes both the Brownian motion and the thermophoresis effects with non-linear radiation. The nonlinear system of ordinary differential equations are obtained using a suitable transformation. The converted system of equations are then numerically solved using shooting method. The numerically-obtained results for the skin friction, local Nusselt number and the local Sherwood number as well as velocity profile, temperature distribution and concentration of nanoparticle are illustrated for different physical parameters through graphs and tables. On the behalf of the whole studies, final conclusions are made and it is observed that multiple solutions are achieved for certain values of the suction parameter. Further, the non-Newtonian parameter reduces the velocity of the fluid and increases the temperature and the concentration profiles for the first solution while the reverse trend is seen for the second solution. Finally, a comparative analysis is made through previous studies in limiting cases and shown good correlation.

Numerical study for nonlinear radiative peristaltic flow in a rotating frame

Peristaltic flow of third-grade fluid in a tapered asymmetric channel is discussed. The whole system is considered in a rotating frame. Unlike the traditional situation, the nonlinear version of thermal radiation is invoked. The resulting problems are solved numerically. Comparative study between rotating and inertial frames is presented. The results of velocity, temperature, and heat transfer rate are analyzed for different parameters of interest.

Fallopian tube analysis of the peristaltic-ciliary flow of third grade fluid in a finite narrow tube

The present prospective theoretical investigation deals with analysis of the peristaltic-ciliary transport of a developing embryo within the fallopian tubal fluid in the human fallopian tube. A mathematical model of peristalsis-cilia induced flow of viscoelastic fluid characterized by the third grade fluid model within the fallopian tubal fluid in a finite two dimensional narrow tube is developed. Non-linear partial differential equation resulting from the modelling of the proposed model is solved using perturbation method. Flow variables like axial and radial velocities, appropriate residue time over tube length, pressure difference over wavelength and stream function are analyzed for embedded parameters and constants. Salient features of the pumping characteristics and trapping phenomenon are discussed in detail. The analysis showed that embedded parameters and constants have opposite effects on axial velocity and appropriate residue time over tube length. Moreover, a comparison of the peristaltic flow with the peristaltic-ciliary flow and the third grade fluid with the linearly viscous fluid is made as a special case. The relevance of the current results to the transport of a developing embryo within the fallopian tubal fluid is also explored. It reveals that, third grade fluid instead of the linearly viscous fluid and the inclusion of cilia along with peristalsis help to complete the required mitotic divisions while transporting the developing embryo within the fallopian tubal fluid in the human fallopian tube.

Mechanisms of double stratification and magnetic field in flow of third grade fluid over a slendering stretching surface with variable thermal conductivity

Abstract This article addresses the magnetohydrodynamic (MHD) stagnation point flow of third grade fluid towards a nonlinear stretching sheet. Energy expression is based through involvement of variable thermal conductivity. Heat and mass transfer aspects are described within the frame of double stratification effects. Boundary layer partial differential systems are deduced. Governing systems are then converted into ordinary differential systems by invoking appropriate variables. The transformed expressions are solved through homotopic technique. Impact of embedded variables on velocity, thermal and concentration fields are displayed and argued. Numerical computations are presented to obtain the results of skin friction coefficient and local Nusselt and Sherwood numbers. It is revealed that larger values of magnetic parameter reduces the velocity field while reverse situation is noticed due to wall thickness variable. Temperature field and local Nusselt number are quite reverse for heat generation/absorption parameter. Moreover qualitative behaviors of concentration field and local Sherwood number are similar for solutal stratification parameter.

Computational modeling of unsteady third-grade fluid flow over a vertical cylinder: A study of heat transfer visualization

Abstract The present paper aims to investigate the effect of Prandtl number for unsteady third-grade fluid flow over a uniformly heated vertical cylinder using Bejan’s heat function concept. The mathematical model of this problem is given by highly time-dependent non-linear coupled equations and are resolved by an efficient unconditionally stable implicit scheme. The time histories of average values of momentum and heat transport coefficients as well as the steady-state flow variables are displayed graphically for distinct values of non-dimensional control parameters arising in the system. As the non-dimensional parameter value gets amplified, the time taken for the fluid flow variables to attain the time-independent state is decreasing. The dimensionless heat function values are closely associated with an overall rate of heat transfer. Thermal energy transfer visualization implies that the heat function contours are compact in the neighborhood of the leading edge of the hot cylindrical wall. It is noticed that the deviations of flow-field variables from the hot wall for a non-Newtonian third-grade fluid flow are significant compared to the usual Newtonian fluid flow.

