Carreau Fluid Flow Research Articles

Characteristics of convective heat transfer in the MHD peristalsis of Carreau fluid with Joule heating

This article addresses the characteristics of convective heat transfer and radially imposed magnetic field on peristaltic flow of an incompressible Carreau fluid in a curved channel. Joule heating is also present. Mathematical analysis has been carried out under long wavelength and low Reynolds number considerations. Solutions of the resulting non-linear system for small values of Weissenberg number are constructed. The salient features of flow quantities are pointed out with particular focus to pumping, velocity, temperature and trapping. It is observed pressure gradient enhances for larger values of power law index parameter. The velocity and temperature are decreasing functions of radial magnetic field parameter. Further the impact of Weissenberg and Biot numbers on the temperature are opposite.

Magnetohydrodynamic flow of Carreau fluid over a convectively heated surface in the presence of non-linear radiation

This paper presents a study of the magnetohydrodynamic (MHD) boundary layer flow of a non-Newtonian Carreau fluid over a convectively heated surface. The analysis of heat transfer is further performed in the presence of non-linear thermal radiation. The appropriate transformations are employed to bring the governing equations into dimensionless form. The numerical solutions of the partially coupled non-linear ordinary differential equations are obtained by using the Runge-Kutta Fehlberg integration scheme. The influence of non-dimensional governing parameters on the velocity, temperature, local skin friction coefficient and local Nusselt number is studied and discussed with the help of graphs and tables. Results proved that there is significant decrease in the velocity and the corresponding momentum boundary layer thickness with the growth in the magnetic parameter. However, a quite the opposite is true for the temperature and the corresponding thermal boundary layer thickness.

Physiological flow of Carreau fluid due to ciliary motion

In this paper, we have explained the ciliary motion of a Carreau fluid inside a symmetrical channel with ciliated walls. Carreau fluid equations for the two dimensional channel are interpreted by employing the low Reynolds number and long wave-length approximations. The analytical series solutions are found by employing the Homotopy perturbation method. Solutions are presented through graphs. The results for the distinct values of the constants are described by generating graphs of velocity, pressure gradient, pressure rise and stream lines.

Unsteady boundary layer flow of Carreau fluid over a permeable stretching surface

The main objective of the present work is to present numerical solutions of the unsteady two-dimensional boundary layer flow and heat transfer of an incompressible Carreau fluid over a permeable time dependent stretching sheet. Using suitable transformations, the time dependent partial differential equations are converted to non-linear ordinary differential equations. The numerical results of these non-linear ordinary differential equations with associated boundary conditions are determined by using the bvp4c function in MATLAB. The numerical results are investigated for the emerging parameters namely, the unsteadiness parameter A, mass transfer parameter S, Prandtl number Pr, power law index n and Weissenberg number We. It is important to state that both the momentum and thermal boundary layer thicknesses diminish with increasing values of the unsteadiness and mass transfer parameters. A comparison with the available literature in limiting cases is performed and found to be in good agreement.

Heat transfer squeezed flow of Carreau fluid over a sensor surface with variable thermal conductivity: A numerical study

Present phenomenon is dedicated to investigate the heat transfer and squeezed flow of Carreau fluid over a sensor surface. The thermal conductivity of the fluid is assumed to be temperature dependent. After assimilating these assumptions, the appropriate transformations are used to formulate the partial differential equations into non-dimensional system of ordinary differential equations. Solutions for the boundary layer momentum and heat equations are accomplished by a well-known numerical technique namely shooting method. The related essential physical parameters are visualized through graphs and tables. It is found that the velocity profile increases by increasing squeezed flow parameter b, permeable velocity parameter f0, power law index n and Weissenberg number We Similarly, temperature profile increases by increasing small parameter ∊.

Steady flow of a non-Newtonian Carreau fluid across an unconfined circular cylinder

The flow of a non-Newtonian, Carreau fluid, directed normally to a horizontal, stationary, circular cylinder is considered in the present paper. The problem is investigated numerically using the commercial code ANSYS FLUENT with a very large calculation domain in order that the flow could be considered unbounded. The investigation covers the power-law index from 0.2 up to 2, the Reynolds number range from 0.1 up to 40 and the Carreau number from 0.1 up to 20. Wake lengths and drag coefficients have been calculated for many combinations of the above three parameters. At low power-law index the wake length changes non-linearly with increasing Reynolds number and as the power-law index rises the variation becomes linear. The drag coefficient reduces in shear-thinning fluids and grows in shear-thickening fluids with increasing Carreau number. At the same Carreau number the drag coefficient is higher is shear-thickening fluids compared to that of shear-thinning fluids.

Analytical solutions for the flow of Carreau and Cross fluids in circular pipes and thin slits

In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.

Non-similar Blasius and Sakiadis flow of a non-Newtonian Carreau fluid

The Blasius and Sakiadis flow of a non-Newtonian Carreau fluid is considered in the present paper. The boundary layer equations are transformed into non-dimensional form and a new dimensionless parameter (Deborah number) is introduced. The transformed boundary layer equations are solved with the finite difference method. The problem is non-similar and is governed by the Deborah number, the power-law index and the non-dimensional distance along the plate. Velocity profiles and wall shear stress have been calculated for both cases and a comparison is made between Blasius and Sakiadis flow.

Boundary layer flow of Carreau fluid over a convectively heated stretching sheet

Two-dimensional boundary layer flow of Carreau fluid past a permeable stretching sheet is studied. Heat transfer subject to convective boundary conditions is analyzed. The relevant equations are first simplified by using boundary layer assumptions and reduced to self-similar forms by appropriate transformations. The problem is governed by various interesting parameters including power-law index (n), relaxation time (λ1), Prandtl number (Pr) and the Biot number (Bi). Series solutions are computed by homotopy analysis method (HAM). Fields are influenced appreciably with the variations of embedded parameters. Numerical values of skin friction coefficient and local Nusselt number are also tabulated.

Heat transfer enhancement in laminar impinging flows with a non-newtonian inelastic fluid

Non-Newtonian rheology, even when relatively benign, can alter the developing velocity field characteristics in laminar and turbulent impinging flows and thereby affect heat transfer distributions along the impinging surface. We consider steady laminar axisymmetric impinging jet flow of an inelastic Carreau fluid and analyze the effects of rheology on Nusselt number profiles at the impinging surface. Numerical calculations are presented for nozzle Reynolds numbers up to 750 and geometrical aspect ratios from 14 to 4, while the chosen rheological parameter range allows for local viscosity variation of three orders of magnitude within high strain rate domains in the wall jet region of the flow. Our results demonstrate that substantial enhancement in heat transfer rates occur both in the impinging zone and in the wall jet. The calculations show that the local Nusselt number can be up to an order of magnitude larger, and the enhancement may persist for several nozzle diameters downstream of the stagnation point. The inclusion of even moderate temperature dependent viscosity behavior serves to augment the enhancement. We use the numerical results to identify those features of the developing velocity field that are primarily responsible for the observed heat transfer enhancement, and conclude that different underlying mechanisms are relevant in the impinging zone and in the wall jet region of the flow. Consideration also is given to the effects of viscous heating, which are shown to depend significantly on the geometrical aspect ratio. Suitably defined average Nusselt numbers are computed to quantify the extent of heat transfer enhancement as a function of the governing parameters describing fluid rheology and the developing flow field, and specific results are presented for impinging jet heat transfer with a 0.125% polyacrylamide solution.

MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: Dual solutions

Present analysis is carried out to study the two-dimensional stagnation-point flow of an in-compressible Carreau fluid toward a shrinking surface. The formulation of the Carreau fluid model has been developed first time for boundary layer problem of shrinking sheet and the governing partial differential equations are rehabilitated into ordinary differential equations using similarity transformations. The simplified nonlinear boundary value problem is solved by Runge-Kutta method after converting into the system of initial value problem using shooting method. Dual solutions are obtained graphically and results are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients are also computed.