On some results of third-grade non-Newtonian fluid flow between two parallel plates

In this paper, the main focus is to discuss the non-Newtonian third-grade fluid flow between two parallel plates. The mathematical model is consequent to the continuity and momentum equations. Three cases have been discussed such as the plane Couette flow, the plane Poiseuille flow and the last one is a plane Couette-Poiseuille flow. The modeled differential equations are converted into dimensionless form by suitable non-dimensional parameters, then they are solved by the variational iteration method (VIM). It is noticed that the variational iteration method is convenient to apply and is very helpful for finding solutions of a wide class of nonlinear problems.

CATTANEO–CHRISTOV HEAT FLUX MODEL FOR SQUEEZED FLOW OF THIRD GRADE FLUID

This paper addresses the squeezed flow of third grade fluid between two parallel disks. Heat transfer in present flow is characterized by Cattaneo–Christov theory. Thermal relaxation time effects on the boundary layer is examined. Suitable transformations are invoked for a system of ordinary differential equations. Convergent series solutions are thus obtained using homotopic approach. Influences of different parameters on the velocity and temperature profile are discussed.

HAM on MHD Convective Flow of a Third grade Fluid through Porous Medium during Wire Coating Analysis with Hall effects

In this study, wire coating is performed using MHD convective flow of third grade fluid through porous medium taking Hall current into account. The governing equations are first modelled and then solved analytically by utilizing the Homotopy analysis method (HAM). The convergence of the series solution is established. The effect of pertinent parameters on the velocity field and temperature profile is shown with the help of graphs. It is observed that the velocity profiles increase as the value of visco-elastic third grade fluid parameter β increase and decrease as the Hartmann number M and permeability parameter K increase. It is also observed that the temperature profiles increases as the Brinkman number Br, permeability parameter K, magnetic parameter M and third grade fluid parameter β increase.

Numerical simulations of a third-grade fluid flow on a tube through a contraction

Based on a director theory approach related to fluid dynamics we reduce the nonlinear three-dimensional equations governing the axisymmetric unsteady motion of a non-Newtonian incompressible third-grade fluid to a one-dimensional system of ordinary differential equations depending on time and on a single spatial variable. From this new system we obtain the unsteady equation for the mean pressure gradient and the wall shear stress both depending on the volume flow rate, Womersley number and viscoelastic parameters over a finite section of a straight, rigid and impermeable tube with variable circular cross-section. We present some numerical simulations of unsteady flows regimes through a tube with a contraction using a nine-directors theory.

Axisymmetric squeezing flow of third grade fluid in presence of convective conditions

This article examines unsteady axisymmetric flow of third grade fluid between two disks. Upper disk is being squeezed towards the lower porous disk. Electrically conducting fluid and convective boundary conditions are used. Heat transfer analysis is carried out in the presence of Joule heating, viscous dissipation and thermal radiation effects. Partial differential equations are reduced into ordinary differential equations by using suitable transformations. Convergent series solutions of velocity and temperature are obtained. Effects of various dimensionless parameters are observed on the velocity and temperature. Numerical values of skin friction coefficient and Nusselt number are also computed and examined.

Magnetohydrodynamic stagnation point flow of third-grade liquid toward variable sheet thickness

The current study examines the boundary layer stagnation point flow of third-grade fluid toward a stretching surface with variable thickness. Electrically conducting fluid in the flow is addressed. The resulting equation by suitable transformation yields nonlinear problem which is solved for the convergent solutions. Convergence region is particularly determined for the obtained solutions. Variables highlights for velocity are shown and examined with the help of different graphs. Numerical values of the drag force (skin friction coefficient) are also presented in the tabular form. From given results, it is found that velocity field overshoots for larger values of material parameters of third-grade fluid.

Stabilized approximation of steady flow of third grade fluid in presence of partial slip

This article presents a stable numerical solution to the steady flow of thermodynamic compatible third grade fluid past a porous plate. Problem formulation is completed through partial slip condition. The inability of classical Lagrange-Galerkin methods to provide a stable approximate solution to the envisaged flow problem is demystified. To prevail over the instability issues, a streamline-upwind-Petrov-Galerkin method is invoked. The results thus substantiate an apposite agreement with theory. The stability of the approximate solution is testified and appropriate conclusions on flow profile are delineated.