Series solution of unsteady peristaltic flow of a Carreau fluid in eccentric cylinders

In the present analysis, the unsteady peristaltic flow of an incompressible Carreau fluid is investigated in eccentric cylinders. The problem is measured in cylindrical coordinates. The governing equations are observed under the conditions of long wavelength and low Reynolds number approximations. The resulting highly nonlinear second order partial differential equations are solved by series solution technique. The relation for pressure rise is evaluated numerically by built-in technique with the help of mathematics software. As a special case, the present results are compared with the existing results given in the literature. The obtained results are then plotted to see the influence of different physical parameters on the velocity, pressure gradient and pressure rise expressions. The velocity profile is drawn for both two and three dimensions. The trapping boluses are also discussed through streamlines.

Flow of MHD Carreau fluid in a curved channel

Analysis has been made for the curvature effects on the MHD peristaltic flow of an incompressible Carreau fluid in a channel. The flow problem is first reduced in the wave frame of reference and then solved after employing the long wavelength and low Reynolds number approximations. Expressions of stream function, pressure gradient, magnetic force function, induced magnetic field and current density are derived and then examined for various parameters of interest.

Flow of MHD Carreau fluid in a curved channel

Analysis has been made for the curvature effects on the MHD peristaltic flow of an incompressible Carreau fluid in a channel. The flow problem is first reduced in the wave frame of reference and th...

Flow of MHD Carreau Fluid in a Curved Channel

Analysis has been made for the curvature effects on the MHD peristaltic flow of an incompressible Carreau fluid in a channel. The flow problem is first reduced in the wave frame of reference and then solved after employing the long wavelength and low Reynolds number approximations. Expressions of stream function, pressure gradient, magnetic force function, induced magnetic field and current density are derived and then examined for various parameters of interest.

Peristaltic Flow of Carreau Fluid in a Rectangular Duct through a Porous Medium

We have examined the peristaltic flow of Carreau fluid in a rectangular channel through a porous medium. The governing equations of motion are simplified by applying the long wavelength and low Reynolds number approximations. The reduced highly nonlinear partial differential equations are solved jointly by homotopy perturbation and Eigen function expansion methods. The expression for pressure rise is computed numerically by evaluating the numerical integration. The physical features of pertinent parameters have been discussed by plotting graphs of velocity, pressure rise, pressure gradient, and stream functions.

The flow of a Carreau fluid down an incline with a free surface

This paper deals with the effect of a Carreau fluid flow down an inclined plane with a free surface. The fluid film is thin, so that lubrication approximation may be applied. In general, the flow equations resulting from the variable viscosity model must be solved numerically. However, when the viscosity variation is small, then an asymptotic approximation is possible. The full solutions for the velocity and temperature profiles are derived using the fourth order Runge-Kutta numerical method. The flow controlling parameters such as the non-dimensional viscosity variation parameter, the Biot and the Brinkman numbers, are found to have a profound effect on the resulting flow profiles. Key words: Lubrication theory, Carreau fluid, viscosity.

Influence of induced magnetic field and heat transfer on peristaltic transport of a Carreau fluid

The effect of an induced magnetic field on peristaltic flow of an incompressible Carreau fluid in an asymmetric channel is analyzed. Perturbation solution to equations under long wavelength approximation is derived in terms of small Weissenberg number. Expressions have been constructed for the stream function, the axial induced magnetic field, the magnetic force function, the current density distribution and the temperature. Trapping phenomenon is examined with respect to emerging parameters of interest.

Magnetohydrodynamic Flow of a Carreau Fluid in a Channel with Different Wave Forms

Magnetohydrodynamic Flow of a Carreau Fluid in a Channel with Different Wave Forms

Effects of Heat and Mass Transfer on Peristaltic Flow of Carreau Fluid in a Vertical Annulus

This article is devoted to the study of peristaltic transport of a Carreau fluid in a vertical annulus under the consideration of long wavelength. The flow is investigated in a wave frame of reference moving with the velocity of the wave. Exact solutions have been evaluated for temperature and concentration field, while approximated analytical and numerical solutions are found for the velocity field using (i) the perturbation method and (ii) the shooting method. The effects of various emerging parameters are investigated graphically.