MHD mixed convection flow of third grade liquid subject to non-linear thermal radiation and convective condition

Magnetohydrodynamic (MHD) mixed convection flow of third grade fluid by an exponentially stretching sheet is addressed. Energy expression involves the convective condition and non-linear thermal radiation. Non-linear ordinary differential systems are first constructed and then solved successfully. Interval of convergence via numerical data and plots are developed and verified. Impact of various influential variables on the dimensionless velocity and temperature are graphically analyzed. The coefficient of skin friction and local Nusselt number are discussed numerically. Opposite response of velocity and temperature profiles have been noticed for higher mixed convection. Also temperature is an increasing function of thermal radiation.

An optimal study for Darcy-Forchheimer flow with generalized Fourier’s and Fick’s laws

This article addresses boundary-layer flow of third grade fluid saturating a non-Darcy porous medium. Induced flow is by a stretchable surface. Flow in porous media is described by employing the Darcy-Forchheimer based model. Generalized versions of Fourier’s and Fick’s laws via Cattaneo-Christov double diffusion expressions are utilized. Transformation method is employed for reduction process of nonlinear partial differential systems into the nonlinear ordinary differential systems. Optimal homotopy analysis method (OHAM) develops the computations. The optimal values of nonzero auxiliary parameters are computed and analyzed. The optimal solutions of temperature and concentration fields are presented through the plots. The skin friction coefficient and local Nusselt and Sherwood numbers are also studied through numerical data. Our results reveal that the local Nusselt and Sherwood numbers are higher for larger values of thermal and concentration relaxation parameters.

Impact of chemical reaction on third grade fluid flow with Cattaneo-Christov heat flux

Abstract The present article deals with the two-dimensional flow of third grade fluid induced by a linear stretching sheet. Analysis of thermal relaxation time is made by using Cattaneo-Christov heat flux model. Effects of chemical reaction are also taken into account. Suitable transformations lead to a strongly nonlinear differential system which is solved through homotopic technique. Convergent series solutions are derived. Effects of the emerging parameters on the dimensionless velocity, temperature and concentration are investigated. It is found that increasing values of thermal relaxation time corresponds to low temperature. Skin friction coefficient and Sherwood number are also computed and addressed.

Irreversibility analysis for reactive third-grade fluid flow and heat transfer with convective wall cooling

Inherent irreversibility in the flow of a reactive third grade fluid though a channel with convective heating is examined. It is well known that heat dissipated from the exothermic chemical reaction passes through fluid in an irreversible manner and as a result entropy is generated continuously within the channel. Analytical solutions of the resulting dimensionless nonlinear boundary-value-problems arising from the governing equations were obtained by using perturbation method. These solutions are utilized to obtain the entropy generation rate and Bejan number for the system. The influence of various important parameters on the entropy generation rate and Bejan number are shown graphically and discussed accordingly.

Perturbation Solutions for Hagen-Poiseuille Flow and Heat Transfer of Third-Grade Fluid with Temperature-Dependent Viscosities and Internal Heat Generation

Regular perturbation technique is applied to analyze the fluid flow and heat transfer in a pipe containing third-grade fluid with temperature-dependent viscosities and heat generation under slip and no slip conditions. The obtained approximate solutions were used to investigate the effects of slip on the heat transfer characteristics of the laminar flow in a pipe under Reynolds’s and Vogel’s temperature-dependent viscosities. Also, the effects of parameters such as variable viscosity, non-Newtonian parameter, viscous dissipation, and pressure gradient at various values were established. The results of this work were compared with the numerical results found in literature and good agreements were established. The results can be used to advance the analysis and study of the behavior of third-grade fluid flow and steady state heat transfer processes such as those found in coal slurries, polymer solutions, textiles, ceramics, catalytic reactors, and oil recovery applications.

Fully Developed Flow of Third-Grade Fluid in the Plane Duct with Convection on the Walls

In this paper, an appropriate analysis has been performed to study the incompressible fully developed flow of a non-Newtonian third-grade fluid in a plane duct with convection on the walls. The governing equations, continuity, momentum and energy for this problem are reduced to a nonlinear ordinary form. The momentum nonlinear equation and the resulting energy equation with Robin mixed boundary condition are solved with the collocation method. The effects of non-Newtonian parameter on dimensionless velocity profiles, dimensionless temperature profiles and also effect of Biot number on dimensionless temperature profiles have been shown. Finally, the results show that the collocation method was successfully used for solving nonlinear differential equations with Robin mixed condition.